From 8a57a9c85f25b3bbb23cfe22ab323e4db9d084d8 Mon Sep 17 00:00:00 2001 From: Tanguy BARTHELEMY Date: Thu, 21 Mar 2024 19:17:43 +0100 Subject: [PATCH 1/6] add LICENSE file --- .Rbuildignore | 1 + DESCRIPTION | 2 +- LICENSE | 185 ++++ NEWS.md | 3 + .../mathjax-27/config/AM_CHTML-full.js | 53 + .../mathjax-27/config/AM_CHTML.js | 49 + .../mathjax-27/config/AM_SVG-full.js | 53 + .../mathjax-27/config/AM_SVG.js | 47 + .../mathjax-27/config/MML_CHTML-full.js | 53 + .../mathjax-27/config/MML_CHTML.js | 49 + .../mathjax-27/config/MML_SVG-full.js | 53 + .../mathjax-27/config/MML_SVG.js | 49 + .../mathjax-27/config/MMLorHTML.js | 19 + .../mathjax-27/config/Safe.js | 19 + .../config/TeX-AMS-MML_HTMLorMML.js | 69 ++ .../mathjax-27/config/TeX-AMS-MML_SVG-full.js | 67 ++ .../mathjax-27/config/TeX-AMS-MML_SVG.js | 63 ++ .../mathjax-27/config/TeX-AMS_CHTML-full.js | 61 ++ .../mathjax-27/config/TeX-AMS_CHTML.js | 57 + .../mathjax-27/config/TeX-AMS_SVG-full.js | 61 ++ .../mathjax-27/config/TeX-AMS_SVG.js | 57 + .../config/TeX-MML-AM_CHTML-full.js | 73 ++ .../mathjax-27/config/TeX-MML-AM_CHTML.js | 69 ++ .../mathjax-27/config/TeX-MML-AM_SVG-full.js | 73 ++ .../mathjax-27/config/TeX-MML-AM_SVG.js | 69 ++ .../mathjax-27/extensions/AssistiveMML.js | 19 + .../mathjax-27/extensions/CHTML-preview.js | 19 + .../mathjax-27/extensions/FontWarnings.js | 19 + .../extensions/HTML-CSS/handle-floats.js | 19 + .../mathjax-27/extensions/HelpDialog.js | 19 + .../mathjax-27/extensions/MatchWebFonts.js | 19 + .../mathjax-27/extensions/MathEvents.js | 19 + .../extensions/MathML/content-mathml.js | 19 + .../mathjax-27/extensions/MathML/mml3.js | 19 + .../mathjax-27/extensions/MathMenu.js | 19 + .../mathjax-27/extensions/MathZoom.js | 19 + .../mathjax-27/extensions/Safe.js | 19 + .../mathjax-27/extensions/TeX/AMScd.js | 19 + .../mathjax-27/extensions/TeX/AMSmath.js | 19 + .../mathjax-27/extensions/TeX/AMSsymbols.js | 19 + .../mathjax-27/extensions/TeX/HTML.js | 19 + .../mathjax-27/extensions/TeX/action.js | 19 + .../mathjax-27/extensions/TeX/autobold.js | 19 + .../mathjax-27/extensions/TeX/autoload-all.js | 19 + .../mathjax-27/extensions/TeX/bbox.js | 19 + .../mathjax-27/extensions/TeX/begingroup.js | 19 + .../mathjax-27/extensions/TeX/boldsymbol.js | 19 + .../mathjax-27/extensions/TeX/cancel.js | 19 + .../mathjax-27/extensions/TeX/color.js | 19 + .../mathjax-27/extensions/TeX/enclose.js | 19 + .../mathjax-27/extensions/TeX/extpfeil.js | 19 + .../mathjax-27/extensions/TeX/mathchoice.js | 19 + .../extensions/TeX/mediawiki-texvc.js | 19 + .../mathjax-27/extensions/TeX/mhchem.js | 19 + .../extensions/TeX/mhchem3/mhchem.js | 291 ++++++ .../mathjax-27/extensions/TeX/newcommand.js | 19 + .../mathjax-27/extensions/TeX/noErrors.js | 19 + .../mathjax-27/extensions/TeX/noUndefined.js | 19 + .../mathjax-27/extensions/TeX/unicode.js | 19 + .../mathjax-27/extensions/TeX/verb.js | 19 + .../extensions/a11y/accessibility-menu.js | 1 + .../extensions/a11y/auto-collapse.js | 1 + .../mathjax-27/extensions/a11y/collapsible.js | 1 + .../mathjax-27/extensions/a11y/explorer.js | 1 + .../extensions/a11y/invalid_keypress.mp3 | Bin 0 -> 9030 bytes .../extensions/a11y/invalid_keypress.ogg | Bin 0 -> 5353 bytes .../mathjax-27/extensions/a11y/mathjax-sre.js | 985 ++++++++++++++++++ .../a11y/mathmaps/en/functions/algebra.js | 1 + .../a11y/mathmaps/en/functions/elementary.js | 1 + .../a11y/mathmaps/en/functions/hyperbolic.js | 1 + .../mathmaps/en/functions/trigonometry.js | 1 + .../a11y/mathmaps/en/symbols/greek-capital.js | 1 + .../en/symbols/greek-mathfonts-bold.js | 1 + .../en/symbols/greek-mathfonts-italic.js | 1 + .../greek-mathfonts-sans-serif-bold.js | 1 + .../a11y/mathmaps/en/symbols/greek-scripts.js | 1 + .../a11y/mathmaps/en/symbols/greek-small.js | 1 + .../a11y/mathmaps/en/symbols/greek-symbols.js | 1 + .../mathmaps/en/symbols/hebrew_letters.js | 1 + .../en/symbols/latin-lower-double-accent.js | 1 + .../mathmaps/en/symbols/latin-lower-normal.js | 1 + .../en/symbols/latin-lower-phonetic.js | 1 + .../en/symbols/latin-lower-single-accent.js | 1 + .../symbols/latin-mathfonts-bold-fraktur.js | 1 + .../en/symbols/latin-mathfonts-bold-script.js | 1 + .../en/symbols/latin-mathfonts-bold.js | 1 + .../symbols/latin-mathfonts-double-struck.js | 1 + .../en/symbols/latin-mathfonts-fraktur.js | 1 + .../en/symbols/latin-mathfonts-italic.js | 1 + .../en/symbols/latin-mathfonts-monospace.js | 1 + .../latin-mathfonts-sans-serif-bold.js | 1 + .../latin-mathfonts-sans-serif-italic.js | 1 + .../en/symbols/latin-mathfonts-sans-serif.js | 1 + .../en/symbols/latin-mathfonts-script.js | 1 + .../a11y/mathmaps/en/symbols/latin-rest.js | 1 + .../en/symbols/latin-upper-double-accent.js | 1 + .../mathmaps/en/symbols/latin-upper-normal.js | 1 + .../en/symbols/latin-upper-single-accent.js | 1 + .../a11y/mathmaps/en/symbols/math_angles.js | 1 + .../a11y/mathmaps/en/symbols/math_arrows.js | 1 + .../mathmaps/en/symbols/math_characters.js | 1 + .../mathmaps/en/symbols/math_delimiters.js | 1 + .../a11y/mathmaps/en/symbols/math_digits.js | 1 + .../a11y/mathmaps/en/symbols/math_geometry.js | 1 + .../a11y/mathmaps/en/symbols/math_harpoons.js | 1 + .../en/symbols/math_non_characters.js | 1 + .../a11y/mathmaps/en/symbols/math_symbols.js | 1 + .../mathmaps/en/symbols/math_whitespace.js | 1 + .../a11y/mathmaps/en/symbols/other_stars.js | 1 + .../a11y/mathmaps/en/units/energy.js | 1 + .../a11y/mathmaps/en/units/length.js | 1 + .../a11y/mathmaps/en/units/memory.js | 1 + .../a11y/mathmaps/en/units/other.js | 1 + .../a11y/mathmaps/en/units/speed.js | 1 + .../a11y/mathmaps/en/units/temperature.js | 1 + .../extensions/a11y/mathmaps/en/units/time.js | 1 + .../a11y/mathmaps/en/units/volume.js | 1 + .../a11y/mathmaps/en/units/weight.js | 1 + .../a11y/mathmaps/es/functions/algebra.js | 1 + .../a11y/mathmaps/es/functions/elementary.js | 1 + .../a11y/mathmaps/es/functions/hyperbolic.js | 1 + .../mathmaps/es/functions/trigonometry.js | 1 + .../a11y/mathmaps/es/symbols/greek-capital.js | 1 + .../es/symbols/greek-mathfonts-bold.js | 1 + .../es/symbols/greek-mathfonts-italic.js | 1 + .../greek-mathfonts-sans-serif-bold.js | 1 + .../a11y/mathmaps/es/symbols/greek-scripts.js | 1 + .../a11y/mathmaps/es/symbols/greek-small.js | 1 + .../a11y/mathmaps/es/symbols/greek-symbols.js | 1 + .../mathmaps/es/symbols/hebrew_letters.js | 1 + .../es/symbols/latin-lower-double-accent.js | 1 + .../mathmaps/es/symbols/latin-lower-normal.js | 1 + .../es/symbols/latin-lower-phonetic.js | 1 + .../es/symbols/latin-lower-single-accent.js | 1 + .../symbols/latin-mathfonts-bold-fraktur.js | 1 + .../es/symbols/latin-mathfonts-bold-script.js | 1 + .../es/symbols/latin-mathfonts-bold.js | 1 + .../symbols/latin-mathfonts-double-struck.js | 1 + .../es/symbols/latin-mathfonts-fraktur.js | 1 + .../es/symbols/latin-mathfonts-italic.js | 1 + .../es/symbols/latin-mathfonts-monospace.js | 1 + .../latin-mathfonts-sans-serif-bold.js | 1 + .../latin-mathfonts-sans-serif-italic.js | 1 + .../es/symbols/latin-mathfonts-sans-serif.js | 1 + .../es/symbols/latin-mathfonts-script.js | 1 + .../a11y/mathmaps/es/symbols/latin-rest.js | 1 + .../es/symbols/latin-upper-double-accent.js | 1 + .../mathmaps/es/symbols/latin-upper-normal.js | 1 + .../es/symbols/latin-upper-single-accent.js | 1 + .../a11y/mathmaps/es/symbols/math_angles.js | 1 + .../a11y/mathmaps/es/symbols/math_arrows.js | 1 + .../mathmaps/es/symbols/math_characters.js | 1 + .../mathmaps/es/symbols/math_delimiters.js | 1 + .../a11y/mathmaps/es/symbols/math_digits.js | 1 + .../a11y/mathmaps/es/symbols/math_geometry.js | 1 + .../a11y/mathmaps/es/symbols/math_harpoons.js | 1 + .../es/symbols/math_non_characters.js | 1 + .../a11y/mathmaps/es/symbols/math_symbols.js | 1 + .../mathmaps/es/symbols/math_whitespace.js | 1 + .../a11y/mathmaps/es/symbols/other_stars.js | 1 + .../a11y/mathmaps/es/units/energy.js | 1 + .../a11y/mathmaps/es/units/length.js | 1 + .../a11y/mathmaps/es/units/memory.js | 1 + .../a11y/mathmaps/es/units/other.js | 1 + .../a11y/mathmaps/es/units/speed.js | 1 + .../a11y/mathmaps/es/units/temperature.js | 1 + .../extensions/a11y/mathmaps/es/units/time.js | 1 + .../a11y/mathmaps/es/units/volume.js | 1 + .../a11y/mathmaps/es/units/weight.js | 1 + .../extensions/a11y/mathmaps/mathmaps_ie.js | 308 ++++++ .../extensions/a11y/semantic-enrich.js | 1 + .../extensions/a11y/wgxpath.install.js | 77 ++ .../mathjax-27/extensions/asciimath2jax.js | 19 + .../mathjax-27/extensions/fast-preview.js | 19 + .../mathjax-27/extensions/jsMath2jax.js | 19 + .../mathjax-27/extensions/mml2jax.js | 19 + .../mathjax-27/extensions/tex2jax.js | 19 + .../mathjax-27/extensions/toMathML.js | 19 + .../HTML-CSS/TeX/otf/MathJax_AMS-Regular.otf | Bin 0 -> 58528 bytes .../TeX/otf/MathJax_Caligraphic-Bold.otf | Bin 0 -> 12348 bytes .../TeX/otf/MathJax_Caligraphic-Regular.otf | Bin 0 -> 12024 bytes .../HTML-CSS/TeX/otf/MathJax_Fraktur-Bold.otf | Bin 0 -> 26900 bytes .../TeX/otf/MathJax_Fraktur-Regular.otf | Bin 0 -> 25876 bytes .../HTML-CSS/TeX/otf/MathJax_Main-Bold.otf | Bin 0 -> 46800 bytes .../HTML-CSS/TeX/otf/MathJax_Main-Italic.otf | Bin 0 -> 28224 bytes .../HTML-CSS/TeX/otf/MathJax_Main-Regular.otf | Bin 0 -> 47636 bytes .../TeX/otf/MathJax_Math-BoldItalic.otf | Bin 0 -> 27096 bytes .../HTML-CSS/TeX/otf/MathJax_Math-Italic.otf | Bin 0 -> 26384 bytes .../HTML-CSS/TeX/otf/MathJax_Math-Regular.otf | Bin 0 -> 26328 bytes .../TeX/otf/MathJax_SansSerif-Bold.otf | Bin 0 -> 22156 bytes .../TeX/otf/MathJax_SansSerif-Italic.otf | Bin 0 -> 18572 bytes .../TeX/otf/MathJax_SansSerif-Regular.otf | Bin 0 -> 15920 bytes .../TeX/otf/MathJax_Script-Regular.otf | Bin 0 -> 14616 bytes .../TeX/otf/MathJax_Size1-Regular.otf | Bin 0 -> 8252 bytes .../TeX/otf/MathJax_Size2-Regular.otf | Bin 0 -> 7608 bytes .../TeX/otf/MathJax_Size3-Regular.otf | Bin 0 -> 4712 bytes .../TeX/otf/MathJax_Size4-Regular.otf | Bin 0 -> 7364 bytes .../TeX/otf/MathJax_Typewriter-Regular.otf | Bin 0 -> 24184 bytes .../HTML-CSS/TeX/otf/MathJax_Vector-Bold.otf | Bin 0 -> 1584 bytes .../TeX/otf/MathJax_Vector-Regular.otf | Bin 0 -> 1664 bytes .../TeX/otf/MathJax_WinChrome-Regular.otf | Bin 0 -> 4408 bytes .../TeX/otf/MathJax_WinIE6-Regular.otf | Bin 0 -> 28100 bytes .../mathjax-27/jax/element/mml/jax.js | 19 + .../jax/element/mml/optable/Arrows.js | 19 + .../jax/element/mml/optable/BasicLatin.js | 19 + .../element/mml/optable/CombDiacritMarks.js | 19 + .../mml/optable/CombDiactForSymbols.js | 19 + .../jax/element/mml/optable/Dingbats.js | 19 + .../element/mml/optable/GeneralPunctuation.js | 19 + .../element/mml/optable/GeometricShapes.js | 19 + .../jax/element/mml/optable/GreekAndCoptic.js | 19 + .../element/mml/optable/Latin1Supplement.js | 19 + .../element/mml/optable/LetterlikeSymbols.js | 19 + .../jax/element/mml/optable/MathOperators.js | 19 + .../element/mml/optable/MiscMathSymbolsA.js | 19 + .../element/mml/optable/MiscMathSymbolsB.js | 19 + .../mml/optable/MiscSymbolsAndArrows.js | 19 + .../jax/element/mml/optable/MiscTechnical.js | 19 + .../element/mml/optable/SpacingModLetters.js | 19 + .../element/mml/optable/SuppMathOperators.js | 19 + .../mml/optable/SupplementalArrowsA.js | 19 + .../mml/optable/SupplementalArrowsB.js | 19 + .../mathjax-27/jax/input/AsciiMath/config.js | 19 + .../mathjax-27/jax/input/AsciiMath/jax.js | 19 + .../mathjax-27/jax/input/MathML/config.js | 19 + .../mathjax-27/jax/input/MathML/entities/a.js | 19 + .../mathjax-27/jax/input/MathML/entities/b.js | 19 + .../mathjax-27/jax/input/MathML/entities/c.js | 19 + .../mathjax-27/jax/input/MathML/entities/d.js | 19 + .../mathjax-27/jax/input/MathML/entities/e.js | 19 + .../mathjax-27/jax/input/MathML/entities/f.js | 19 + .../jax/input/MathML/entities/fr.js | 19 + .../mathjax-27/jax/input/MathML/entities/g.js | 19 + .../mathjax-27/jax/input/MathML/entities/h.js | 19 + .../mathjax-27/jax/input/MathML/entities/i.js | 19 + .../mathjax-27/jax/input/MathML/entities/j.js | 19 + .../mathjax-27/jax/input/MathML/entities/k.js | 19 + .../mathjax-27/jax/input/MathML/entities/l.js | 19 + .../mathjax-27/jax/input/MathML/entities/m.js | 19 + .../mathjax-27/jax/input/MathML/entities/n.js | 19 + .../mathjax-27/jax/input/MathML/entities/o.js | 19 + .../jax/input/MathML/entities/opf.js | 19 + .../mathjax-27/jax/input/MathML/entities/p.js | 19 + .../mathjax-27/jax/input/MathML/entities/q.js | 19 + .../mathjax-27/jax/input/MathML/entities/r.js | 19 + .../mathjax-27/jax/input/MathML/entities/s.js | 19 + .../jax/input/MathML/entities/scr.js | 19 + .../mathjax-27/jax/input/MathML/entities/t.js | 19 + .../mathjax-27/jax/input/MathML/entities/u.js | 19 + .../mathjax-27/jax/input/MathML/entities/v.js | 19 + .../mathjax-27/jax/input/MathML/entities/w.js | 19 + .../mathjax-27/jax/input/MathML/entities/x.js | 19 + .../mathjax-27/jax/input/MathML/entities/y.js | 19 + .../mathjax-27/jax/input/MathML/entities/z.js | 19 + .../mathjax-27/jax/input/MathML/jax.js | 19 + .../mathjax-27/jax/input/TeX/config.js | 19 + .../mathjax-27/jax/input/TeX/jax.js | 19 + .../CommonHTML/autoload/annotation-xml.js | 19 + .../jax/output/CommonHTML/autoload/maction.js | 19 + .../output/CommonHTML/autoload/menclose.js | 19 + .../jax/output/CommonHTML/autoload/mglyph.js | 19 + .../CommonHTML/autoload/mmultiscripts.js | 19 + .../jax/output/CommonHTML/autoload/ms.js | 19 + .../jax/output/CommonHTML/autoload/mtable.js | 19 + .../output/CommonHTML/autoload/multiline.js | 19 + .../jax/output/CommonHTML/config.js | 19 + .../CommonHTML/fonts/TeX/AMS-Regular.js | 19 + .../CommonHTML/fonts/TeX/Caligraphic-Bold.js | 19 + .../CommonHTML/fonts/TeX/Fraktur-Bold.js | 19 + .../CommonHTML/fonts/TeX/Fraktur-Regular.js | 19 + .../output/CommonHTML/fonts/TeX/Main-Bold.js | 19 + .../CommonHTML/fonts/TeX/Math-BoldItalic.js | 19 + .../CommonHTML/fonts/TeX/SansSerif-Bold.js | 19 + .../CommonHTML/fonts/TeX/SansSerif-Italic.js | 19 + .../CommonHTML/fonts/TeX/SansSerif-Regular.js | 19 + .../CommonHTML/fonts/TeX/Script-Regular.js | 19 + .../fonts/TeX/Typewriter-Regular.js | 19 + .../CommonHTML/fonts/TeX/fontdata-extra.js | 19 + .../output/CommonHTML/fonts/TeX/fontdata.js | 19 + .../mathjax-27/jax/output/CommonHTML/jax.js | 19 + .../HTML-CSS/autoload/annotation-xml.js | 19 + .../jax/output/HTML-CSS/autoload/maction.js | 19 + .../jax/output/HTML-CSS/autoload/menclose.js | 19 + .../jax/output/HTML-CSS/autoload/mglyph.js | 19 + .../output/HTML-CSS/autoload/mmultiscripts.js | 19 + .../jax/output/HTML-CSS/autoload/ms.js | 19 + .../jax/output/HTML-CSS/autoload/mtable.js | 19 + .../jax/output/HTML-CSS/autoload/multiline.js | 19 + .../mathjax-27/jax/output/HTML-CSS/config.js | 19 + .../STIX/General/Bold/AlphaPresentForms.js | 19 + .../fonts/STIX/General/Bold/Arrows.js | 19 + .../fonts/STIX/General/Bold/BBBold.js | 19 + .../fonts/STIX/General/Bold/BoldFraktur.js | 19 + .../fonts/STIX/General/Bold/BoxDrawing.js | 19 + .../STIX/General/Bold/CombDiacritMarks.js | 19 + .../STIX/General/Bold/CombDiactForSymbols.js | 19 + .../STIX/General/Bold/ControlPictures.js | 19 + .../STIX/General/Bold/CurrencySymbols.js | 19 + .../fonts/STIX/General/Bold/Cyrillic.js | 19 + .../STIX/General/Bold/EnclosedAlphanum.js | 19 + .../STIX/General/Bold/GeneralPunctuation.js | 19 + .../STIX/General/Bold/GeometricShapes.js | 19 + .../fonts/STIX/General/Bold/GreekAndCoptic.js | 19 + .../fonts/STIX/General/Bold/GreekBold.js | 19 + .../fonts/STIX/General/Bold/GreekSSBold.js | 19 + .../fonts/STIX/General/Bold/IPAExtensions.js | 19 + .../STIX/General/Bold/Latin1Supplement.js | 19 + .../fonts/STIX/General/Bold/LatinExtendedA.js | 19 + .../General/Bold/LatinExtendedAdditional.js | 19 + .../fonts/STIX/General/Bold/LatinExtendedB.js | 19 + .../fonts/STIX/General/Bold/LatinExtendedD.js | 19 + .../STIX/General/Bold/LetterlikeSymbols.js | 19 + .../HTML-CSS/fonts/STIX/General/Bold/Main.js | 19 + .../fonts/STIX/General/Bold/MathBold.js | 19 + .../fonts/STIX/General/Bold/MathOperators.js | 19 + .../fonts/STIX/General/Bold/MathSSBold.js | 19 + .../STIX/General/Bold/MiscMathSymbolsA.js | 19 + .../STIX/General/Bold/MiscMathSymbolsB.js | 19 + .../fonts/STIX/General/Bold/MiscSymbols.js | 19 + .../fonts/STIX/General/Bold/MiscTechnical.js | 19 + .../fonts/STIX/General/Bold/NumberForms.js | 19 + .../STIX/General/Bold/PhoneticExtensions.js | 19 + .../STIX/General/Bold/SpacingModLetters.js | 19 + .../STIX/General/Bold/SuperAndSubscripts.js | 19 + .../STIX/General/Bold/SuppMathOperators.js | 19 + .../General/BoldItalic/AlphaPresentForms.js | 19 + .../STIX/General/BoldItalic/BasicLatin.js | 19 + .../STIX/General/BoldItalic/BoxDrawing.js | 19 + .../General/BoldItalic/CombDiactForSymbols.js | 19 + .../General/BoldItalic/ControlPictures.js | 19 + .../General/BoldItalic/CurrencySymbols.js | 19 + .../fonts/STIX/General/BoldItalic/Cyrillic.js | 19 + .../General/BoldItalic/EnclosedAlphanum.js | 19 + .../General/BoldItalic/GeneralPunctuation.js | 19 + .../STIX/General/BoldItalic/GreekAndCoptic.js | 19 + .../General/BoldItalic/GreekBoldItalic.js | 19 + .../General/BoldItalic/GreekSSBoldItalic.js | 19 + .../STIX/General/BoldItalic/IPAExtensions.js | 19 + .../General/BoldItalic/Latin1Supplement.js | 19 + .../STIX/General/BoldItalic/LatinExtendedA.js | 19 + .../BoldItalic/LatinExtendedAdditional.js | 19 + .../STIX/General/BoldItalic/LatinExtendedB.js | 19 + .../General/BoldItalic/LetterlikeSymbols.js | 19 + .../fonts/STIX/General/BoldItalic/Main.js | 19 + .../STIX/General/BoldItalic/MathBoldItalic.js | 19 + .../STIX/General/BoldItalic/MathBoldScript.js | 19 + .../STIX/General/BoldItalic/MathOperators.js | 19 + .../General/BoldItalic/MathSSItalicBold.js | 19 + .../General/BoldItalic/SpacingModLetters.js | 19 + .../STIX/General/Italic/AlphaPresentForms.js | 19 + .../fonts/STIX/General/Italic/BoxDrawing.js | 19 + .../General/Italic/CombDiactForSymbols.js | 19 + .../STIX/General/Italic/ControlPictures.js | 19 + .../STIX/General/Italic/CurrencySymbols.js | 19 + .../fonts/STIX/General/Italic/Cyrillic.js | 19 + .../STIX/General/Italic/EnclosedAlphanum.js | 19 + .../STIX/General/Italic/GeneralPunctuation.js | 19 + .../STIX/General/Italic/GreekAndCoptic.js | 19 + .../fonts/STIX/General/Italic/GreekItalic.js | 19 + .../STIX/General/Italic/IPAExtensions.js | 19 + .../STIX/General/Italic/Latin1Supplement.js | 19 + .../STIX/General/Italic/LatinExtendedA.js | 19 + .../General/Italic/LatinExtendedAdditional.js | 19 + .../STIX/General/Italic/LatinExtendedB.js | 19 + .../STIX/General/Italic/LetterlikeSymbols.js | 19 + .../fonts/STIX/General/Italic/Main.js | 19 + .../fonts/STIX/General/Italic/MathItalic.js | 19 + .../STIX/General/Italic/MathOperators.js | 19 + .../fonts/STIX/General/Italic/MathSSItalic.js | 19 + .../fonts/STIX/General/Italic/MathScript.js | 19 + .../STIX/General/Italic/SpacingModLetters.js | 19 + .../HTML-CSS/fonts/STIX/General/Italic/ij.js | 19 + .../STIX/General/Regular/AlphaPresentForms.js | 19 + .../fonts/STIX/General/Regular/Arrows.js | 19 + .../fonts/STIX/General/Regular/BBBold.js | 19 + .../STIX/General/Regular/BlockElements.js | 19 + .../fonts/STIX/General/Regular/BoldFraktur.js | 19 + .../fonts/STIX/General/Regular/BoxDrawing.js | 19 + .../fonts/STIX/General/Regular/CJK.js | 19 + .../STIX/General/Regular/CombDiacritMarks.js | 19 + .../General/Regular/CombDiactForSymbols.js | 19 + .../STIX/General/Regular/ControlPictures.js | 19 + .../STIX/General/Regular/CurrencySymbols.js | 19 + .../fonts/STIX/General/Regular/Cyrillic.js | 19 + .../fonts/STIX/General/Regular/Dingbats.js | 19 + .../STIX/General/Regular/EnclosedAlphanum.js | 19 + .../fonts/STIX/General/Regular/Fraktur.js | 19 + .../General/Regular/GeneralPunctuation.js | 19 + .../STIX/General/Regular/GeometricShapes.js | 19 + .../STIX/General/Regular/GreekAndCoptic.js | 19 + .../fonts/STIX/General/Regular/GreekBold.js | 19 + .../STIX/General/Regular/GreekBoldItalic.js | 19 + .../fonts/STIX/General/Regular/GreekItalic.js | 19 + .../fonts/STIX/General/Regular/GreekSSBold.js | 19 + .../STIX/General/Regular/GreekSSBoldItalic.js | 19 + .../fonts/STIX/General/Regular/Hiragana.js | 19 + .../STIX/General/Regular/IPAExtensions.js | 19 + .../STIX/General/Regular/Latin1Supplement.js | 19 + .../STIX/General/Regular/LatinExtendedA.js | 19 + .../Regular/LatinExtendedAdditional.js | 19 + .../STIX/General/Regular/LatinExtendedB.js | 19 + .../STIX/General/Regular/LatinExtendedD.js | 19 + .../STIX/General/Regular/LetterlikeSymbols.js | 19 + .../fonts/STIX/General/Regular/Main.js | 19 + .../fonts/STIX/General/Regular/MathBold.js | 19 + .../STIX/General/Regular/MathBoldItalic.js | 19 + .../STIX/General/Regular/MathBoldScript.js | 19 + .../fonts/STIX/General/Regular/MathItalic.js | 19 + .../STIX/General/Regular/MathOperators.js | 19 + .../fonts/STIX/General/Regular/MathSS.js | 19 + .../fonts/STIX/General/Regular/MathSSBold.js | 19 + .../STIX/General/Regular/MathSSItalic.js | 19 + .../STIX/General/Regular/MathSSItalicBold.js | 19 + .../fonts/STIX/General/Regular/MathScript.js | 19 + .../fonts/STIX/General/Regular/MathTT.js | 19 + .../STIX/General/Regular/MiscMathSymbolsA.js | 19 + .../STIX/General/Regular/MiscMathSymbolsB.js | 19 + .../fonts/STIX/General/Regular/MiscSymbols.js | 19 + .../General/Regular/MiscSymbolsAndArrows.js | 19 + .../STIX/General/Regular/MiscTechnical.js | 19 + .../fonts/STIX/General/Regular/NumberForms.js | 19 + .../General/Regular/PhoneticExtensions.js | 19 + .../STIX/General/Regular/SpacingModLetters.js | 19 + .../fonts/STIX/General/Regular/Specials.js | 19 + .../General/Regular/SuperAndSubscripts.js | 19 + .../STIX/General/Regular/SuppMathOperators.js | 19 + .../General/Regular/SupplementalArrowsA.js | 19 + .../General/Regular/SupplementalArrowsB.js | 19 + .../HTML-CSS/fonts/STIX/General/Regular/ij.js | 19 + .../fonts/STIX/IntegralsD/Bold/All.js | 19 + .../fonts/STIX/IntegralsD/Regular/All.js | 19 + .../fonts/STIX/IntegralsD/Regular/Main.js | 19 + .../fonts/STIX/IntegralsSm/Bold/All.js | 19 + .../fonts/STIX/IntegralsSm/Regular/All.js | 19 + .../fonts/STIX/IntegralsSm/Regular/Main.js | 19 + .../fonts/STIX/IntegralsUp/Bold/All.js | 19 + .../fonts/STIX/IntegralsUp/Regular/All.js | 19 + .../HTML-CSS/fonts/STIX/fontdata-1.0.js | 19 + .../HTML-CSS/fonts/STIX/fontdata-beta.js | 19 + .../HTML-CSS/fonts/STIX/fontdata-extra.js | 19 + .../output/HTML-CSS/fonts/STIX/fontdata.js | 19 + 441 files changed, 8422 insertions(+), 1 deletion(-) create mode 100644 LICENSE create mode 100644 NEWS.md create mode 100644 revisions_report_files/mathjax-27/config/AM_CHTML-full.js create mode 100644 revisions_report_files/mathjax-27/config/AM_CHTML.js create mode 100644 revisions_report_files/mathjax-27/config/AM_SVG-full.js create mode 100644 revisions_report_files/mathjax-27/config/AM_SVG.js create mode 100644 revisions_report_files/mathjax-27/config/MML_CHTML-full.js create mode 100644 revisions_report_files/mathjax-27/config/MML_CHTML.js create mode 100644 revisions_report_files/mathjax-27/config/MML_SVG-full.js create mode 100644 revisions_report_files/mathjax-27/config/MML_SVG.js create mode 100644 revisions_report_files/mathjax-27/config/MMLorHTML.js create mode 100644 revisions_report_files/mathjax-27/config/Safe.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-AMS-MML_HTMLorMML.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-AMS-MML_SVG-full.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-AMS-MML_SVG.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-AMS_CHTML-full.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-AMS_CHTML.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-AMS_SVG-full.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-AMS_SVG.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-MML-AM_CHTML-full.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-MML-AM_CHTML.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-MML-AM_SVG-full.js create mode 100644 revisions_report_files/mathjax-27/config/TeX-MML-AM_SVG.js create mode 100644 revisions_report_files/mathjax-27/extensions/AssistiveMML.js create mode 100644 revisions_report_files/mathjax-27/extensions/CHTML-preview.js create mode 100644 revisions_report_files/mathjax-27/extensions/FontWarnings.js create mode 100644 revisions_report_files/mathjax-27/extensions/HTML-CSS/handle-floats.js create mode 100644 revisions_report_files/mathjax-27/extensions/HelpDialog.js create mode 100644 revisions_report_files/mathjax-27/extensions/MatchWebFonts.js create mode 100644 revisions_report_files/mathjax-27/extensions/MathEvents.js create mode 100644 revisions_report_files/mathjax-27/extensions/MathML/content-mathml.js create mode 100644 revisions_report_files/mathjax-27/extensions/MathML/mml3.js create mode 100644 revisions_report_files/mathjax-27/extensions/MathMenu.js create mode 100644 revisions_report_files/mathjax-27/extensions/MathZoom.js create mode 100644 revisions_report_files/mathjax-27/extensions/Safe.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/AMScd.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/AMSmath.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/AMSsymbols.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/HTML.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/action.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/autobold.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/autoload-all.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/bbox.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/begingroup.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/boldsymbol.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/cancel.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/color.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/enclose.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/extpfeil.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/mathchoice.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/mediawiki-texvc.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/mhchem.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/mhchem3/mhchem.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/newcommand.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/noErrors.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/noUndefined.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/unicode.js create mode 100644 revisions_report_files/mathjax-27/extensions/TeX/verb.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/accessibility-menu.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/auto-collapse.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/collapsible.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/explorer.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/invalid_keypress.mp3 create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/invalid_keypress.ogg create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathjax-sre.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/functions/algebra.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/functions/elementary.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/functions/hyperbolic.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/functions/trigonometry.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/greek-capital.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/greek-mathfonts-bold.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/greek-mathfonts-italic.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/greek-mathfonts-sans-serif-bold.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/greek-scripts.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/greek-small.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/greek-symbols.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/hebrew_letters.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-lower-double-accent.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-lower-normal.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-lower-phonetic.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-lower-single-accent.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-bold-fraktur.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-bold-script.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-bold.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-double-struck.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-fraktur.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-italic.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-monospace.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-sans-serif-bold.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-sans-serif-italic.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-sans-serif.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-mathfonts-script.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-rest.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-upper-double-accent.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-upper-normal.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/latin-upper-single-accent.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/math_angles.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/math_arrows.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/math_characters.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/math_delimiters.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/math_digits.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/math_geometry.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/math_harpoons.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/math_non_characters.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/math_symbols.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/math_whitespace.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/symbols/other_stars.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/units/energy.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/units/length.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/units/memory.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/units/other.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/units/speed.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/units/temperature.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/units/time.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/units/volume.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/en/units/weight.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/functions/algebra.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/functions/elementary.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/functions/hyperbolic.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/functions/trigonometry.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/greek-capital.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/greek-mathfonts-bold.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/greek-mathfonts-italic.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/greek-mathfonts-sans-serif-bold.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/greek-scripts.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/greek-small.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/greek-symbols.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/hebrew_letters.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-lower-double-accent.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-lower-normal.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-lower-phonetic.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-lower-single-accent.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-bold-fraktur.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-bold-script.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-bold.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-double-struck.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-fraktur.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-italic.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-monospace.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-sans-serif-bold.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-sans-serif-italic.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-sans-serif.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-mathfonts-script.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-rest.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-upper-double-accent.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-upper-normal.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/latin-upper-single-accent.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/math_angles.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/math_arrows.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/math_characters.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/math_delimiters.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/math_digits.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/math_geometry.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/math_harpoons.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/math_non_characters.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/math_symbols.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/math_whitespace.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/symbols/other_stars.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/units/energy.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/units/length.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/units/memory.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/units/other.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/units/speed.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/units/temperature.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/units/time.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/units/volume.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/es/units/weight.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/mathmaps/mathmaps_ie.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/semantic-enrich.js create mode 100644 revisions_report_files/mathjax-27/extensions/a11y/wgxpath.install.js create mode 100644 revisions_report_files/mathjax-27/extensions/asciimath2jax.js create mode 100644 revisions_report_files/mathjax-27/extensions/fast-preview.js create mode 100644 revisions_report_files/mathjax-27/extensions/jsMath2jax.js create mode 100644 revisions_report_files/mathjax-27/extensions/mml2jax.js create mode 100644 revisions_report_files/mathjax-27/extensions/tex2jax.js create mode 100644 revisions_report_files/mathjax-27/extensions/toMathML.js create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_AMS-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Caligraphic-Bold.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Caligraphic-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Fraktur-Bold.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Fraktur-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Main-Bold.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Main-Italic.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Main-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Math-BoldItalic.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Math-Italic.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Math-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_SansSerif-Bold.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_SansSerif-Italic.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_SansSerif-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Script-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Size1-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Size2-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Size3-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Size4-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Typewriter-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Vector-Bold.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_Vector-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_WinChrome-Regular.otf create mode 100644 revisions_report_files/mathjax-27/fonts/HTML-CSS/TeX/otf/MathJax_WinIE6-Regular.otf create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/jax.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/Arrows.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/BasicLatin.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/CombDiacritMarks.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/CombDiactForSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/Dingbats.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/GeneralPunctuation.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/GeometricShapes.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/GreekAndCoptic.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/Latin1Supplement.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/LetterlikeSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/MathOperators.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/MiscMathSymbolsA.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/MiscMathSymbolsB.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/MiscSymbolsAndArrows.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/MiscTechnical.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/SpacingModLetters.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/SuppMathOperators.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/SupplementalArrowsA.js create mode 100644 revisions_report_files/mathjax-27/jax/element/mml/optable/SupplementalArrowsB.js create mode 100644 revisions_report_files/mathjax-27/jax/input/AsciiMath/config.js create mode 100644 revisions_report_files/mathjax-27/jax/input/AsciiMath/jax.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/config.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/a.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/b.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/c.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/d.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/e.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/f.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/fr.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/g.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/h.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/i.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/j.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/k.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/l.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/m.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/n.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/o.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/opf.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/p.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/q.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/r.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/s.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/scr.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/t.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/u.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/v.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/w.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/x.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/y.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/entities/z.js create mode 100644 revisions_report_files/mathjax-27/jax/input/MathML/jax.js create mode 100644 revisions_report_files/mathjax-27/jax/input/TeX/config.js create mode 100644 revisions_report_files/mathjax-27/jax/input/TeX/jax.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/autoload/annotation-xml.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/autoload/maction.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/autoload/menclose.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/autoload/mglyph.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/autoload/mmultiscripts.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/autoload/ms.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/autoload/mtable.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/autoload/multiline.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/config.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/AMS-Regular.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/Caligraphic-Bold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/Fraktur-Bold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/Fraktur-Regular.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/Main-Bold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/Math-BoldItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/SansSerif-Bold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/SansSerif-Italic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/SansSerif-Regular.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/Script-Regular.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/Typewriter-Regular.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/fontdata-extra.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/fonts/TeX/fontdata.js create mode 100644 revisions_report_files/mathjax-27/jax/output/CommonHTML/jax.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/autoload/annotation-xml.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/autoload/maction.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/autoload/menclose.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/autoload/mglyph.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/autoload/mmultiscripts.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/autoload/ms.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/autoload/mtable.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/autoload/multiline.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/config.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/AlphaPresentForms.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/Arrows.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/BBBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/BoldFraktur.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/BoxDrawing.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/CombDiacritMarks.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/CombDiactForSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/ControlPictures.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/CurrencySymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/Cyrillic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/EnclosedAlphanum.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/GeneralPunctuation.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/GeometricShapes.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/GreekAndCoptic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/GreekBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/GreekSSBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/IPAExtensions.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/Latin1Supplement.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/LatinExtendedA.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/LatinExtendedAdditional.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/LatinExtendedB.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/LatinExtendedD.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/LetterlikeSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/Main.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/MathBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/MathOperators.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/MathSSBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/MiscMathSymbolsA.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/MiscMathSymbolsB.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/MiscSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/MiscTechnical.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/NumberForms.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/PhoneticExtensions.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/SpacingModLetters.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/SuperAndSubscripts.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Bold/SuppMathOperators.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/AlphaPresentForms.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/BasicLatin.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/BoxDrawing.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/CombDiactForSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/ControlPictures.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/CurrencySymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/Cyrillic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/EnclosedAlphanum.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/GeneralPunctuation.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/GreekAndCoptic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/GreekBoldItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/GreekSSBoldItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/IPAExtensions.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/Latin1Supplement.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/LatinExtendedA.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/LatinExtendedAdditional.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/LatinExtendedB.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/LetterlikeSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/Main.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/MathBoldItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/MathBoldScript.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/MathOperators.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/MathSSItalicBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/BoldItalic/SpacingModLetters.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/AlphaPresentForms.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/BoxDrawing.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/CombDiactForSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/ControlPictures.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/CurrencySymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/Cyrillic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/EnclosedAlphanum.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/GeneralPunctuation.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/GreekAndCoptic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/GreekItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/IPAExtensions.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/Latin1Supplement.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/LatinExtendedA.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/LatinExtendedAdditional.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/LatinExtendedB.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/LetterlikeSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/Main.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/MathItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/MathOperators.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/MathSSItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/MathScript.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/SpacingModLetters.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Italic/ij.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/AlphaPresentForms.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/Arrows.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/BBBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/BlockElements.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/BoldFraktur.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/BoxDrawing.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/CJK.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/CombDiacritMarks.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/CombDiactForSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/ControlPictures.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/CurrencySymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/Cyrillic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/Dingbats.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/EnclosedAlphanum.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/Fraktur.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/GeneralPunctuation.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/GeometricShapes.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/GreekAndCoptic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/GreekBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/GreekBoldItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/GreekItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/GreekSSBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/GreekSSBoldItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/Hiragana.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/IPAExtensions.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/Latin1Supplement.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/LatinExtendedA.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/LatinExtendedAdditional.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/LatinExtendedB.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/LatinExtendedD.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/LetterlikeSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/Main.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathBoldItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathBoldScript.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathOperators.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathSS.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathSSBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathSSItalic.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathSSItalicBold.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathScript.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MathTT.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MiscMathSymbolsA.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MiscMathSymbolsB.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MiscSymbols.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MiscSymbolsAndArrows.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/MiscTechnical.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/NumberForms.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/PhoneticExtensions.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/SpacingModLetters.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/Specials.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/SuperAndSubscripts.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/SuppMathOperators.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/SupplementalArrowsA.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/SupplementalArrowsB.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/General/Regular/ij.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/IntegralsD/Bold/All.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/IntegralsD/Regular/All.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/IntegralsD/Regular/Main.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/IntegralsSm/Bold/All.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/IntegralsSm/Regular/All.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/IntegralsSm/Regular/Main.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/IntegralsUp/Bold/All.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/IntegralsUp/Regular/All.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/fontdata-1.0.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/fontdata-beta.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/fontdata-extra.js create mode 100644 revisions_report_files/mathjax-27/jax/output/HTML-CSS/fonts/STIX/fontdata.js diff --git a/.Rbuildignore b/.Rbuildignore index b546a3f..9fae064 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -6,3 +6,4 @@ ^docs$ ^pkgdown$ ^\.github$ +^LICENSE$ diff --git a/DESCRIPTION b/DESCRIPTION index 8c3ceca..8e16840 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -26,7 +26,7 @@ Suggest: readxl, formattable, kableExtra -SystemRequirements: Java JRE 17 or higher +SystemRequirements: Java (>= 17) License: EUPL Encoding: UTF-8 Collate: diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..20fc266 --- /dev/null +++ b/LICENSE @@ -0,0 +1,185 @@ +EUROPEAN UNION PUBLIC LICENCE v. 1.2 + +EUPL © the European Union 2007, 2016 + +This European Union Public Licence (the ‘EUPL’) applies to the Work (as defined below) which is provided under the terms of this Licence. Any use of the Work, other than as authorised under this Licence is prohibited (to the extent such use is covered by a right of the copyright holder of the Work). + +The Work is provided under the terms of this Licence when the Licensor (as defined below) has placed the following notice immediately following the copyright notice for the Work: + +Licensed under the EUPL + +or has expressed by any other means his willingness to license under the EUPL. + + +1. Definitions + +In this Licence, the following terms have the following meaning: + +— ‘The Licence’: this Licence. + +— ‘The Original Work’: the work or software distributed or communicated by the Licensor under this Licence, available as Source Code and also as Executable Code as the case may be. + +— ‘Derivative Works’: the works or software that could be created by the Licensee, based upon the Original Work or modifications thereof. This Licence does not define the extent of modification or dependence on the Original Work required in order to classify a work as a Derivative Work; this extent is determined by copyright law applicable in the country mentioned in Article 15. + +— ‘The Work’: the Original Work or its Derivative Works. + +— ‘The Source Code’: the human-readable form of the Work which is the most convenient for people to study and modify. + +— ‘The Executable Code’: any code which has generally been compiled and which is meant to be interpreted by a computer as a program. + +— ‘The Licensor’: the natural or legal person that distributes or communicates the Work under the Licence. + +— ‘Contributor(s)’: any natural or legal person who modifies the Work under the Licence, or otherwise contributes to the creation of a Derivative Work. + +— ‘The Licensee’ or ‘You’: any natural or legal person who makes any usage of the Work under the terms of the Licence. + +— ‘Distribution’ or ‘Communication’: any act of selling, giving, lending, renting, distributing, communicating, transmitting, or otherwise making available, online or offline, copies of the Work or providing access to its essential functionalities at the disposal of any other natural or legal person. + + +2. Scope of the rights granted by the Licence + +The Licensor hereby grants You a worldwide, royalty-free, non-exclusive, sublicensable licence to do the following, for the duration of copyright vested in the Original Work: + +— use the Work in any circumstance and for all usage, + +— reproduce the Work, + +— modify the Work, and make Derivative Works based upon the Work, + +— communicate to the public, including the right to make available or display the Work or copies thereof to the public and perform publicly, as the case may be, the Work, + +— distribute the Work or copies thereof, + +— lend and rent the Work or copies thereof, + +— sublicense rights in the Work or copies thereof. + +Those rights can be exercised on any media, supports and formats, whether now known or later invented, as far as the applicable law permits so. + +In the countries where moral rights apply, the Licensor waives his right to exercise his moral right to the extent allowed by law in order to make effective the licence of the economic rights here above listed. + +The Licensor grants to the Licensee royalty-free, non-exclusive usage rights to any patents held by the Licensor, to the extent necessary to make use of the rights granted on the Work under this Licence. + + +3. Communication of the Source Code + +The Licensor may provide the Work either in its Source Code form, or as Executable Code. If the Work is provided as Executable Code, the Licensor provides in addition a machine-readable copy of the Source Code of the Work along with each copy of the Work that the Licensor distributes or indicates, in a notice following the copyright notice attached to the Work, a repository where the Source Code is easily and freely accessible for as long as the Licensor continues to distribute or communicate the Work. + + +4. Limitations on copyright + +Nothing in this Licence is intended to deprive the Licensee of the benefits from any exception or limitation to the exclusive rights of the rights owners in the Work, of the exhaustion of those rights or of other applicable limitations thereto. + + +5. Obligations of the Licensee + +The grant of the rights mentioned above is subject to some restrictions and obligations imposed on the Licensee. Those obligations are the following: + + Attribution right: The Licensee shall keep intact all copyright, patent or trademarks notices and all notices that refer to the Licence and to the disclaimer of warranties. The Licensee must include a copy of such notices and a copy of the Licence with every copy of the Work he/she distributes or communicates. The Licensee must cause any Derivative Work to carry prominent notices stating that the Work has been modified and the date of modification. + Copyleft clause: If the Licensee distributes or communicates copies of the Original Works or Derivative Works, this Distribution or Communication will be done under the terms of this Licence or of a later version of this Licence unless the Original Work is expressly distributed only under this version of the Licence — for example by communicating ‘EUPL v. 1.2 only’. The Licensee (becoming Licensor) cannot offer or impose any additional terms or conditions on the Work or Derivative Work that alter or restrict the terms of the Licence. + Compatibility clause: If the Licensee Distributes or Communicates Derivative Works or copies thereof based upon both the Work and another work licensed under a Compatible Licence, this Distribution or Communication can be done under the terms of this Compatible Licence. For the sake of this clause, ‘Compatible Licence’ refers to the licences listed in the appendix attached to this Licence. Should the Licensee's obligations under the Compatible Licence conflict with his/her obligations under this Licence, the obligations of the Compatible Licence shall prevail. + Provision of Source Code: When distributing or communicating copies of the Work, the Licensee will provide a machine-readable copy of the Source Code or indicate a repository where this Source will be easily and freely available for as long as the Licensee continues to distribute or communicate the Work. + Legal Protection: This Licence does not grant permission to use the trade names, trademarks, service marks, or names of the Licensor, except as required for reasonable and customary use in describing the origin of the Work and reproducing the content of the copyright notice. + + +6. Chain of Authorship + +The original Licensor warrants that the copyright in the Original Work granted hereunder is owned by him/her or licensed to him/her and that he/she has the power and authority to grant the Licence. + +Each Contributor warrants that the copyright in the modifications he/she brings to the Work are owned by him/her or licensed to him/her and that he/she has the power and authority to grant the Licence. + +Each time You accept the Licence, the original Licensor and subsequent Contributors grant You a licence to their contributions to the Work, under the terms of this Licence. + + +7. Disclaimer of Warranty + +The Work is a work in progress, which is continuously improved by numerous Contributors. It is not a finished work and may therefore contain defects or ‘bugs’ inherent to this type of development. + +For the above reason, the Work is provided under the Licence on an ‘as is’ basis and without warranties of any kind concerning the Work, including without limitation merchantability, fitness for a particular purpose, absence of defects or errors, accuracy, non-infringement of intellectual property rights other than copyright as stated in Article 6 of this Licence. + +This disclaimer of warranty is an essential part of the Licence and a condition for the grant of any rights to the Work. + + +8. Disclaimer of Liability + +Except in the cases of wilful misconduct or damages directly caused to natural persons, the Licensor will in no event be liable for any direct or indirect, material or moral, damages of any kind, arising out of the Licence or of the use of the Work, including without limitation, damages for loss of goodwill, work stoppage, computer failure or malfunction, loss of data or any commercial damage, even if the Licensor has been advised of the possibility of such damage. However, the Licensor will be liable under statutory product liability laws as far such laws apply to the Work. + + +9. Additional agreements + +While distributing the Work, You may choose to conclude an additional agreement, defining obligations or services consistent with this Licence. However, if accepting obligations, You may act only on your own behalf and on your sole responsibility, not on behalf of the original Licensor or any other Contributor, and only if You agree to indemnify, defend, and hold each Contributor harmless for any liability incurred by, or claims asserted against such Contributor by the fact You have accepted any warranty or additional liability. + + +10. Acceptance of the Licence + +The provisions of this Licence can be accepted by clicking on an icon ‘I agree’ placed under the bottom of a window displaying the text of this Licence or by affirming consent in any other similar way, in accordance with the rules of applicable law. Clicking on that icon indicates your clear and irrevocable acceptance of this Licence and all of its terms and conditions. + +Similarly, you irrevocably accept this Licence and all of its terms and conditions by exercising any rights granted to You by Article 2 of this Licence, such as the use of the Work, the creation by You of a Derivative Work or the Distribution or Communication by You of the Work or copies thereof. + + +11. Information to the public + +In case of any Distribution or Communication of the Work by means of electronic communication by You (for example, by offering to download the Work from a remote location) the distribution channel or media (for example, a website) must at least provide to the public the information requested by the applicable law regarding the Licensor, the Licence and the way it may be accessible, concluded, stored and reproduced by the Licensee. + + +12. Termination of the Licence + +The Licence and the rights granted hereunder will terminate automatically upon any breach by the Licensee of the terms of the Licence. + +Such a termination will not terminate the licences of any person who has received the Work from the Licensee under the Licence, provided such persons remain in full compliance with the Licence. + + +13. Miscellaneous + +Without prejudice of Article 9 above, the Licence represents the complete agreement between the Parties as to the Work. + +If any provision of the Licence is invalid or unenforceable under applicable law, this will not affect the validity or enforceability of the Licence as a whole. Such provision will be construed or reformed so as necessary to make it valid and enforceable. + +The European Commission may publish other linguistic versions or new versions of this Licence or updated versions of the Appendix, so far this is required and reasonable, without reducing the scope of the rights granted by the Licence. New versions of the Licence will be published with a unique version number. + +All linguistic versions of this Licence, approved by the European Commission, have identical value. Parties can take advantage of the linguistic version of their choice. + + +14. Jurisdiction + +Without prejudice to specific agreement between parties, + +— any litigation resulting from the interpretation of this License, arising between the European Union institutions, bodies, offices or agencies, as a Licensor, and any Licensee, will be subject to the jurisdiction of the Court of Justice of the European Union, as laid down in article 272 of the Treaty on the Functioning of the European Union, + +— any litigation arising between other parties and resulting from the interpretation of this License, will be subject to the exclusive jurisdiction of the competent court where the Licensor resides or conducts its primary business. + + +15. Applicable Law + +Without prejudice to specific agreement between parties, + +— this Licence shall be governed by the law of the European Union Member State where the Licensor has his seat, resides or has his registered office, + +— this licence shall be governed by Belgian law if the Licensor has no seat, residence or registered office inside a European Union Member State. +Appendix + +‘Compatible Licences’ according to Article 5 EUPL are: + +— GNU General Public License (GPL) v. 2, v. 3 + +— GNU Affero General Public License (AGPL) v. 3 + +— Open Software License (OSL) v. 2.1, v. 3.0 + +— Eclipse Public License (EPL) v. 1.0 + +— CeCILL v. 2.0, v. 2.1 + +— Mozilla Public Licence (MPL) v. 2 + +— GNU Lesser General Public Licence (LGPL) v. 2.1, v. 3 + +— Creative Commons Attribution-ShareAlike v. 3.0 Unported (CC BY-SA 3.0) for works other than software + +— European Union Public Licence (EUPL) v. 1.1, v. 1.2 + +— Québec Free and Open-Source Licence — Reciprocity (LiLiQ-R) or Strong Reciprocity (LiLiQ-R+) + +The European Commission may update this Appendix to later versions of the above licences without producing a new version of the EUPL, as long as they provide the rights granted in Article 2 of this Licence and protect the covered Source Code from exclusive appropriation. + +All other changes or additions to this Appendix require the production of a new EUPL version. diff --git a/NEWS.md b/NEWS.md new file mode 100644 index 0000000..7460369 --- /dev/null +++ b/NEWS.md @@ -0,0 +1,3 @@ +# rjd3revisions 1.1.0 + +* Initial CRAN submission. diff --git a/revisions_report_files/mathjax-27/config/AM_CHTML-full.js b/revisions_report_files/mathjax-27/config/AM_CHTML-full.js new file mode 100644 index 0000000..20db1ec --- /dev/null +++ b/revisions_report_files/mathjax-27/config/AM_CHTML-full.js @@ -0,0 +1,53 @@ +/* + * /MathJax/config/AM_CHTML-full.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/CommonHTML/jax.js", + "[MathJax]/jax/output/CommonHTML/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); +MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.asciimath2jax={version:"2.7.6",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(aa){var g;var X=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ab){if(ab.parent){ab.parent.removeChild(ab)}if(this.lastChild){this.lastChild.nextSibling=ab}if(!this.firstChild){this.firstChild=ab}this.childNodes.push(ab);ab.parent=this;this.lastChild=ab;return ab},removeChild:function(ad){for(var ac=0,ab=this.childNodes.length;ac=ab-1){this.lastChild=ae}this.childNodes[ad]=ae;ae.nextSibling=ac.nextSibling;ac.nextSibling=ac.parent=null;return ac},hasChildNodes:function(ab){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var ab=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ac=ab.apply(this,arguments)||this;ac.childNodes=ac.data;ac.nodeName=ac.type;return ac},appendChild:function(af){if(af.parent){af.parent.removeChild(af)}var ad=arguments;if(af.isa(X)){ad=af.childNodes;af.data=af.childNodes=[];af.firstChild=af.lastChild=null}for(var ae=0,ac=ad.length;ae=ac-1){this.lastChild=af}this.SetData(ae,af);af.nextSibling=ad.nextSibling;ad.nextSibling=ad.parent=null;return ad},hasChildNodes:function(ac){return(this.childNodes.length>0)},setAttribute:function(ac,ad){this[ac]=ad}})};var Q={};var e={getElementById:true,createElementNS:function(ac,ab){var ad=g[ab]();if(ab==="mo"&&aa.config.useMathMLspacing){ad.useMMLspacing=128}return ad},createTextNode:function(ab){return g.chars(ab).With({nodeValue:ab})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var C="blue";var o=true;var v=true;var d=".";var f=true;var l=(J.appName.slice(0,9)=="Microsoft");function E(ab){if(l){return e.createElement(ab)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",ab)}}var W="http://www.w3.org/1998/Math/MathML";function P(ab){if(l){return e.createElement("m:"+ab)}else{return e.createElementNS(W,ab)}}function O(ab,ad){var ac;if(l){ac=e.createElement("m:"+ab)}else{ac=e.createElementNS(W,ab)}if(ad){ac.appendChild(ad)}return ac}function u(ab,ac){z.push({input:ab,tag:"mo",output:ac,tex:null,ttype:V});B()}function r(ab){z.push(ab);B()}var D=["\uD835\uDC9C","\u212C","\uD835\uDC9E","\uD835\uDC9F","\u2130","\u2131","\uD835\uDCA2","\u210B","\u2110","\uD835\uDCA5","\uD835\uDCA6","\u2112","\u2133","\uD835\uDCA9","\uD835\uDCAA","\uD835\uDCAB","\uD835\uDCAC","\u211B","\uD835\uDCAE","\uD835\uDCAF","\uD835\uDCB0","\uD835\uDCB1","\uD835\uDCB2","\uD835\uDCB3","\uD835\uDCB4","\uD835\uDCB5","\uD835\uDCB6","\uD835\uDCB7","\uD835\uDCB8","\uD835\uDCB9","\u212F","\uD835\uDCBB","\u210A","\uD835\uDCBD","\uD835\uDCBE","\uD835\uDCBF","\uD835\uDCC0","\uD835\uDCC1","\uD835\uDCC2","\uD835\uDCC3","\u2134","\uD835\uDCC5","\uD835\uDCC6","\uD835\uDCC7","\uD835\uDCC8","\uD835\uDCC9","\uD835\uDCCA","\uD835\uDCCB","\uD835\uDCCC","\uD835\uDCCD","\uD835\uDCCE","\uD835\uDCCF"];var H=["\uD835\uDD04","\uD835\uDD05","\u212D","\uD835\uDD07","\uD835\uDD08","\uD835\uDD09","\uD835\uDD0A","\u210C","\u2111","\uD835\uDD0D","\uD835\uDD0E","\uD835\uDD0F","\uD835\uDD10","\uD835\uDD11","\uD835\uDD12","\uD835\uDD13","\uD835\uDD14","\u211C","\uD835\uDD16","\uD835\uDD17","\uD835\uDD18","\uD835\uDD19","\uD835\uDD1A","\uD835\uDD1B","\uD835\uDD1C","\u2128","\uD835\uDD1E","\uD835\uDD1F","\uD835\uDD20","\uD835\uDD21","\uD835\uDD22","\uD835\uDD23","\uD835\uDD24","\uD835\uDD25","\uD835\uDD26","\uD835\uDD27","\uD835\uDD28","\uD835\uDD29","\uD835\uDD2A","\uD835\uDD2B","\uD835\uDD2C","\uD835\uDD2D","\uD835\uDD2E","\uD835\uDD2F","\uD835\uDD30","\uD835\uDD31","\uD835\uDD32","\uD835\uDD33","\uD835\uDD34","\uD835\uDD35","\uD835\uDD36","\uD835\uDD37"];var w=["\uD835\uDD38","\uD835\uDD39","\u2102","\uD835\uDD3B","\uD835\uDD3C","\uD835\uDD3D","\uD835\uDD3E","\u210D","\uD835\uDD40","\uD835\uDD41","\uD835\uDD42","\uD835\uDD43","\uD835\uDD44","\u2115","\uD835\uDD46","\u2119","\u211A","\u211D","\uD835\uDD4A","\uD835\uDD4B","\uD835\uDD4C","\uD835\uDD4D","\uD835\uDD4E","\uD835\uDD4F","\uD835\uDD50","\u2124","\uD835\uDD52","\uD835\uDD53","\uD835\uDD54","\uD835\uDD55","\uD835\uDD56","\uD835\uDD57","\uD835\uDD58","\uD835\uDD59","\uD835\uDD5A","\uD835\uDD5B","\uD835\uDD5C","\uD835\uDD5D","\uD835\uDD5E","\uD835\uDD5F","\uD835\uDD60","\uD835\uDD61","\uD835\uDD62","\uD835\uDD63","\uD835\uDD64","\uD835\uDD65","\uD835\uDD66","\uD835\uDD67","\uD835\uDD68","\uD835\uDD69","\uD835\uDD6A","\uD835\uDD6B"];var c=0,A=1,U=2,i=3,b=4,h=5,a=6,L=7,V=8,m=9,Y=10,K=15;var k={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:Y};var z=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:c},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:c},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:c},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:c},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:c},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:c},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:c},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:c},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:c},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:c},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:c},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:c},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"lamda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lamda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:c},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:c},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:c},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:c},{input:"phi",tag:"mi",output:f?"\u03D5":"\u03C6",tex:null,ttype:c},{input:"varphi",tag:"mi",output:f?"\u03C6":"\u03D5",tex:null,ttype:c},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:c},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:c},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:c},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:c},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:c},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:c},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:c},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:c},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:c},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:c},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:c},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:c},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:c},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:c},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:c},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:c},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:c},{input:"**",tag:"mo",output:"\u2217",tex:"ast",ttype:c},{input:"***",tag:"mo",output:"\u22C6",tex:"star",ttype:c},{input:"//",tag:"mo",output:"/",tex:null,ttype:c},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:c},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:c},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:c},{input:"|><",tag:"mo",output:"\u22C9",tex:"ltimes",ttype:c},{input:"><|",tag:"mo",output:"\u22CA",tex:"rtimes",ttype:c},{input:"|><|",tag:"mo",output:"\u22C8",tex:"bowtie",ttype:c},{input:"-:",tag:"mo",output:"\u00F7",tex:"div",ttype:c},{input:"divide",tag:"mo",output:"-:",tex:null,ttype:V},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:c},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:c},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:c},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:c},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:L},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:L},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:c},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:L},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:c},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:L},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:c},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:L},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:c},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:L},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:c},{input:":=",tag:"mo",output:":=",tex:null,ttype:c},{input:"lt",tag:"mo",output:"<",tex:null,ttype:c},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:c},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:c},{input:"gt",tag:"mo",output:">",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:"left(",ttype:b},{input:")",tag:"mo",output:")",tex:"right)",ttype:h},{input:"[",tag:"mo",output:"[",tex:"left[",ttype:b},{input:"]",tag:"mo",output:"]",tex:"right]",ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:m},{input:":|:",tag:"mo",output:"|",tex:null,ttype:c},{input:"|:",tag:"mo",output:"|",tex:null,ttype:b},{input:":|",tag:"mo",output:"|",tex:null,ttype:h},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:":'",tag:"mo",output:"\u2235",tex:"because",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"frown",tag:"mo",output:"\u2322",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"Sin",tag:"mo",output:"Sin",tex:null,ttype:A,func:true},{input:"Cos",tag:"mo",output:"Cos",tex:null,ttype:A,func:true},{input:"Tan",tag:"mo",output:"Tan",tex:null,ttype:A,func:true},{input:"Arcsin",tag:"mo",output:"Arcsin",tex:null,ttype:A,func:true},{input:"Arccos",tag:"mo",output:"Arccos",tex:null,ttype:A,func:true},{input:"Arctan",tag:"mo",output:"Arctan",tex:null,ttype:A,func:true},{input:"Sinh",tag:"mo",output:"Sinh",tex:null,ttype:A,func:true},{input:"Cosh",tag:"mo",output:"Cosh",tex:null,ttype:A,func:true},{input:"Tanh",tag:"mo",output:"Tanh",tex:null,ttype:A,func:true},{input:"Cot",tag:"mo",output:"Cot",tex:null,ttype:A,func:true},{input:"Sec",tag:"mo",output:"Sec",tex:null,ttype:A,func:true},{input:"Csc",tag:"mo",output:"Csc",tex:null,ttype:A,func:true},{input:"Log",tag:"mo",output:"Log",tex:null,ttype:A,func:true},{input:"Ln",tag:"mo",output:"Ln",tex:null,ttype:A,func:true},{input:"Abs",tag:"mo",output:"abs",tex:null,ttype:A,notexcopy:true,rewriteleftright:["|","|"]},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:i},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"overset",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"underset",tag:"munder",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:i},{input:"^",tag:"msup",output:"^",tex:null,ttype:i},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"overarc",tag:"mover",output:"\u23DC",tex:"overparen",ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"id",tag:"mrow",ttype:U},{input:"class",tag:"mrow",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},k,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ac,ab){if(ac.input>ab.input){return 1}else{return -1}}var S=[];function n(){var ac;var ab=z.length;for(ac=0;ac>1;if(ac[ab]=S[ab]}s=y;if(af!=""){y=z[ae].ttype;return z[ae]}y=c;ab=1;ak=ah.slice(0,1);var ai=true;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}if(ak==d){ak=ah.slice(ab,ab+1);if("0"<=ak&&ak<="9"){ai=false;ab++;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}}}if((ai&&ab>1)||ab>2){ak=ah.slice(0,ab-1);aj="mn"}else{ab=2;ak=ah.slice(0,1);aj=(("A">ak||ak>"Z")&&("a">ak||ak>"z")?"mo":"mi")}if(ak=="-"&&s==i){y=i;return{input:ak,tag:aj,output:ak,ttype:A,func:true}}return{input:ak,tag:aj,output:ak,ttype:c}}function R(ac){var ab;if(!ac.hasChildNodes()){return}if(ac.firstChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.firstChild.firstChild.nodeValue;if(ab=="("||ab=="["||ab=="{"){ac.removeChild(ac.firstChild)}}if(ac.lastChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.lastChild.firstChild.nodeValue;if(ab==")"||ab=="]"||ab=="}"){ac.removeChild(ac.lastChild)}}}var F,s,y;function G(ai){var ad,ac,al,af,ak,ag=e.createDocumentFragment();ai=p(ai,0);ad=j(ai);if(ad==null||ad.ttype==h&&F>0){return[null,ai]}if(ad.ttype==V){ai=ad.output+p(ai,ad.input.length);ad=j(ai)}switch(ad.ttype){case L:case c:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai];case b:F++;ai=p(ai,ad.input.length);al=q(ai,true);F--;if(typeof ad.invisible=="boolean"&&ad.invisible){ac=O("mrow",al[0])}else{ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0])}return[ac,al[1]];case Y:if(ad!=k){ai=p(ai,ad.input.length)}if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}else{if(ad==k){af=ai.slice(1).indexOf('"')+1}else{af=0}}}}if(af==-1){af=ai.length}ak=ai.slice(1,af);if(ak.charAt(0)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ag.appendChild(O(ad.tag,e.createTextNode(ak)));if(ak.charAt(ak.length-1)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ai=p(ai,af+1);return[O("mrow",ag),ai];case K:case A:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O(ad.tag,e.createTextNode(ad.output)),ai]}if(typeof ad.func=="boolean"&&ad.func){ak=ai.charAt(0);if(ak=="^"||ak=="_"||ak=="/"||ak=="|"||ak==","||(ad.input.length==1&&ad.input.match(/\w/)&&ak!="(")){return[O(ad.tag,e.createTextNode(ad.output)),ai]}else{ac=O("mrow",O(ad.tag,e.createTextNode(ad.output)));ac.appendChild(al[0]);return[ac,al[1]]}}R(al[0]);if(ad.input=="sqrt"){return[O(ad.tag,al[0]),al[1]]}else{if(typeof ad.rewriteleftright!="undefined"){ac=O("mrow",O("mo",e.createTextNode(ad.rewriteleftright[0])));ac.appendChild(al[0]);ac.appendChild(O("mo",e.createTextNode(ad.rewriteleftright[1])));return[ac,al[1]]}else{if(ad.input=="cancel"){ac=O(ad.tag,al[0]);ac.setAttribute("notation","updiagonalstrike");return[ac,al[1]]}else{if(typeof ad.acc=="boolean"&&ad.acc){ac=O(ad.tag,al[0]);var ah=O("mo",e.createTextNode(ad.output));if(ad.input=="vec"&&((al[0].nodeName=="mrow"&&al[0].childNodes.length==1&&al[0].firstChild.firstChild.nodeValue!==null&&al[0].firstChild.firstChild.nodeValue.length==1)||(al[0].firstChild.nodeValue!==null&&al[0].firstChild.nodeValue.length==1))){ah.setAttribute("stretchy",false)}ac.appendChild(ah);return[ac,al[1]]}else{if(!l&&typeof ad.codes!="undefined"){for(af=0;af64&&ak.charCodeAt(ae)<91){aj=aj+ad.codes[ak.charCodeAt(ae)-65]}else{if(ak.charCodeAt(ae)>96&&ak.charCodeAt(ae)<123){aj=aj+ad.codes[ak.charCodeAt(ae)-71]}else{aj=aj+ak.charAt(ae)}}}if(al[0].nodeName=="mi"){al[0]=O("mo").appendChild(e.createTextNode(aj))}else{al[0].replaceChild(O("mo").appendChild(e.createTextNode(aj)),al[0].childNodes[af])}}}}ac=O(ad.tag,al[0]);ac.setAttribute(ad.atname,ad.atval);return[ac,al[1]]}}}}case U:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(al[0]);var ab=G(al[1]);if(ab[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(ab[0]);if(["color","class","id"].indexOf(ad.input)>=0){if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}}}ak=ai.slice(1,af);ac=O(ad.tag,ab[0]);if(ad.input==="color"){ac.setAttribute("mathcolor",ak)}else{if(ad.input==="class"){ac.setAttribute("class",ak)}else{if(ad.input==="id"){ac.setAttribute("id",ak)}}}return[ac,ab[1]]}if(ad.input=="root"||ad.output=="stackrel"){ag.appendChild(ab[0])}ag.appendChild(al[0]);if(ad.input=="frac"){ag.appendChild(ab[0])}return[O(ad.tag,ag),ab[1]];case i:ai=p(ai,ad.input.length);return[O("mo",e.createTextNode(ad.output)),ai];case a:ai=p(ai,ad.input.length);ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);ag.appendChild(O(ad.tag,e.createTextNode(ad.output)));ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);return[O("mrow",ag),ai];case m:F++;ai=p(ai,ad.input.length);al=q(ai,false);F--;ak="";if(al[0].lastChild!=null){ak=al[0].lastChild.firstChild.nodeValue}if(ak=="|"&&ai.charAt(0)!==","){ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0]);return[ac,al[1]]}else{ac=O("mo",e.createTextNode("\u2223"));ac=O("mrow",ac);return[ac,ai]}default:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai]}}function t(ah){var af,ai,ag,ae,ab,ad;ah=p(ah,0);ai=j(ah);ab=G(ah);ae=ab[0];ah=ab[1];af=j(ah);if(af.ttype==i&&af.input!="/"){ah=p(ah,af.input.length);ab=G(ah);if(ab[0]==null){ab[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ab[0])}ah=ab[1];ad=(ai.ttype==L||ai.ttype==K);if(af.input=="_"){ag=j(ah);if(ag.input=="^"){ah=p(ah,ag.input.length);var ac=G(ah);R(ac[0]);ah=ac[1];ae=O((ad?"munderover":"msubsup"),ae);ae.appendChild(ab[0]);ae.appendChild(ac[0]);ae=O("mrow",ae)}else{ae=O((ad?"munder":"msub"),ae);ae.appendChild(ab[0])}}else{if(af.input=="^"&&ad){ae=O("mover",ae);ae.appendChild(ab[0])}else{ae=O(af.tag,ae);ae.appendChild(ab[0])}}if(typeof ai.func!="undefined"&&ai.func){ag=j(ah);if(ag.ttype!=i&&ag.ttype!=h){ab=t(ah);ae=O("mrow",ae);ae.appendChild(ab[0]);ah=ab[1]}}}return[ae,ah]}function q(ak,aj){var ao,al,ag,ar,ah=e.createDocumentFragment();do{ak=p(ak,0);ag=t(ak);al=ag[0];ak=ag[1];ao=j(ak);if(ao.ttype==i&&ao.input=="/"){ak=p(ak,ao.input.length);ag=t(ak);if(ag[0]==null){ag[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ag[0])}ak=ag[1];R(al);al=O(ao.tag,al);al.appendChild(ag[0]);ah.appendChild(al);ao=j(ak)}else{if(al!=undefined){ah.appendChild(al)}}}while((ao.ttype!=h&&(ao.ttype!=m||aj)||F==0)&&ao!=null&&ao.output!="");if(ao.ttype==h||ao.ttype==m){var at=ah.childNodes.length;if(at>0&&ah.childNodes[at-1].nodeName=="mrow"&&ah.childNodes[at-1].lastChild&&ah.childNodes[at-1].lastChild.firstChild){var av=ah.childNodes[at-1].lastChild.firstChild.nodeValue;if(av==")"||av=="]"){var ac=ah.childNodes[at-1].firstChild.firstChild.nodeValue;if(ac=="("&&av==")"&&ao.output!="}"||ac=="["&&av=="]"){var ad=[];var ap=true;var am=ah.childNodes.length;for(ar=0;ap&&ar1){ap=ad[ar].length==ad[ar-2].length}}ap=ap&&(ad.length>1||ad[0].length>0);var af=[];if(ap){var ae,ab,ai,an,au=e.createDocumentFragment();for(ar=0;ar2){ah.removeChild(ah.firstChild);ah.removeChild(ah.firstChild)}au.appendChild(O("mtr",ae))}al=O("mtable",au);al.setAttribute("columnlines",af.join(" "));if(typeof ao.invisible=="boolean"&&ao.invisible){al.setAttribute("columnalign","left")}ah.replaceChild(al,ah.firstChild)}}}}ak=p(ak,ao.input.length);if(typeof ao.invisible!="boolean"||!ao.invisible){al=O("mo",e.createTextNode(ao.output));ah.appendChild(al)}}return[ah,ak]}function M(ad,ac){var ae,ab;F=0;ad=ad.replace(/ /g,"");ad=ad.replace(/>/g,">");ad=ad.replace(/</g,"<");ae=q(ad.replace(/^\s+/g,""),false)[0];ab=O("mstyle",ae);if(C!=""){ab.setAttribute("mathcolor",C)}if(mathfontsize!=""){ab.setAttribute("fontsize",mathfontsize);ab.setAttribute("mathsize",mathfontsize)}if(mathfontfamily!=""){ab.setAttribute("fontfamily",mathfontfamily);ab.setAttribute("mathvariant",mathfontfamily)}if(o){ab.setAttribute("displaystyle","true")}ab=O("math",ab);if(v){ab.setAttribute("title",ad.replace(/\s+/g," "))}return ab}v=false;mathfontfamily="";C="";mathfontsize="";(function(){for(var ac=0,ab=z.length;ac *":{position:"absolute"},".MJXc-bevelled > *":{display:"inline-block"},".mjx-stack":{display:"inline-block"},".mjx-op":{display:"block"},".mjx-under":{display:"table-cell"},".mjx-over":{display:"block"},".mjx-over > *":{"padding-left":"0px!important","padding-right":"0px!important"},".mjx-under > *":{"padding-left":"0px!important","padding-right":"0px!important"},".mjx-stack > .mjx-sup":{display:"block"},".mjx-stack > .mjx-sub":{display:"block"},".mjx-prestack > .mjx-presup":{display:"block"},".mjx-prestack > .mjx-presub":{display:"block"},".mjx-delim-h > .mjx-char":{display:"inline-block"},".mjx-surd":{"vertical-align":"top"},".mjx-mphantom *":{visibility:"hidden"},".mjx-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"2px 3px","font-style":"normal","font-size":"90%"},".mjx-annotation-xml":{"line-height":"normal"},".mjx-menclose > svg":{fill:"none",stroke:"currentColor"},".mjx-mtr":{display:"table-row"},".mjx-mlabeledtr":{display:"table-row"},".mjx-mtd":{display:"table-cell","text-align":"center"},".mjx-label":{display:"table-row"},".mjx-box":{display:"inline-block"},".mjx-block":{display:"block"},".mjx-span":{display:"inline"},".mjx-char":{display:"block","white-space":"pre"},".mjx-itable":{display:"inline-table",width:"auto"},".mjx-row":{display:"table-row"},".mjx-cell":{display:"table-cell"},".mjx-table":{display:"table",width:"100%"},".mjx-line":{display:"block",height:0},".mjx-strut":{width:0,"padding-top":k+"em"},".mjx-vsize":{width:0},".MJXc-space1":{"margin-left":".167em"},".MJXc-space2":{"margin-left":".222em"},".MJXc-space3":{"margin-left":".278em"},".mjx-chartest":{display:"block",visibility:"hidden",position:"absolute",top:0,"line-height":"normal","font-size":"500%"},".mjx-chartest .mjx-char":{display:"inline"},".mjx-chartest .mjx-box":{"padding-top":"1000px"},".MJXc-processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MJXc-processed":{display:"none"},".mjx-test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".mjx-test.mjx-test-display":{display:"table!important"},".mjx-test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".mjx-test.mjx-test-default":{display:"block!important",clear:"both"},".mjx-ex-box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .mjx-left-box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .mjx-right-box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .mjx-right-box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_CHTML_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401,position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}};var i=1000000;var n=5;var c={},r=MathJax.Hub.config;a.Augment({settings:f.config.menuSettings,config:{styles:p},Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var s=this.settings;if(s.scale){this.config.scale=s.scale}this.require.push(this.fontDir+"/TeX/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js");c=this.config.linebreaks},Startup:function(){e=MathJax.Extension.MathEvents.Event;q=MathJax.Extension.MathEvents.Touch;h=MathJax.Extension.MathEvents.Hover;this.ContextMenu=e.ContextMenu;this.Mousedown=e.AltContextMenu;this.Mouseover=h.Mouseover;this.Mouseout=h.Mouseout;this.Mousemove=h.Mousemove;var s=a.addElement(document.body,"mjx-block",{style:{display:"block",width:"5in"}});this.pxPerInch=s.offsetWidth/5;s.parentNode.removeChild(s);this.TestSpan=a.Element("mjx-test",{style:{left:"1em"}},[["mjx-left-box"],["mjx-ex-box"],["mjx-right-box"]]);return o.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){this.getDefaultExEm();if(this.defaultEm){return}var s=MathJax.Callback();o.timer.start(o,function(t){if(t.time(s)){f.signal.Post(["CommonHTML Jax - no default em size"]);return}a.getDefaultExEm();if(a.defaultEm){s()}else{setTimeout(t,t.delay)}},this.defaultEmDelay,this.defaultEmTimeout);return s},defaultEmDelay:100,defaultEmTimeout:1000,getDefaultExEm:function(){var s=document.body.appendChild(this.TestSpan.cloneNode(true));s.className+=" mjx-test-inline mjx-test-default";this.defaultEm=this.getFontSize(s);this.defaultEx=s.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,s.lastChild.offsetLeft-s.firstChild.offsetLeft-2);document.body.removeChild(s)},getFontSize:(window.getComputedStyle?function(t){var s=window.getComputedStyle(t);return parseFloat(s.fontSize)}:function(s){return s.style.pixelLeft}),getMaxWidth:(window.getComputedStyle?function(t){var s=window.getComputedStyle(t);if(s.maxWidth!=="none"){return parseFloat(s.maxWidth)}return 0}:function(t){var s=t.currentStyle.maxWidth;if(s!=="none"){if(s.match(/\d*px/)){return parseFloat(s)}var u=t.style.left;t.style.left=s;s=t.style.pixelLeft;t.style.left=u;return s}return 0}),loadFont:function(s){f.RestartAfter(o.Require(this.fontDir+"/"+s))},fontLoaded:function(s){if(!s.match(/-|fontdata/)){s+="-Regular"}if(!s.match(/\.js$/)){s+=".js"}MathJax.Callback.Queue(["Post",f.Startup.signal,"CommonHTML - font data loaded for "+s],["loadComplete",o,this.fontDir+"/"+s])},Element:function(s,u,t){if(s.substr(0,4)==="mjx-"){if(!u){u={}}if(u.isMathJax==null){u.isMathJax=true}if(u.className){u.className=s+" "+u.className}else{u.className=s}s="span"}return this.HTMLElement(s,u,t)},addElement:function(u,s,v,t){return u.appendChild(this.Element(s,v,t))},HTMLElement:m.Element,ucMatch:m.ucMatch,setScript:m.setScript,getNode:function(x,w){var u=RegExp("\\b"+w+"\\b");var t=[];while(x){for(var v=0,s=x.childNodes.length;v=x.CHTMLlast+x.CHTMLchunk){this.postTranslate(x);x.CHTMLchunk=Math.floor(x.CHTMLchunk*this.config.EqnChunkFactor);x.CHTMLdelay=true}},initCHTML:function(t,s){},savePreview:function(s){var t=s.MathJax.preview;if(t&&t.parentNode){s.MathJax.tmpPreview=document.createElement("span");t.parentNode.replaceChild(s.MathJax.tmpPreview,t)}},restorePreview:function(s){var t=s.MathJax.tmpPreview;if(t){t.parentNode.replaceChild(s.MathJax.preview,t);delete s.MathJax.tmpPreview}},getMetrics:function(s){var t=s.CHTML;this.jax=s;this.em=t.em;this.outerEm=t.outerEm;this.scale=t.scale;this.cwidth=t.cwidth;this.linebreakWidth=t.lineWidth},postTranslate:function(x){var t=x.jax[this.id];for(var v=x.CHTMLlast,s=x.CHTMLeqn;vC.h){t.marginTop=a.Em(C.t-C.h)}if(C.b>C.d){t.marginBottom=a.Em(C.b-C.d)}if(C.l<0){t.paddingLeft=a.Em(-C.l)}if(C.r>C.w){t.marginRight=a.Em(C.r-C.w)}t.position="absolute";var z=v.offsetWidth,x=v.offsetHeight,D=A.firstChild.offsetHeight,w=A.firstChild.offsetWidth;v.style.position="";return{Y:-e.getBBox(B).h,mW:w,mH:D,zW:z,zH:x}},Remove:function(s){var t=document.getElementById(s.inputID+"-Frame");if(t&&s.CHTML.display){t=t.parentNode}if(t){t.parentNode.removeChild(t)}delete s.CHTML},ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18,thin:0.04,medium:0.06,thick:0.1,infinity:i},SPACECLASS:{thinmathspace:"MJXc-space1",mediummathspace:"MJXc-space2",thickmathspace:"MJXc-space3"},pxPerInch:96,em:16,maxStretchyParts:1000,FONTDEF:{},TEXDEF:{x_height:0.442,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.45,big_op_spacing5:0.1,surd_height:0.075,scriptspace:0.05,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},isChar:function(s){if(s.length===1){return true}if(s.length!==2){return false}var t=s.charCodeAt(0);return(t>=55296&&t<56319)},unicodeChar:function(s){if(s<65535){return String.fromCharCode(s)}s-=65536;return String.fromCharCode((s>>10)+55296)+String.fromCharCode((s&1023)+56320)},getUnicode:function(s){var t=s.text.charCodeAt(s.i);s.i++;if(t>=55296&&t<56319){t=(((t-55296)<<10)+(s.text.charCodeAt(s.i)-56320))+65536;s.i++}return t},getCharList:function(w,v){var u,z,s=w.cache,B=v;if(s[v]){return s[v]}if(v>65535&&this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(v,w);v=y.n;w=y.variant}var t=this.FONTDATA.RANGES,A=this.FONTDATA.VARIANT;if(v>=t[0].low&&v<=t[t.length-1].high){for(u=0,z=t.length;u=t[u].low&&v<=t[u].high){if(t[u].remap&&t[u].remap[v]){v=x+t[u].remap[v]}else{v=v-t[u].low+x;if(t[u].add){v+=t[u].add}}if(w["variant"+t[u].offset]){w=A[w["variant"+t[u].offset]]}break}}}s[B]=this.remapChar(w,v,0);return s[B]},remapChar:function(t,y,w){var v=[],x=this.FONTDATA.VARIANT;if(t.remap&&t.remap[y]){y=t.remap[y];if(t.remap.variant){t=x[t.remap.variant]}}else{if(this.FONTDATA.REMAP[y]&&!t.noRemap){y=this.FONTDATA.REMAP[y]}}if(g(y)){if(y[2]){w=n}t=x[y[1]];y=y[0]}if(typeof(y)==="string"){var s={text:y,i:0,length:y.length};while(s.i(B.a||0)){B.a=u.a}u.className=w.className;var t=w[D.n];if(A){var v=w;if(g(A)){v=a.FONTDATA.FONTS[A[1]];A=A[0];if(typeof(v)==="string"){a.loadFont(v)}}if(v[D.n]){a.fixChar(v[D.n],D.n)}t=a.fixChar(v[A],A);u.className=v.className}u.text+=t.c;if(B.hB.w+t[3]){B.l=B.w+t[3]}if(B.rw.a){w.a=u.a}}s=this.flushText(s,u,t.style);if(v[2]<3){s.style.width=a.Em(v[2])}},flushText:function(t,u,s){t=a.addElement(t,"mjx-charbox",{className:u.className,style:s},[u.text]);if(u.a){t.style.paddingBottom=a.Em(u.a)}u.text="";u.className=null;u.a=0;u.flushed=true;return t}},handleText:function(u,x,t,w){if(u.childNodes.length===0){a.addElement(u,"mjx-char");w=a.BBOX.empty(w)}if(typeof(t)==="string"){t=this.FONTDATA.VARIANT[t]}if(!t){t=this.FONTDATA.VARIANT[d.VARIANT.NORMAL]}var s={text:x,i:0,length:x.length},v=[];if(t.style&&s.length){v.push(this.styledText(t,x))}else{while(s.i-w.b){u.firstChild.style.paddingBottom=this.EmRounded(w.d+w.b)}return w},createDelimiter:function(x,s,u,A,v){if(!s){var B=this.BBOX.zero();B.w=B.r=this.TEX.nulldelimiterspace;a.addElement(x,"mjx-box",{style:{width:B.w}});return B}if(!(u instanceof Array)){u=[u,u]}var z=u[1];u=u[0];var t={alias:s};while(t.alias){s=t.alias;t=this.FONTDATA.DELIMITERS[s];if(!t){t={HW:[0,this.FONTDATA.VARIANT[d.VARIANT.NORMAL]]}}}if(t.load){f.RestartAfter(o.Require(this.fontDir+"/TeX/fontdata-"+t.load+".js"))}for(var y=0,w=t.HW.length;y=u-0.01||(y==w-1&&!t.stretch)){if(t.HW[y][3]){s=t.HW[y][3]}B=this.createChar(x,[s,t.HW[y][1]],(t.HW[y][2]||1),v);B.offset=0.6*B.w;if(A){B.scale=A.scale;A.rscale=A.rscale}return B}}if(!t.stretch){return B}return this["extendDelimiter"+t.dir](x,z,t.stretch,A,v)},extendDelimiterV:function(E,x,P,w,C){E=a.addElement(E,"mjx-delim-v");var N=a.Element("span");var B,A,O,v,I,t,F,y,G=1,M;I=this.createChar(N,(P.top||P.ext),1,C);B=N.removeChild(N.firstChild);t=this.createChar(N,(P.bot||P.ext),1,C);A=N.removeChild(N.firstChild);F=y=a.BBOX.zero();var J=I.h+I.d+t.h+t.d-l;E.appendChild(B);if(P.mid){F=this.createChar(N,P.mid,1,C);O=N.removeChild(N.firstChild);J+=F.h+F.d;G=2}if(P.min&&xJ){y=this.createChar(N,P.ext,1,C);v=N.removeChild(N.firstChild);var L=y.h+y.d,u=L-l;var D=Math.min(Math.ceil((x-J)/(G*u)),this.maxStretchyParts);if(P.fullExtenders){x=D*G*u+J}else{u=(x-J)/(G*D)}M=y.d+y.a-L/2;v.style.margin=v.style.padding="";v.style.lineHeight=a.Em(u);v.style.marginBottom=a.Em(M-l/2/G);v.style.marginTop=a.Em(-M-l/2/G);var K=v.textContent,z="\n"+K;while(--D>0){K+=z}v.textContent=K;E.appendChild(v);if(P.mid){E.appendChild(O);E.appendChild(v.cloneNode(true))}}else{M=(x-J-l)/G;B.style.marginBottom=a.Em(M+parseFloat(B.style.marginBottom||"0"));if(P.mid){E.appendChild(O)}A.style.marginTop=a.Em(M+parseFloat(A.style.marginTop||"0"))}E.appendChild(A);var s=a.BBOX({w:Math.max(I.w,y.w,t.w,F.w),l:Math.min(I.l,y.l,t.l,F.l),r:Math.max(I.r,y.r,t.r,F.r),h:x-t.d,d:t.d,t:x-t.d,b:t.d});s.offset=0.5*s.w;if(w){s.scale=w.scale;s.rscale=w.rscale}return s},extendDelimiterH:function(F,s,P,v,D){F=a.addElement(F,"mjx-delim-h");var N=a.Element("span");var t,M,O,u,K,C,x,G,z,H=1;C=this.createChar(N,(P.left||P.rep),1,D);t=N.removeChild(N.firstChild);x=this.createChar(N,(P.right||P.rep),1,D);M=N.removeChild(N.firstChild);z=this.createChar(N,P.rep,1,D);u=N.removeChild(N.firstChild);t.style.marginLeft=a.Em(-C.l);M.style.marginRight=a.Em(x.r-x.w);F.appendChild(t);var Q=a.BBOX.zero();Q.h=Math.max(C.h,x.h,z.h);Q.d=Math.max(C.D||C.d,x.D||x.d,z.D||z.d);var y=(C.r-C.l)+(x.r-x.l)-l;if(P.mid){G=this.createChar(N,P.mid,1,D);O=N.removeChild(N.firstChild);O.style.marginleft=a.Em(-G.l);O.style.marginRight=a.Em(G.r-G.w);y+=G.r-G.l+l;H=2;if(G.h>Q.h){Q.h=G.h}if(G.d>Q.d){Q.d=G.d}}if(P.min&&sy){var B=z.r-z.l,J=B-l;var E=Math.min(Math.ceil((s-y)/(H*J)),this.maxStretchyParts);if(P.fullExtenders){s=E*H*J+y}else{J=(s-y)/(H*E)}var L=(B-J+l/H)/2;u.style.marginLeft=a.Em(-z.l-L);u.style.marginRight=a.Em(z.r-z.w+L);u.style.letterSpacing=a.Em(-(z.w-J));t.style.marginRight=a.Em(C.r-C.w);M.style.marginleft=a.Em(-x.l);var I=u.textContent,A=I;while(--E>0){I+=A}u.textContent=I;F.appendChild(u);if(P.mid){F.appendChild(O);K=F.appendChild(u.cloneNode(true))}}else{L=(s-y-l/H)/2;t.style.marginRight=a.Em(C.r-C.w+L);if(P.mid){F.appendChild(O)}M.style.marginLeft=a.Em(-x.l+L)}F.appendChild(M);this.adjustHeights([t,u,O,K,M],[C,z,G,z,x],Q);if(v){Q.scale=v.scale;Q.rscale=v.rscale}return Q},adjustHeights:function(t,w,x){var u=x.h,y=x.d;if(x.d<0){y=-x.d;x.D=x.d;x.d=0}for(var v=0,s=t.length;v0){delete this.D}},rescale:function(s){this.w*=s;this.h*=s;this.d*=s;this.l*=s;this.r*=s;this.t*=s;this.b*=s;if(this.L){this.L*=s}if(this.R){this.R*=s}if(this.D){this.D*=s}},combine:function(t,s,v){t.X=s;t.Y=v;var u=t.rscale;if(s+u*t.r>this.r){this.r=s+u*t.r}if(s+u*t.lthis.w){this.w=s+u*(t.w+(t.L||0)+(t.R||0))}if(v+u*t.h>this.h){this.h=v+u*t.h}if(t.D&&(this.D==null||u*t.D-v>this.D)&&u*t.D>this.d){this.D=u*t.D-v}else{if(t.D==null&&this.D){delete this.D}}if(u*t.d-v>this.d){this.d=u*t.d-v}if(v+u*t.t>this.t){this.t=v+u*t.t}if(u*t.b-v>this.b){this.b=u*t.b-v}},append:function(t){var u=t.rscale;var s=this.w;if(s+u*t.r>this.r){this.r=s+u*t.r}if(s+u*t.lthis.h){this.h=u*t.h}if(t.D&&(this.D==null||u*t.D>this.D)&&u*t.D>this.d){this.D=u*t.D}else{if(t.D==null&&this.D){delete this.D}}if(u*t.d>this.d){this.d=u*t.d}if(u*t.t>this.t){this.t=u*t.t}if(u*t.b>this.b){this.b=u*t.b}},updateFrom:function(s){this.h=s.h;this.d=s.d;this.w=s.w;this.r=s.r;this.l=s.l;this.t=s.t;this.b=s.b;if(s.pwidth){this.pwidth=s.pwidth}if(s.D){this.D=s.D}else{delete this.D}},adjust:function(t,s,v,u){this[s]+=a.length2em(t,1,this.scale);if(u==null){if(this[s]>this[v]){this[v]=this[s]}}else{if(this[v]z.r){z.r=z.w}if(t.h>z.h){z.h=t.h}if(t.d>z.d){z.d=t.d}if(t.t>z.t){z.t=t.t}if(t.b>z.b){z.b=t.b}}}},CHTMLstretchChildH:function(v,s,x){var y=this.data[v];if(y){var z=this.CHTML,u=y.CHTML;if(u.stretch||(u.stretch==null&&y.CHTMLcanStretch("Horizontal",s))){var t=u.w;u=y.CHTMLstretchH(this.CHTMLchildNode(x,v),s);z.w+=u.w-t;if(z.w>z.r){z.r=z.w}if(u.h>z.h){z.h=u.h}if(u.d>z.d){z.d=u.d}if(u.t>z.t){z.t=u.t}if(u.b>z.b){z.b=u.b}}}},CHTMLupdateFrom:function(s){this.CHTML.updateFrom(s);if(this.inferRow){this.data[0].CHTML.updateFrom(s)}},CHTMLcanStretch:function(w,u,v){var t=false;if(this.isEmbellished()){var s=this.Core();if(s&&s!==this){t=s.CHTMLcanStretch(w,u,v)}}this.CHTML.stretch=t;return t},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));return this.CHTML},CHTMLstretchCoreH:function(t,s){return this.Core().CHTMLstretchH(this.CHTMLcoreNode(t),s)},CHTMLcreateNode:function(s){if(!this.CHTML){this.CHTML={}}this.CHTML=a.BBOX.zero();if(this.href){s=a.addElement(s,"a",{href:this.href,isMathJax:true})}if(!this.CHTMLnodeID){this.CHTMLnodeID=a.GetID()}var t=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+a.idPostfix;return this.CHTMLhandleAttributes(a.addElement(s,"mjx-"+this.type,{id:t}))},CHTMLnodeElement:function(){if(!this.CHTMLnodeID){return null}return document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+a.idPostfix)},CHTMLlength2em:function(t,s){return a.length2em(t,s,this.CHTML.scale)},CHTMLhandleAttributes:function(v){if(this["class"]){if(v.className){v.className+=" "+this["class"]}else{v.className=this["class"]}}if(this.attrNames){var z=this.attrNames,u=d.nocopyAttributes,y=f.config.ignoreMMLattributes;var w=(this.type==="mstyle"?d.math.prototype.defaults:this.defaults);for(var t=0,s=z.length;t2){s.scriptlevel=2}x=Math.pow(this.Get("scriptsizemultiplier"),s.scriptlevel);s.scriptminsize=a.length2em(this.Get("scriptminsize"),0.8,1);if(x600?"bold":"normal")}var t=s.mathvariant;if(this.variantForm){t="-TeX-variant"}if(s.family&&!s.hasVariant){if(!s.weight&&s.mathvariant.match(/bold/)){s.weight="bold"}if(!s.style&&s.mathvariant.match(/italic/)){s.style="italic"}this.CHTMLvariant={fonts:[],noRemap:true,cache:{},style:{"font-family":s.family,"font-weight":s.weight||"normal","font-style":s.style||"normal"}};return}if(s.weight==="bold"){t={normal:d.VARIANT.BOLD,italic:d.VARIANT.BOLDITALIC,fraktur:d.VARIANT.BOLDFRAKTUR,script:d.VARIANT.BOLDSCRIPT,"sans-serif":d.VARIANT.BOLDSANSSERIF,"sans-serif-italic":d.VARIANT.SANSSERIFBOLDITALIC}[t]||t}else{if(s.weight==="normal"){t={bold:d.VARIANT.normal,"bold-italic":d.VARIANT.ITALIC,"bold-fraktur":d.VARIANT.FRAKTUR,"bold-script":d.VARIANT.SCRIPT,"bold-sans-serif":d.VARIANT.SANSSERIF,"sans-serif-bold-italic":d.VARIANT.SANSSERIFITALIC}[t]||t}}if(s.style==="italic"){t={normal:d.VARIANT.ITALIC,bold:d.VARIANT.BOLDITALIC,"sans-serif":d.VARIANT.SANSSERIFITALIC,"bold-sans-serif":d.VARIANT.SANSSERIFBOLDITALIC}[t]||t}else{if(s.style==="normal"){t={italic:d.VARIANT.NORMAL,"bold-italic":d.VARIANT.BOLD,"sans-serif-italic":d.VARIANT.SANSSERIF,"sans-serif-bold-italic":d.VARIANT.BOLDSANSSERIF}[t]||t}}this.CHTMLvariant=a.FONTDATA.VARIANT[t]||a.FONTDATA.VARIANT[d.VARIANT.NORMAL]},CHTMLbboxFor:function(s){if(this.data[s]&&this.data[s].CHTML){return this.data[s].CHTML}return a.BBOX.zero()},CHTMLdrawBBox:function(t,u){if(!u){u=this.CHTML}var s=a.Element("mjx-box",{style:{opacity:0.25,"margin-left":a.Em(-(u.w+(u.R||0)))}},[["mjx-box",{style:{height:a.Em(u.h),width:a.Em(u.w),"background-color":"red"}}],["mjx-box",{style:{height:a.Em(u.d),width:a.Em(u.w),"margin-left":a.Em(-u.w),"vertical-align":a.Em(-u.d),"background-color":"green"}}]]);if(t.nextSibling){t.parentNode.insertBefore(s,t.nextSibling)}else{t.parentNode.appendChild(s)}},CHTMLnotEmpty:function(s){while(s&&s.data.length<2&&(s.type==="mrow"||s.type==="texatom")){s=s.data[0]}return !!s}},{CHTMLautoload:function(){this.constructor.Augment({toCommonHTML:d.mbase.CHTMLautoloadFail});var s=a.autoloadDir+"/"+this.type+".js";f.RestartAfter(o.Require(s))},CHTMLautoloadFail:function(){throw Error("CommonHTML can't autoload '"+this.type+"'")},CHTMLautoloadList:{},CHTMLautoloadFile:function(s){if(d.mbase.CHTMLautoloadList.hasOwnProperty(s)){throw Error("CommonHTML can't autoload file '"+s+"'")}d.mbase.CHTMLautoloadList[s]=true;var t=a.autoloadDir+"/"+s+".js";f.RestartAfter(o.Require(t))},CHTMLstretchV:function(s,t){this.Core().CHTMLstretchV(s,t);this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.chars.Augment({toCommonHTML:function(t,s){this.CHTML=null;if(s==null){s={}}var u=this.toString();if(s.remap){u=s.remap(u,s.remapchars)}this.CHTMLhandleText(t,u,s.variant||this.parent.CHTMLvariant)}});d.entity.Augment({toCommonHTML:function(t,s){if(s==null){s={}}var u=this.toString();if(s.remapchars){u=s.remap(u,s.remapchars)}this.CHTMLhandleText(t,u,s.variant||this.parent.CHTMLvariant)}});d.math.Augment({toCommonHTML:function(x){x=this.CHTMLdefaultNode(x);if(this.CHTML.w<0){x.parentNode.style.width="0px";x.parentNode.style.marginRight=a.Em(this.CHTML.w)}var v=this.Get("alttext");if(v&&!x.getAttribute("aria-label")){x.setAttribute("aria-label",v)}if(this.CHTML.pwidth){x.parentNode.style.minWidth=this.CHTML.mwidth||a.Em(this.CHTML.w);x.parentNode.className="mjx-full-width "+x.parentNode.className;x.style.width=this.CHTML.pwidth}else{if(!this.isMultiline&&this.Get("display")==="block"){var u=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(u.indentalignfirst!==d.INDENTALIGN.INDENTALIGN){u.indentalign=u.indentalignfirst}if(u.indentalign===d.INDENTALIGN.AUTO){u.indentalign=r.displayAlign}if(u.indentshiftfirst!==d.INDENTSHIFT.INDENTSHIFT){u.indentshift=u.indentshiftfirst}if(u.indentshift==="auto"){u.indentshift="0"}var t=this.CHTMLlength2em(u.indentshift,a.cwidth);if(r.displayIndent!=="0"){var s=this.CHTMLlength2em(r.displayIndent,a.cwidth);t+=(u.indentalign===d.INDENTALIGN.RIGHT?-s:s)}var w=x.parentNode.parentNode.style;x.parentNode.style.textAlign=w.textAlign=u.indentalign;if(t){t*=a.em/a.outerEm;f.Insert(w,({left:{marginLeft:a.Em(t)},right:{marginRight:a.Em(-t)},center:{marginLeft:a.Em(t),marginRight:a.Em(-t)}})[u.indentalign])}}}return x}});d.mi.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&!a.isChar(t)){delete u.skew}if(u.r>u.w&&a.isChar(t)&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mn.Augment({CHTMLremapMinus:function(s){return s.replace(/^-/,"\u2212")},toCommonHTML:function(s){s=this.CHTMLdefaultNode(s,{childOptions:{remap:this.CHTMLremapMinus}});var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&!a.isChar(t)){delete u.skew}if(u.r>u.w&&a.isChar(t)&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mo.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLgetVariant();this.CHTMLhandleScale(v);a.BBOX.empty(this.CHTML);var t=this.getValues("displaystyle","largeop");t.variant=this.CHTMLvariant;t.text=this.data.join("");if(t.text==""){if(this.fence){v.style.width=a.Em(a.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(t);this.CHTMLadjustVariant(t);for(var u=0,s=this.data.length;u0){if(!this.hasValue("lspace")){t.lspace=0.15}if(!this.hasValue("rspace")){t.rspace=0.15}}var s=this,u=this.Parent();while(u&&u.isEmbellished()&&u.Core()===s){s=u;u=u.Parent();v=s.CHTMLnodeElement()}if(t.lspace){v.style.paddingLeft=a.Em(t.lspace)}if(t.rspace){v.style.paddingRight=a.Em(t.rspace)}this.CHTML.L=t.lspace;this.CHTML.R=t.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(u){var t=this.CoreParent();u.parent=t;if(a.isChar(u.text)&&t&&t.isa(d.munderover)){var v=t.data[t.over],s=t.data[t.under];if(v&&this===v.CoreMO()&&t.Get("accent")){u.remapchars=a.FONTDATA.REMAPACCENT}else{if(s&&this===s.CoreMO()&&t.Get("accentunder")){u.remapchars=a.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(t){var s=t.parent,u=(s&&s.isa(d.msubsup)&&this!==s.data[s.base]);if(t.largeop){t.mathvariant=(t.displaystyle?"-largeOp":"-smallOp")}if(u){t.remapchars=this.remapChars;if(t.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){t.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(s){s=s.firstChild;var t=a.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});s.insertBefore(t,s.firstChild)},CHTMLcenterOp:function(s){var u=this.CHTML;var t=(u.h-u.d)/2-a.TEX.axis_height;if(Math.abs(t)>0.001){s.style.verticalAlign=a.Em(-t)}u.h-=t;u.d+=t;if(u.r>u.w){u.ic=u.r-u.w;u.w=u.r;s.style.paddingRight=a.Em(u.ic)}},CHTMLcanStretch:function(w,u,v){if(!this.Get("stretchy")){return false}var x=this.data.join("");if(!a.isChar(x)){return false}var t={text:x};this.CHTMLadjustAccent(t);if(t.remapchars){x=t.remapchars[x]||x}x=a.FONTDATA.DELIMITERS[x.charCodeAt(0)];var s=(x&&x.dir===w.substr(0,1));if(s){s=(this.CHTML.h!==u||this.CHTML.d!==v||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(s){this.CHTML.stretch=true}}return s},CHTMLstretchV:function(v,y){var w=this.CHTMLnodeElement(),x=this.CHTML;var t=this.getValues("symmetric","maxsize","minsize");var u,s=a.TEX.axis_height;if(t.symmetric){u=2*Math.max(v-s,y+s)}else{u=v+y}t.maxsize=this.CHTMLlength2em(t.maxsize,x.h+x.d);t.minsize=this.CHTMLlength2em(t.minsize,x.h+x.d);u=Math.max(t.minsize,Math.min(t.maxsize,u));if(u!==x.sH){if(u!=t.minsize){u=[Math.max(u*a.TEX.delimiterfactor/1000,u-a.TEX.delimitershortfall),u]}while(w.firstChild){w.removeChild(w.firstChild)}this.CHTML=x=a.createDelimiter(w,this.data.join("").charCodeAt(0),u,x);x.sH=(u instanceof Array?u[1]:u);if(t.symmetric){u=(x.h+x.d)/2+s}else{u=(x.h+x.d)*v/(v+y)}u-=x.h;if(Math.abs(u)>0.05){w.style.verticalAlign=a.Em(u);x.h+=u;x.d-=u;x.t+=u;x.b-=u}}return this.CHTML},CHTMLstretchH:function(u,s){var v=this.CHTML;var t=this.getValues("maxsize","minsize","mathvariant","fontweight");if((t.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(t.fontweight)>=600)&&!this.Get("mathvariant",true)){t.mathvariant=d.VARIANT.BOLD}t.maxsize=this.CHTMLlength2em(t.maxsize,v.w);t.minsize=this.CHTMLlength2em(t.minsize,v.w);s=Math.max(t.minsize,Math.min(t.maxsize,s));if(s!==v.sW){while(u.firstChild){u.removeChild(u.firstChild)}this.CHTML=v=a.createDelimiter(u,this.data.join("").charCodeAt(0),s,v,t.mathvariant);v.sW=s}return this.CHTML}});d.mtext.Augment({CHTMLgetVariant:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){var u=(a.config.scale/100)/a.scale;var t={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:u,style:{"font-size":a.Percent(u)}};var s=this.Get("mathvariant");if(s.match(/bold/)){t.style["font-weight"]="bold"}if(s.match(/italic|-tex-mathit/)){t.style["font-style"]="italic"}if(s==="monospace"){t.className+=" MJXc-monospace-font"}if(s==="double-struck"){t.className+=" MJXc-double-struck-font"}if(s.match(/fraktur/)){t.className+=" MJXc-fraktur-font"}if(s.match(/sans-serif/)){t.className+=" MJXc-sans-serif-font"}if(s.match(/script/)){t.className+=" MJXc-script-font"}this.CHTMLvariant=t}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});d.merror.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var t=this.CHTML;t.rescale(0.9);t.h+=3/a.em;if(t.h>t.t){t.t=t.h}t.d+=3/a.em;if(t.d>t.b){t.b=t.d}t.w+=8/a.em;t.r=t.w;t.l=0;return s}});d.mspace.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);var t=this.getValues("height","depth","width");var s=this.CHTMLlength2em(t.width),u=this.CHTMLlength2em(t.height),y=this.CHTMLlength2em(t.depth);var x=this.CHTML;x.w=x.r=s;x.h=x.t=u;x.d=x.b=y;x.l=0;if(s<0){v.style.marginRight=a.Em(s);s=0}v.style.width=a.Em(s);v.style.height=a.Em(Math.max(0,u+y));if(y){v.style.verticalAlign=a.Em(-y)}this.CHTMLhandleBBox(v);this.CHTMLhandleColor(v);return v}});d.mpadded.Augment({toCommonHTML:function(t,F){var s;if(F&&F.stretch){t=t.firstChild;s=t.firstChild}else{t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:true});s=t.firstChild;t=a.addElement(t,"mjx-block");t.appendChild(s);a.addElement(t,"mjx-strut")}var z=this.CHTMLbboxFor(0);var D=this.getValues("width","height","depth","lspace","voffset");var B=0,A=0,C=z.w,u=z.h,v=z.d;s.style.width=0;s.style.margin=a.Em(-u)+" 0 "+a.Em(-v);if(D.width!==""){C=this.CHTMLdimen(D.width,"w",C,0)}if(D.height!==""){u=this.CHTMLdimen(D.height,"h",u,0)}if(D.depth!==""){v=this.CHTMLdimen(D.depth,"d",v,0)}if(D.voffset!==""){A=this.CHTMLdimen(D.voffset);if(A){s.style.position="relative";s.style.top=a.Em(-A)}}if(D.lspace!==""){B=this.CHTMLdimen(D.lspace);if(B){s.style.position="relative";s.style.left=a.Em(B)}}t.style.width=0;t.style.marginTop=a.Em(u-k);t.style.padding="0 "+a.Em(C)+" "+a.Em(v)+" 0";var E=a.BBOX({w:C,h:u,d:v,l:0,r:C,t:u,b:v,scale:this.CHTML.scale,rscale:this.CHTML.rscale});E.combine(z,B,A);E.w=C;E.h=u;E.d=v;this.CHTML=E;return t.parentNode},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLdimen:function(w,y,x,s){if(s==null){s=-i}w=String(w);var t=w.match(/width|height|depth/);var u=(t?this.CHTML[t[0].charAt(0)]:(y?this.CHTML[y]:0));var v=(this.CHTMLlength2em(w,u)||0);if(w.match(/^[-+]/)&&x!=null){v+=x}if(s!=null){v=Math.max(s,v)}return v}});d.munderover.Augment({toCommonHTML:function(w,G){var E=this.getValues("displaystyle","accent","accentunder","align");var u=this.data[this.base];if(!E.displaystyle&&u!=null&&(u.movablelimits||u.CoreMO().Get("movablelimits"))){return d.msubsup.prototype.toCommonHTML.call(this,w,t)}var B,z,s=[],t=false;if(G&&G.stretch){if(this.data[this.base]){u=a.getNode(w,"mjx-op")}if(this.data[this.under]){B=a.getNode(w,"mjx-under")}if(this.data[this.over]){z=a.getNode(w,"mjx-over")}s[0]=u;s[1]=B||z;s[2]=z;t=true}else{var y=["mjx-op","mjx-under","mjx-over"];if(this.over===1){y[1]=y[2]}w=this.CHTMLdefaultNode(w,{childNodes:y,noBBox:true,forceChild:true,minChildren:2});s[0]=u=w.removeChild(w.firstChild);s[1]=B=z=w.removeChild(w.firstChild);if(w.firstChild){s[2]=z=w.removeChild(w.firstChild)}}var x=[],v=this.CHTMLgetBBoxes(x,s,E);var F=x[this.base],C=this.CHTML;C.w=v;C.h=F.h;C.d=F.d;if(F.h<0.35){u.style.marginTop=a.Em(F.h-0.35)}if(E.accent&&F.hu){u=s}}if(u===-i){u=s}for(y=0;yD.w){D.skew+=(D.w-(A.x+u*A.w))/2}}}else{y=a.TEX.big_op_spacing1;x=a.TEX.big_op_spacing3;v=Math.max(y,x-Math.max(0,u*A.d))}A.x+=E/2;A.y=D.h+v+w+u*A.d;if(v){B.style.paddingBottom=a.Em(v/u)}if(w){B.style.paddingTop=a.Em(w/u)}return C},CHTMLaddUnderscript:function(B,z,E,D,t,A,s){var C=this.CHTML;var y,x,w=a.TEX.big_op_spacing5,v;var F=z[this.under],u=F.rscale;if(!s){a.addElement(t,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);t.firstChild.firstChild.firstChild.appendChild(A);t.firstChild.lastChild.appendChild(B)}if(F.D){F.d=F.D}if(F.d<0){B.firstChild.style.verticalAlign="top";t.firstChild.style.marginBottom=a.Em(F.d)}if(E.accentunder){v=2*a.TEX.rule_thickness;w=0}else{y=a.TEX.big_op_spacing2;x=a.TEX.big_op_spacing4;v=Math.max(y,x-u*F.h)}F.x=-D/2;F.y=-(C.d+v+w+u*F.h);if(v){B.style.paddingTop=a.Em(v/u)}if(w){B.style.paddingBottom=a.Em(w/u)}},CHTMLplaceBoxes:function(s,B,A,E,z){var t=this.CHTML.w,y,v=z.length,x;var D=a.BBOX.zero();D.scale=this.CHTML.scale;D.rscale=this.CHTML.rscale;z[this.base].x=z[this.base].y=0;var F=i;for(y=0;y0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=a.Em(N/B);z.style.paddingBottom=a.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=a.Em(Y/w);z.style.paddingRight=a.Em(N/w);E.style.verticalAlign=a.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.mfrac.Augment({toCommonHTML:function(N){N=this.CHTMLdefaultNode(N,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var x=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var O=x.displaystyle;var D=N.firstChild,w=N.lastChild;var y=a.addElement(N,"mjx-box");y.appendChild(D);y.appendChild(w);N.appendChild(y);if(x.numalign!=="center"){D.style.textAlign=x.numalign}if(x.denomalign!=="center"){w.style.textAlign=x.denomalign}var P=this.CHTMLbboxFor(0),B=this.CHTMLbboxFor(1),C=a.BBOX.empty(this.CHTML),F=P.rscale,z=B.rscale;x.linethickness=Math.max(0,a.thickness2em(x.linethickness||"0",C.scale));var M=a.TEX.min_rule_thickness/a.em,T=a.TEX.axis_height;var J=x.linethickness,L,K,I,G;if(x.bevelled){y.className+=" MJXc-bevelled";var S=(O?0.4:0.15);var E=Math.max(F*(P.h+P.d),z*(B.h+B.d))+2*S;var R=a.Element("mjx-bevel");y.insertBefore(R,w);var s=a.createDelimiter(R,47,E);I=F*(P.d-P.h)/2+T+S;G=z*(B.d-B.h)/2+T-S;if(I){D.style.verticalAlign=a.Em(I/F)}if(G){w.style.verticalAlign=a.Em(G/z)}R.style.marginLeft=R.style.marginRight=a.Em(-S/2);C.combine(P,0,I);C.combine(s,F*P.w-S/2,0);C.combine(B,F*P.w+s.w-S,G);C.clean()}else{y.className+=" MJXc-stacked";if(O){I=a.TEX.num1;G=a.TEX.denom1}else{I=(J===0?a.TEX.num3:a.TEX.num2);G=a.TEX.denom2}if(J===0){L=Math.max((O?7:3)*a.TEX.rule_thickness,2*M);K=(I-P.d*F)-(B.h*z-G);if(KD){s=((A.h+A.d)-(D-G))/2}D=F.h+s+G;var B=this.CHTMLaddRoot(w,A,A.h+A.d-D);v.style.paddingTop=a.Em(s);v.style.borderTop=a.Px(y*F.scale,1)+" solid";E.style.paddingTop=a.Em(2*G-y);F.h+=s+2*G;C.combine(A,B,D-A.h);C.combine(F,B+A.w,0);C.clean();return w},CHTMLaddRoot:function(){return 0},CHTMLhandleBBox:function(s){var t=this.CHTMLbboxFor(0);delete t.pwidth;this.SUPER(arguments).CHTMLhandleBBox.apply(this,arguments)}});d.mroot.Augment({toCommonHTML:d.msqrt.prototype.toCommonHTML,CHTMLhandleBBox:d.msqrt.prototype.CHTMLhandleBBox,CHTMLaddRoot:function(A,u,v){if(!this.data[1]){return}var z=this.CHTML,B=this.data[1].CHTML,x=A.firstChild;var s=B.rscale;var t=this.CHTMLrootHeight(B,u,s)-v;var y=Math.min(B.w,B.r);var C=Math.max(y,u.offset/s);if(t){x.style.verticalAlign=a.Em(t/s)}if(C>y){x.firstChild.style.paddingLeft=a.Em(C-y)}C-=u.offset/s;x.style.width=a.Em(C);z.combine(B,0,t);return C*s},CHTMLrootHeight:function(u,s,t){return 0.45*(s.h+s.d-0.9)+s.offset+Math.max(0,u.d-0.075)}});d.mfenced.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);this.CHTMLaddChild(v,"open",{});for(var u=0,s=this.data.length;ua.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(s,t){this.CHTMLstretchChildV(this.CoreIndex(),s,t);return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLstretchChildH(this.CoreIndex(),s,t);return this.CHTML}});d.TeXAtom.Augment({toCommonHTML:function(x,w){if(!w||!w.stretch){x=this.CHTMLdefaultNode(x)}if(this.texClass===d.TEXCLASS.VCENTER){var s=a.TEX.axis_height,u=this.CHTML;var t=s-(u.h+u.d)/2+u.d;if(Math.abs(t)>0.001){x.style.verticalAlign=a.Em(t);u.h+=t;u.t+=t;u.d-=t;u.b-=t}}return x},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.semantics.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);if(this.data[0]){this.data[0].toCommonHTML(s);this.CHTMLupdateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(s)}return s}});d.annotation.Augment({toCommonHTML:function(s){return this.CHTMLcreateNode(s)}});d["annotation-xml"].Augment({toCommonHTML:d.mbase.CHTMLautoload});d.ms.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mglyph.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.menclose.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.maction.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mmultiscripts.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mtable.Augment({toCommonHTML:d.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(f.config.menuSettings.zoom!=="None"){o.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML); +MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var g="2.7.6";var b=MathJax.ElementJax.mml,a=MathJax.Hub.config,e=MathJax.OutputJax.CommonHTML,d=MathJax.Hub.SplitList;var c=-1,f=1000000;b.mtable.Augment({toCommonHTML:function(l){var m={rows:[],labels:[],labeled:false};l=this.CHTMLdefaultNode(l,{noBBox:true,childOptions:m});var k=e.Element("mjx-table");while(l.firstChild){k.appendChild(l.firstChild)}l.appendChild(k);var h=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width","side","minlabelspacing","useHeight");var j=e.TEX.min_rule_thickness/e.em;m.t=e.Px(j*this.CHTML.scale,1);this.CHTMLgetBoxSizes(h,m);this.CHTMLgetAttributes(h,m);this.CHTMLadjustCells(h,m);if(h.frame){k.style.border=m.t+" "+h.frame}this.CHTMLalignV(h,m,l);this.CHTMLcolumnWidths(h,m,l);this.CHTMLstretchCells(h,m);if(m.labeled){this.CHTMLaddLabels(h,m,l,k)}var i=this.CHTML;i.w=i.r=m.R;i.h=i.t=m.T-m.B;i.d=i.b=m.B;if(!h.frame&&!i.pwidth){l.style.padding="0 "+e.Em(1/6);i.L=i.R=1/6}this.CHTMLhandleSpace(l);this.CHTMLhandleBBox(l);this.CHTMLhandleColor(l);return l},CHTMLgetBoxSizes:function(z,k){var r=e.FONTDATA.lineH*z.useHeight,t=e.FONTDATA.lineD*z.useHeight;var y=[],h=[],l=[],w=-1,q,n;for(q=0,n=this.data.length;qw){w=p}}var u=B.data[p-A].CHTML;if(u.h>y[q]){y[q]=u.h}if(u.d>h[q]){h[q]=u.d}if(u.w>l[p]){l[p]=u.w}}}if(z.equalrows){k.HD=true;var x=Math.max.apply(Math,y);var o=Math.max.apply(Math,h);for(q=0,n=y.length;qt||m<=0){m=null}}else{w.align=this.defaults.align}var p=0,l=0,u=e.TEX.axis_height;if(w.fspace){p+=k.FSPACE[1]}if(w.frame){p+=2/e.em;l+=1/e.em}for(var q=0;q=m){l+=r+s+x[q]}}}if(!m){l=({top:p,bottom:0,center:p/2,baseline:p/2,axis:p/2-u})[w.align]}if(l){o.style.verticalAlign=e.Em(-l)}k.T=p;k.B=l},CHTMLcolumnWidths:function(l,r,A){var I=r.CWIDTH,K=r.CSPACE,u=r.J,F;var G=0,n=false,y=l.width.match(/%$/);var H,B,v;if(l.width!=="auto"&&!y){G=Math.max(0,this.CHTMLlength2em(l.width,r.R));n=true}if(l.equalcolumns){if(y){var z=e.Percent(1/(u+1));for(F=0;F<=u;F++){I[F]=z}}else{v=Math.max.apply(Math,r.W);if(l.width!=="auto"){var q=(l.fspace?r.FSPACE[0]+(l.frame?2/e.em:0):0);for(F=0;F<=u;F++){q+=K[F]}v=Math.max((G-q)/(u+1),v)}v=e.Em(v);for(F=0;F<=u;F++){I[F]=v}}n=true}var E=0;if(l.fspace){E=r.FSPACE[0]}var s=[],D=[],h=[],o=[];var t=r.rows[0];for(F=0;F<=u;F++){o[F]=r.W[F];if(I[F]==="auto"){s.push(F)}else{if(I[F]==="fit"){D.push(F)}else{if(I[F].match(/%$/)){h.push(F)}else{o[F]=this.CHTMLlength2em(I[F],o[F])}}}E+=o[F]+K[F];if(t[F]){t[F].style.width=e.Em(o[F])}}if(l.frame){E+=2/e.em}var C=(D.length>0);if(n){if(y){for(F=0;F<=u;F++){cell=t[F].style;if(I[F]==="auto"&&!C){cell.width=""}else{if(I[F]==="fit"){cell.width=""}else{if(I[F].match(/%$/)){cell.width=I[F]}else{cell.minWidth=cell.maxWidth=cell.width}}}}}else{if(G>E){var k=0;for(H=0,B=h.length;HE&&D.length){var x=(G-E)/D.length;for(H=0,B=D.length;Ht*z){z=t*p}z+=y;z*=t;D+=z}else{D+=p-t*z+n;z-=t*n;z*=-t}}var o=e.addElement(w,"mjx-box",{style:{width:"100%","text-align":q.indentalign}});o.appendChild(B);var C=e.Element("mjx-itable");B.style.display="inline-table";if(!B.style.width){B.style.width="auto"}C.style.verticalAlign="top";B.style.verticalAlign=e.Em(k.T-k.B-k.H[0]);w.style.verticalAlign="";if(z){if(q.indentalign===b.INDENTALIGN.CENTER){B.style.marginLeft=e.Em(z);B.style.marginRight=e.Em(-z)}else{var u="margin"+(q.indentalign===b.INDENTALIGN.RIGHT?"Right":"Left");B.style[u]=e.Em(z)}}if(k.CALIGN[c]==="left"){w.insertBefore(C,o);C.style.marginRight=e.Em(-k.W[c]-y);if(y){C.style.marginLeft=e.Em(y)}}else{w.appendChild(C);C.style.marginLeft=e.Em(-k.W[c]+y)}var l=k.labels,j=0;if(h.fspace){j=k.FSPACE[0]+(h.frame?1/e.em:0)}for(var x=0,v=l.length;x1){h.h*=k;h.d*=k}}}else{h.w=Math.max(h.w,this.CHTMLlength2em(j,h.w))}}}}return l}});MathJax.Hub.Startup.signal.Post("CommonHTML mtable Ready");MathJax.Ajax.loadComplete(e.autoloadDir+"/mtable.js")}); +(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/AM_CHTML-full.js"); diff --git a/revisions_report_files/mathjax-27/config/AM_CHTML.js b/revisions_report_files/mathjax-27/config/AM_CHTML.js new file mode 100644 index 0000000..251c5c8 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/AM_CHTML.js @@ -0,0 +1,49 @@ +/* + * /MathJax/config/AM_CHTML.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); +MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.asciimath2jax={version:"2.7.6",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(aa){var g;var X=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ab){if(ab.parent){ab.parent.removeChild(ab)}if(this.lastChild){this.lastChild.nextSibling=ab}if(!this.firstChild){this.firstChild=ab}this.childNodes.push(ab);ab.parent=this;this.lastChild=ab;return ab},removeChild:function(ad){for(var ac=0,ab=this.childNodes.length;ac=ab-1){this.lastChild=ae}this.childNodes[ad]=ae;ae.nextSibling=ac.nextSibling;ac.nextSibling=ac.parent=null;return ac},hasChildNodes:function(ab){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var ab=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ac=ab.apply(this,arguments)||this;ac.childNodes=ac.data;ac.nodeName=ac.type;return ac},appendChild:function(af){if(af.parent){af.parent.removeChild(af)}var ad=arguments;if(af.isa(X)){ad=af.childNodes;af.data=af.childNodes=[];af.firstChild=af.lastChild=null}for(var ae=0,ac=ad.length;ae=ac-1){this.lastChild=af}this.SetData(ae,af);af.nextSibling=ad.nextSibling;ad.nextSibling=ad.parent=null;return ad},hasChildNodes:function(ac){return(this.childNodes.length>0)},setAttribute:function(ac,ad){this[ac]=ad}})};var Q={};var e={getElementById:true,createElementNS:function(ac,ab){var ad=g[ab]();if(ab==="mo"&&aa.config.useMathMLspacing){ad.useMMLspacing=128}return ad},createTextNode:function(ab){return g.chars(ab).With({nodeValue:ab})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var C="blue";var o=true;var v=true;var d=".";var f=true;var l=(J.appName.slice(0,9)=="Microsoft");function E(ab){if(l){return e.createElement(ab)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",ab)}}var W="http://www.w3.org/1998/Math/MathML";function P(ab){if(l){return e.createElement("m:"+ab)}else{return e.createElementNS(W,ab)}}function O(ab,ad){var ac;if(l){ac=e.createElement("m:"+ab)}else{ac=e.createElementNS(W,ab)}if(ad){ac.appendChild(ad)}return ac}function u(ab,ac){z.push({input:ab,tag:"mo",output:ac,tex:null,ttype:V});B()}function r(ab){z.push(ab);B()}var D=["\uD835\uDC9C","\u212C","\uD835\uDC9E","\uD835\uDC9F","\u2130","\u2131","\uD835\uDCA2","\u210B","\u2110","\uD835\uDCA5","\uD835\uDCA6","\u2112","\u2133","\uD835\uDCA9","\uD835\uDCAA","\uD835\uDCAB","\uD835\uDCAC","\u211B","\uD835\uDCAE","\uD835\uDCAF","\uD835\uDCB0","\uD835\uDCB1","\uD835\uDCB2","\uD835\uDCB3","\uD835\uDCB4","\uD835\uDCB5","\uD835\uDCB6","\uD835\uDCB7","\uD835\uDCB8","\uD835\uDCB9","\u212F","\uD835\uDCBB","\u210A","\uD835\uDCBD","\uD835\uDCBE","\uD835\uDCBF","\uD835\uDCC0","\uD835\uDCC1","\uD835\uDCC2","\uD835\uDCC3","\u2134","\uD835\uDCC5","\uD835\uDCC6","\uD835\uDCC7","\uD835\uDCC8","\uD835\uDCC9","\uD835\uDCCA","\uD835\uDCCB","\uD835\uDCCC","\uD835\uDCCD","\uD835\uDCCE","\uD835\uDCCF"];var H=["\uD835\uDD04","\uD835\uDD05","\u212D","\uD835\uDD07","\uD835\uDD08","\uD835\uDD09","\uD835\uDD0A","\u210C","\u2111","\uD835\uDD0D","\uD835\uDD0E","\uD835\uDD0F","\uD835\uDD10","\uD835\uDD11","\uD835\uDD12","\uD835\uDD13","\uD835\uDD14","\u211C","\uD835\uDD16","\uD835\uDD17","\uD835\uDD18","\uD835\uDD19","\uD835\uDD1A","\uD835\uDD1B","\uD835\uDD1C","\u2128","\uD835\uDD1E","\uD835\uDD1F","\uD835\uDD20","\uD835\uDD21","\uD835\uDD22","\uD835\uDD23","\uD835\uDD24","\uD835\uDD25","\uD835\uDD26","\uD835\uDD27","\uD835\uDD28","\uD835\uDD29","\uD835\uDD2A","\uD835\uDD2B","\uD835\uDD2C","\uD835\uDD2D","\uD835\uDD2E","\uD835\uDD2F","\uD835\uDD30","\uD835\uDD31","\uD835\uDD32","\uD835\uDD33","\uD835\uDD34","\uD835\uDD35","\uD835\uDD36","\uD835\uDD37"];var w=["\uD835\uDD38","\uD835\uDD39","\u2102","\uD835\uDD3B","\uD835\uDD3C","\uD835\uDD3D","\uD835\uDD3E","\u210D","\uD835\uDD40","\uD835\uDD41","\uD835\uDD42","\uD835\uDD43","\uD835\uDD44","\u2115","\uD835\uDD46","\u2119","\u211A","\u211D","\uD835\uDD4A","\uD835\uDD4B","\uD835\uDD4C","\uD835\uDD4D","\uD835\uDD4E","\uD835\uDD4F","\uD835\uDD50","\u2124","\uD835\uDD52","\uD835\uDD53","\uD835\uDD54","\uD835\uDD55","\uD835\uDD56","\uD835\uDD57","\uD835\uDD58","\uD835\uDD59","\uD835\uDD5A","\uD835\uDD5B","\uD835\uDD5C","\uD835\uDD5D","\uD835\uDD5E","\uD835\uDD5F","\uD835\uDD60","\uD835\uDD61","\uD835\uDD62","\uD835\uDD63","\uD835\uDD64","\uD835\uDD65","\uD835\uDD66","\uD835\uDD67","\uD835\uDD68","\uD835\uDD69","\uD835\uDD6A","\uD835\uDD6B"];var c=0,A=1,U=2,i=3,b=4,h=5,a=6,L=7,V=8,m=9,Y=10,K=15;var k={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:Y};var z=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:c},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:c},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:c},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:c},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:c},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:c},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:c},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:c},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:c},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:c},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:c},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:c},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"lamda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lamda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:c},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:c},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:c},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:c},{input:"phi",tag:"mi",output:f?"\u03D5":"\u03C6",tex:null,ttype:c},{input:"varphi",tag:"mi",output:f?"\u03C6":"\u03D5",tex:null,ttype:c},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:c},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:c},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:c},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:c},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:c},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:c},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:c},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:c},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:c},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:c},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:c},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:c},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:c},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:c},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:c},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:c},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:c},{input:"**",tag:"mo",output:"\u2217",tex:"ast",ttype:c},{input:"***",tag:"mo",output:"\u22C6",tex:"star",ttype:c},{input:"//",tag:"mo",output:"/",tex:null,ttype:c},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:c},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:c},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:c},{input:"|><",tag:"mo",output:"\u22C9",tex:"ltimes",ttype:c},{input:"><|",tag:"mo",output:"\u22CA",tex:"rtimes",ttype:c},{input:"|><|",tag:"mo",output:"\u22C8",tex:"bowtie",ttype:c},{input:"-:",tag:"mo",output:"\u00F7",tex:"div",ttype:c},{input:"divide",tag:"mo",output:"-:",tex:null,ttype:V},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:c},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:c},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:c},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:c},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:L},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:L},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:c},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:L},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:c},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:L},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:c},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:L},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:c},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:L},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:c},{input:":=",tag:"mo",output:":=",tex:null,ttype:c},{input:"lt",tag:"mo",output:"<",tex:null,ttype:c},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:c},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:c},{input:"gt",tag:"mo",output:">",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:"left(",ttype:b},{input:")",tag:"mo",output:")",tex:"right)",ttype:h},{input:"[",tag:"mo",output:"[",tex:"left[",ttype:b},{input:"]",tag:"mo",output:"]",tex:"right]",ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:m},{input:":|:",tag:"mo",output:"|",tex:null,ttype:c},{input:"|:",tag:"mo",output:"|",tex:null,ttype:b},{input:":|",tag:"mo",output:"|",tex:null,ttype:h},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:":'",tag:"mo",output:"\u2235",tex:"because",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"frown",tag:"mo",output:"\u2322",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"Sin",tag:"mo",output:"Sin",tex:null,ttype:A,func:true},{input:"Cos",tag:"mo",output:"Cos",tex:null,ttype:A,func:true},{input:"Tan",tag:"mo",output:"Tan",tex:null,ttype:A,func:true},{input:"Arcsin",tag:"mo",output:"Arcsin",tex:null,ttype:A,func:true},{input:"Arccos",tag:"mo",output:"Arccos",tex:null,ttype:A,func:true},{input:"Arctan",tag:"mo",output:"Arctan",tex:null,ttype:A,func:true},{input:"Sinh",tag:"mo",output:"Sinh",tex:null,ttype:A,func:true},{input:"Cosh",tag:"mo",output:"Cosh",tex:null,ttype:A,func:true},{input:"Tanh",tag:"mo",output:"Tanh",tex:null,ttype:A,func:true},{input:"Cot",tag:"mo",output:"Cot",tex:null,ttype:A,func:true},{input:"Sec",tag:"mo",output:"Sec",tex:null,ttype:A,func:true},{input:"Csc",tag:"mo",output:"Csc",tex:null,ttype:A,func:true},{input:"Log",tag:"mo",output:"Log",tex:null,ttype:A,func:true},{input:"Ln",tag:"mo",output:"Ln",tex:null,ttype:A,func:true},{input:"Abs",tag:"mo",output:"abs",tex:null,ttype:A,notexcopy:true,rewriteleftright:["|","|"]},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:i},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"overset",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"underset",tag:"munder",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:i},{input:"^",tag:"msup",output:"^",tex:null,ttype:i},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"overarc",tag:"mover",output:"\u23DC",tex:"overparen",ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"id",tag:"mrow",ttype:U},{input:"class",tag:"mrow",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},k,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ac,ab){if(ac.input>ab.input){return 1}else{return -1}}var S=[];function n(){var ac;var ab=z.length;for(ac=0;ac>1;if(ac[ab]=S[ab]}s=y;if(af!=""){y=z[ae].ttype;return z[ae]}y=c;ab=1;ak=ah.slice(0,1);var ai=true;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}if(ak==d){ak=ah.slice(ab,ab+1);if("0"<=ak&&ak<="9"){ai=false;ab++;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}}}if((ai&&ab>1)||ab>2){ak=ah.slice(0,ab-1);aj="mn"}else{ab=2;ak=ah.slice(0,1);aj=(("A">ak||ak>"Z")&&("a">ak||ak>"z")?"mo":"mi")}if(ak=="-"&&s==i){y=i;return{input:ak,tag:aj,output:ak,ttype:A,func:true}}return{input:ak,tag:aj,output:ak,ttype:c}}function R(ac){var ab;if(!ac.hasChildNodes()){return}if(ac.firstChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.firstChild.firstChild.nodeValue;if(ab=="("||ab=="["||ab=="{"){ac.removeChild(ac.firstChild)}}if(ac.lastChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.lastChild.firstChild.nodeValue;if(ab==")"||ab=="]"||ab=="}"){ac.removeChild(ac.lastChild)}}}var F,s,y;function G(ai){var ad,ac,al,af,ak,ag=e.createDocumentFragment();ai=p(ai,0);ad=j(ai);if(ad==null||ad.ttype==h&&F>0){return[null,ai]}if(ad.ttype==V){ai=ad.output+p(ai,ad.input.length);ad=j(ai)}switch(ad.ttype){case L:case c:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai];case b:F++;ai=p(ai,ad.input.length);al=q(ai,true);F--;if(typeof ad.invisible=="boolean"&&ad.invisible){ac=O("mrow",al[0])}else{ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0])}return[ac,al[1]];case Y:if(ad!=k){ai=p(ai,ad.input.length)}if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}else{if(ad==k){af=ai.slice(1).indexOf('"')+1}else{af=0}}}}if(af==-1){af=ai.length}ak=ai.slice(1,af);if(ak.charAt(0)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ag.appendChild(O(ad.tag,e.createTextNode(ak)));if(ak.charAt(ak.length-1)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ai=p(ai,af+1);return[O("mrow",ag),ai];case K:case A:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O(ad.tag,e.createTextNode(ad.output)),ai]}if(typeof ad.func=="boolean"&&ad.func){ak=ai.charAt(0);if(ak=="^"||ak=="_"||ak=="/"||ak=="|"||ak==","||(ad.input.length==1&&ad.input.match(/\w/)&&ak!="(")){return[O(ad.tag,e.createTextNode(ad.output)),ai]}else{ac=O("mrow",O(ad.tag,e.createTextNode(ad.output)));ac.appendChild(al[0]);return[ac,al[1]]}}R(al[0]);if(ad.input=="sqrt"){return[O(ad.tag,al[0]),al[1]]}else{if(typeof ad.rewriteleftright!="undefined"){ac=O("mrow",O("mo",e.createTextNode(ad.rewriteleftright[0])));ac.appendChild(al[0]);ac.appendChild(O("mo",e.createTextNode(ad.rewriteleftright[1])));return[ac,al[1]]}else{if(ad.input=="cancel"){ac=O(ad.tag,al[0]);ac.setAttribute("notation","updiagonalstrike");return[ac,al[1]]}else{if(typeof ad.acc=="boolean"&&ad.acc){ac=O(ad.tag,al[0]);var ah=O("mo",e.createTextNode(ad.output));if(ad.input=="vec"&&((al[0].nodeName=="mrow"&&al[0].childNodes.length==1&&al[0].firstChild.firstChild.nodeValue!==null&&al[0].firstChild.firstChild.nodeValue.length==1)||(al[0].firstChild.nodeValue!==null&&al[0].firstChild.nodeValue.length==1))){ah.setAttribute("stretchy",false)}ac.appendChild(ah);return[ac,al[1]]}else{if(!l&&typeof ad.codes!="undefined"){for(af=0;af64&&ak.charCodeAt(ae)<91){aj=aj+ad.codes[ak.charCodeAt(ae)-65]}else{if(ak.charCodeAt(ae)>96&&ak.charCodeAt(ae)<123){aj=aj+ad.codes[ak.charCodeAt(ae)-71]}else{aj=aj+ak.charAt(ae)}}}if(al[0].nodeName=="mi"){al[0]=O("mo").appendChild(e.createTextNode(aj))}else{al[0].replaceChild(O("mo").appendChild(e.createTextNode(aj)),al[0].childNodes[af])}}}}ac=O(ad.tag,al[0]);ac.setAttribute(ad.atname,ad.atval);return[ac,al[1]]}}}}case U:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(al[0]);var ab=G(al[1]);if(ab[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(ab[0]);if(["color","class","id"].indexOf(ad.input)>=0){if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}}}ak=ai.slice(1,af);ac=O(ad.tag,ab[0]);if(ad.input==="color"){ac.setAttribute("mathcolor",ak)}else{if(ad.input==="class"){ac.setAttribute("class",ak)}else{if(ad.input==="id"){ac.setAttribute("id",ak)}}}return[ac,ab[1]]}if(ad.input=="root"||ad.output=="stackrel"){ag.appendChild(ab[0])}ag.appendChild(al[0]);if(ad.input=="frac"){ag.appendChild(ab[0])}return[O(ad.tag,ag),ab[1]];case i:ai=p(ai,ad.input.length);return[O("mo",e.createTextNode(ad.output)),ai];case a:ai=p(ai,ad.input.length);ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);ag.appendChild(O(ad.tag,e.createTextNode(ad.output)));ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);return[O("mrow",ag),ai];case m:F++;ai=p(ai,ad.input.length);al=q(ai,false);F--;ak="";if(al[0].lastChild!=null){ak=al[0].lastChild.firstChild.nodeValue}if(ak=="|"&&ai.charAt(0)!==","){ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0]);return[ac,al[1]]}else{ac=O("mo",e.createTextNode("\u2223"));ac=O("mrow",ac);return[ac,ai]}default:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai]}}function t(ah){var af,ai,ag,ae,ab,ad;ah=p(ah,0);ai=j(ah);ab=G(ah);ae=ab[0];ah=ab[1];af=j(ah);if(af.ttype==i&&af.input!="/"){ah=p(ah,af.input.length);ab=G(ah);if(ab[0]==null){ab[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ab[0])}ah=ab[1];ad=(ai.ttype==L||ai.ttype==K);if(af.input=="_"){ag=j(ah);if(ag.input=="^"){ah=p(ah,ag.input.length);var ac=G(ah);R(ac[0]);ah=ac[1];ae=O((ad?"munderover":"msubsup"),ae);ae.appendChild(ab[0]);ae.appendChild(ac[0]);ae=O("mrow",ae)}else{ae=O((ad?"munder":"msub"),ae);ae.appendChild(ab[0])}}else{if(af.input=="^"&&ad){ae=O("mover",ae);ae.appendChild(ab[0])}else{ae=O(af.tag,ae);ae.appendChild(ab[0])}}if(typeof ai.func!="undefined"&&ai.func){ag=j(ah);if(ag.ttype!=i&&ag.ttype!=h){ab=t(ah);ae=O("mrow",ae);ae.appendChild(ab[0]);ah=ab[1]}}}return[ae,ah]}function q(ak,aj){var ao,al,ag,ar,ah=e.createDocumentFragment();do{ak=p(ak,0);ag=t(ak);al=ag[0];ak=ag[1];ao=j(ak);if(ao.ttype==i&&ao.input=="/"){ak=p(ak,ao.input.length);ag=t(ak);if(ag[0]==null){ag[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ag[0])}ak=ag[1];R(al);al=O(ao.tag,al);al.appendChild(ag[0]);ah.appendChild(al);ao=j(ak)}else{if(al!=undefined){ah.appendChild(al)}}}while((ao.ttype!=h&&(ao.ttype!=m||aj)||F==0)&&ao!=null&&ao.output!="");if(ao.ttype==h||ao.ttype==m){var at=ah.childNodes.length;if(at>0&&ah.childNodes[at-1].nodeName=="mrow"&&ah.childNodes[at-1].lastChild&&ah.childNodes[at-1].lastChild.firstChild){var av=ah.childNodes[at-1].lastChild.firstChild.nodeValue;if(av==")"||av=="]"){var ac=ah.childNodes[at-1].firstChild.firstChild.nodeValue;if(ac=="("&&av==")"&&ao.output!="}"||ac=="["&&av=="]"){var ad=[];var ap=true;var am=ah.childNodes.length;for(ar=0;ap&&ar1){ap=ad[ar].length==ad[ar-2].length}}ap=ap&&(ad.length>1||ad[0].length>0);var af=[];if(ap){var ae,ab,ai,an,au=e.createDocumentFragment();for(ar=0;ar2){ah.removeChild(ah.firstChild);ah.removeChild(ah.firstChild)}au.appendChild(O("mtr",ae))}al=O("mtable",au);al.setAttribute("columnlines",af.join(" "));if(typeof ao.invisible=="boolean"&&ao.invisible){al.setAttribute("columnalign","left")}ah.replaceChild(al,ah.firstChild)}}}}ak=p(ak,ao.input.length);if(typeof ao.invisible!="boolean"||!ao.invisible){al=O("mo",e.createTextNode(ao.output));ah.appendChild(al)}}return[ah,ak]}function M(ad,ac){var ae,ab;F=0;ad=ad.replace(/ /g,"");ad=ad.replace(/>/g,">");ad=ad.replace(/</g,"<");ae=q(ad.replace(/^\s+/g,""),false)[0];ab=O("mstyle",ae);if(C!=""){ab.setAttribute("mathcolor",C)}if(mathfontsize!=""){ab.setAttribute("fontsize",mathfontsize);ab.setAttribute("mathsize",mathfontsize)}if(mathfontfamily!=""){ab.setAttribute("fontfamily",mathfontfamily);ab.setAttribute("mathvariant",mathfontfamily)}if(o){ab.setAttribute("displaystyle","true")}ab=O("math",ab);if(v){ab.setAttribute("title",ad.replace(/\s+/g," "))}return ab}v=false;mathfontfamily="";C="";mathfontsize="";(function(){for(var ac=0,ab=z.length;ac *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/AM_CHTML.js"); diff --git a/revisions_report_files/mathjax-27/config/AM_SVG-full.js b/revisions_report_files/mathjax-27/config/AM_SVG-full.js new file mode 100644 index 0000000..830bc2d --- /dev/null +++ b/revisions_report_files/mathjax-27/config/AM_SVG-full.js @@ -0,0 +1,53 @@ +/* + * /MathJax/config/AM_SVG-full.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/SVG/jax.js", + "[MathJax]/jax/output/SVG/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.asciimath2jax={version:"2.7.6",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(aa){var g;var X=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ab){if(ab.parent){ab.parent.removeChild(ab)}if(this.lastChild){this.lastChild.nextSibling=ab}if(!this.firstChild){this.firstChild=ab}this.childNodes.push(ab);ab.parent=this;this.lastChild=ab;return ab},removeChild:function(ad){for(var ac=0,ab=this.childNodes.length;ac=ab-1){this.lastChild=ae}this.childNodes[ad]=ae;ae.nextSibling=ac.nextSibling;ac.nextSibling=ac.parent=null;return ac},hasChildNodes:function(ab){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var ab=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ac=ab.apply(this,arguments)||this;ac.childNodes=ac.data;ac.nodeName=ac.type;return ac},appendChild:function(af){if(af.parent){af.parent.removeChild(af)}var ad=arguments;if(af.isa(X)){ad=af.childNodes;af.data=af.childNodes=[];af.firstChild=af.lastChild=null}for(var ae=0,ac=ad.length;ae=ac-1){this.lastChild=af}this.SetData(ae,af);af.nextSibling=ad.nextSibling;ad.nextSibling=ad.parent=null;return ad},hasChildNodes:function(ac){return(this.childNodes.length>0)},setAttribute:function(ac,ad){this[ac]=ad}})};var Q={};var e={getElementById:true,createElementNS:function(ac,ab){var ad=g[ab]();if(ab==="mo"&&aa.config.useMathMLspacing){ad.useMMLspacing=128}return ad},createTextNode:function(ab){return g.chars(ab).With({nodeValue:ab})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var C="blue";var o=true;var v=true;var d=".";var f=true;var l=(J.appName.slice(0,9)=="Microsoft");function E(ab){if(l){return e.createElement(ab)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",ab)}}var W="http://www.w3.org/1998/Math/MathML";function P(ab){if(l){return e.createElement("m:"+ab)}else{return e.createElementNS(W,ab)}}function O(ab,ad){var ac;if(l){ac=e.createElement("m:"+ab)}else{ac=e.createElementNS(W,ab)}if(ad){ac.appendChild(ad)}return ac}function u(ab,ac){z.push({input:ab,tag:"mo",output:ac,tex:null,ttype:V});B()}function r(ab){z.push(ab);B()}var D=["\uD835\uDC9C","\u212C","\uD835\uDC9E","\uD835\uDC9F","\u2130","\u2131","\uD835\uDCA2","\u210B","\u2110","\uD835\uDCA5","\uD835\uDCA6","\u2112","\u2133","\uD835\uDCA9","\uD835\uDCAA","\uD835\uDCAB","\uD835\uDCAC","\u211B","\uD835\uDCAE","\uD835\uDCAF","\uD835\uDCB0","\uD835\uDCB1","\uD835\uDCB2","\uD835\uDCB3","\uD835\uDCB4","\uD835\uDCB5","\uD835\uDCB6","\uD835\uDCB7","\uD835\uDCB8","\uD835\uDCB9","\u212F","\uD835\uDCBB","\u210A","\uD835\uDCBD","\uD835\uDCBE","\uD835\uDCBF","\uD835\uDCC0","\uD835\uDCC1","\uD835\uDCC2","\uD835\uDCC3","\u2134","\uD835\uDCC5","\uD835\uDCC6","\uD835\uDCC7","\uD835\uDCC8","\uD835\uDCC9","\uD835\uDCCA","\uD835\uDCCB","\uD835\uDCCC","\uD835\uDCCD","\uD835\uDCCE","\uD835\uDCCF"];var H=["\uD835\uDD04","\uD835\uDD05","\u212D","\uD835\uDD07","\uD835\uDD08","\uD835\uDD09","\uD835\uDD0A","\u210C","\u2111","\uD835\uDD0D","\uD835\uDD0E","\uD835\uDD0F","\uD835\uDD10","\uD835\uDD11","\uD835\uDD12","\uD835\uDD13","\uD835\uDD14","\u211C","\uD835\uDD16","\uD835\uDD17","\uD835\uDD18","\uD835\uDD19","\uD835\uDD1A","\uD835\uDD1B","\uD835\uDD1C","\u2128","\uD835\uDD1E","\uD835\uDD1F","\uD835\uDD20","\uD835\uDD21","\uD835\uDD22","\uD835\uDD23","\uD835\uDD24","\uD835\uDD25","\uD835\uDD26","\uD835\uDD27","\uD835\uDD28","\uD835\uDD29","\uD835\uDD2A","\uD835\uDD2B","\uD835\uDD2C","\uD835\uDD2D","\uD835\uDD2E","\uD835\uDD2F","\uD835\uDD30","\uD835\uDD31","\uD835\uDD32","\uD835\uDD33","\uD835\uDD34","\uD835\uDD35","\uD835\uDD36","\uD835\uDD37"];var w=["\uD835\uDD38","\uD835\uDD39","\u2102","\uD835\uDD3B","\uD835\uDD3C","\uD835\uDD3D","\uD835\uDD3E","\u210D","\uD835\uDD40","\uD835\uDD41","\uD835\uDD42","\uD835\uDD43","\uD835\uDD44","\u2115","\uD835\uDD46","\u2119","\u211A","\u211D","\uD835\uDD4A","\uD835\uDD4B","\uD835\uDD4C","\uD835\uDD4D","\uD835\uDD4E","\uD835\uDD4F","\uD835\uDD50","\u2124","\uD835\uDD52","\uD835\uDD53","\uD835\uDD54","\uD835\uDD55","\uD835\uDD56","\uD835\uDD57","\uD835\uDD58","\uD835\uDD59","\uD835\uDD5A","\uD835\uDD5B","\uD835\uDD5C","\uD835\uDD5D","\uD835\uDD5E","\uD835\uDD5F","\uD835\uDD60","\uD835\uDD61","\uD835\uDD62","\uD835\uDD63","\uD835\uDD64","\uD835\uDD65","\uD835\uDD66","\uD835\uDD67","\uD835\uDD68","\uD835\uDD69","\uD835\uDD6A","\uD835\uDD6B"];var c=0,A=1,U=2,i=3,b=4,h=5,a=6,L=7,V=8,m=9,Y=10,K=15;var k={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:Y};var z=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:c},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:c},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:c},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:c},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:c},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:c},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:c},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:c},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:c},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:c},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:c},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:c},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"lamda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lamda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:c},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:c},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:c},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:c},{input:"phi",tag:"mi",output:f?"\u03D5":"\u03C6",tex:null,ttype:c},{input:"varphi",tag:"mi",output:f?"\u03C6":"\u03D5",tex:null,ttype:c},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:c},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:c},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:c},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:c},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:c},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:c},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:c},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:c},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:c},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:c},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:c},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:c},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:c},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:c},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:c},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:c},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:c},{input:"**",tag:"mo",output:"\u2217",tex:"ast",ttype:c},{input:"***",tag:"mo",output:"\u22C6",tex:"star",ttype:c},{input:"//",tag:"mo",output:"/",tex:null,ttype:c},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:c},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:c},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:c},{input:"|><",tag:"mo",output:"\u22C9",tex:"ltimes",ttype:c},{input:"><|",tag:"mo",output:"\u22CA",tex:"rtimes",ttype:c},{input:"|><|",tag:"mo",output:"\u22C8",tex:"bowtie",ttype:c},{input:"-:",tag:"mo",output:"\u00F7",tex:"div",ttype:c},{input:"divide",tag:"mo",output:"-:",tex:null,ttype:V},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:c},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:c},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:c},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:c},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:L},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:L},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:c},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:L},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:c},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:L},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:c},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:L},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:c},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:L},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:c},{input:":=",tag:"mo",output:":=",tex:null,ttype:c},{input:"lt",tag:"mo",output:"<",tex:null,ttype:c},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:c},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:c},{input:"gt",tag:"mo",output:">",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:"left(",ttype:b},{input:")",tag:"mo",output:")",tex:"right)",ttype:h},{input:"[",tag:"mo",output:"[",tex:"left[",ttype:b},{input:"]",tag:"mo",output:"]",tex:"right]",ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:m},{input:":|:",tag:"mo",output:"|",tex:null,ttype:c},{input:"|:",tag:"mo",output:"|",tex:null,ttype:b},{input:":|",tag:"mo",output:"|",tex:null,ttype:h},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:":'",tag:"mo",output:"\u2235",tex:"because",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"frown",tag:"mo",output:"\u2322",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"Sin",tag:"mo",output:"Sin",tex:null,ttype:A,func:true},{input:"Cos",tag:"mo",output:"Cos",tex:null,ttype:A,func:true},{input:"Tan",tag:"mo",output:"Tan",tex:null,ttype:A,func:true},{input:"Arcsin",tag:"mo",output:"Arcsin",tex:null,ttype:A,func:true},{input:"Arccos",tag:"mo",output:"Arccos",tex:null,ttype:A,func:true},{input:"Arctan",tag:"mo",output:"Arctan",tex:null,ttype:A,func:true},{input:"Sinh",tag:"mo",output:"Sinh",tex:null,ttype:A,func:true},{input:"Cosh",tag:"mo",output:"Cosh",tex:null,ttype:A,func:true},{input:"Tanh",tag:"mo",output:"Tanh",tex:null,ttype:A,func:true},{input:"Cot",tag:"mo",output:"Cot",tex:null,ttype:A,func:true},{input:"Sec",tag:"mo",output:"Sec",tex:null,ttype:A,func:true},{input:"Csc",tag:"mo",output:"Csc",tex:null,ttype:A,func:true},{input:"Log",tag:"mo",output:"Log",tex:null,ttype:A,func:true},{input:"Ln",tag:"mo",output:"Ln",tex:null,ttype:A,func:true},{input:"Abs",tag:"mo",output:"abs",tex:null,ttype:A,notexcopy:true,rewriteleftright:["|","|"]},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:i},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"overset",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"underset",tag:"munder",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:i},{input:"^",tag:"msup",output:"^",tex:null,ttype:i},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"overarc",tag:"mover",output:"\u23DC",tex:"overparen",ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"id",tag:"mrow",ttype:U},{input:"class",tag:"mrow",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},k,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ac,ab){if(ac.input>ab.input){return 1}else{return -1}}var S=[];function n(){var ac;var ab=z.length;for(ac=0;ac>1;if(ac[ab]=S[ab]}s=y;if(af!=""){y=z[ae].ttype;return z[ae]}y=c;ab=1;ak=ah.slice(0,1);var ai=true;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}if(ak==d){ak=ah.slice(ab,ab+1);if("0"<=ak&&ak<="9"){ai=false;ab++;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}}}if((ai&&ab>1)||ab>2){ak=ah.slice(0,ab-1);aj="mn"}else{ab=2;ak=ah.slice(0,1);aj=(("A">ak||ak>"Z")&&("a">ak||ak>"z")?"mo":"mi")}if(ak=="-"&&s==i){y=i;return{input:ak,tag:aj,output:ak,ttype:A,func:true}}return{input:ak,tag:aj,output:ak,ttype:c}}function R(ac){var ab;if(!ac.hasChildNodes()){return}if(ac.firstChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.firstChild.firstChild.nodeValue;if(ab=="("||ab=="["||ab=="{"){ac.removeChild(ac.firstChild)}}if(ac.lastChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.lastChild.firstChild.nodeValue;if(ab==")"||ab=="]"||ab=="}"){ac.removeChild(ac.lastChild)}}}var F,s,y;function G(ai){var ad,ac,al,af,ak,ag=e.createDocumentFragment();ai=p(ai,0);ad=j(ai);if(ad==null||ad.ttype==h&&F>0){return[null,ai]}if(ad.ttype==V){ai=ad.output+p(ai,ad.input.length);ad=j(ai)}switch(ad.ttype){case L:case c:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai];case b:F++;ai=p(ai,ad.input.length);al=q(ai,true);F--;if(typeof ad.invisible=="boolean"&&ad.invisible){ac=O("mrow",al[0])}else{ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0])}return[ac,al[1]];case Y:if(ad!=k){ai=p(ai,ad.input.length)}if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}else{if(ad==k){af=ai.slice(1).indexOf('"')+1}else{af=0}}}}if(af==-1){af=ai.length}ak=ai.slice(1,af);if(ak.charAt(0)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ag.appendChild(O(ad.tag,e.createTextNode(ak)));if(ak.charAt(ak.length-1)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ai=p(ai,af+1);return[O("mrow",ag),ai];case K:case A:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O(ad.tag,e.createTextNode(ad.output)),ai]}if(typeof ad.func=="boolean"&&ad.func){ak=ai.charAt(0);if(ak=="^"||ak=="_"||ak=="/"||ak=="|"||ak==","||(ad.input.length==1&&ad.input.match(/\w/)&&ak!="(")){return[O(ad.tag,e.createTextNode(ad.output)),ai]}else{ac=O("mrow",O(ad.tag,e.createTextNode(ad.output)));ac.appendChild(al[0]);return[ac,al[1]]}}R(al[0]);if(ad.input=="sqrt"){return[O(ad.tag,al[0]),al[1]]}else{if(typeof ad.rewriteleftright!="undefined"){ac=O("mrow",O("mo",e.createTextNode(ad.rewriteleftright[0])));ac.appendChild(al[0]);ac.appendChild(O("mo",e.createTextNode(ad.rewriteleftright[1])));return[ac,al[1]]}else{if(ad.input=="cancel"){ac=O(ad.tag,al[0]);ac.setAttribute("notation","updiagonalstrike");return[ac,al[1]]}else{if(typeof ad.acc=="boolean"&&ad.acc){ac=O(ad.tag,al[0]);var ah=O("mo",e.createTextNode(ad.output));if(ad.input=="vec"&&((al[0].nodeName=="mrow"&&al[0].childNodes.length==1&&al[0].firstChild.firstChild.nodeValue!==null&&al[0].firstChild.firstChild.nodeValue.length==1)||(al[0].firstChild.nodeValue!==null&&al[0].firstChild.nodeValue.length==1))){ah.setAttribute("stretchy",false)}ac.appendChild(ah);return[ac,al[1]]}else{if(!l&&typeof ad.codes!="undefined"){for(af=0;af64&&ak.charCodeAt(ae)<91){aj=aj+ad.codes[ak.charCodeAt(ae)-65]}else{if(ak.charCodeAt(ae)>96&&ak.charCodeAt(ae)<123){aj=aj+ad.codes[ak.charCodeAt(ae)-71]}else{aj=aj+ak.charAt(ae)}}}if(al[0].nodeName=="mi"){al[0]=O("mo").appendChild(e.createTextNode(aj))}else{al[0].replaceChild(O("mo").appendChild(e.createTextNode(aj)),al[0].childNodes[af])}}}}ac=O(ad.tag,al[0]);ac.setAttribute(ad.atname,ad.atval);return[ac,al[1]]}}}}case U:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(al[0]);var ab=G(al[1]);if(ab[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(ab[0]);if(["color","class","id"].indexOf(ad.input)>=0){if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}}}ak=ai.slice(1,af);ac=O(ad.tag,ab[0]);if(ad.input==="color"){ac.setAttribute("mathcolor",ak)}else{if(ad.input==="class"){ac.setAttribute("class",ak)}else{if(ad.input==="id"){ac.setAttribute("id",ak)}}}return[ac,ab[1]]}if(ad.input=="root"||ad.output=="stackrel"){ag.appendChild(ab[0])}ag.appendChild(al[0]);if(ad.input=="frac"){ag.appendChild(ab[0])}return[O(ad.tag,ag),ab[1]];case i:ai=p(ai,ad.input.length);return[O("mo",e.createTextNode(ad.output)),ai];case a:ai=p(ai,ad.input.length);ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);ag.appendChild(O(ad.tag,e.createTextNode(ad.output)));ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);return[O("mrow",ag),ai];case m:F++;ai=p(ai,ad.input.length);al=q(ai,false);F--;ak="";if(al[0].lastChild!=null){ak=al[0].lastChild.firstChild.nodeValue}if(ak=="|"&&ai.charAt(0)!==","){ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0]);return[ac,al[1]]}else{ac=O("mo",e.createTextNode("\u2223"));ac=O("mrow",ac);return[ac,ai]}default:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai]}}function t(ah){var af,ai,ag,ae,ab,ad;ah=p(ah,0);ai=j(ah);ab=G(ah);ae=ab[0];ah=ab[1];af=j(ah);if(af.ttype==i&&af.input!="/"){ah=p(ah,af.input.length);ab=G(ah);if(ab[0]==null){ab[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ab[0])}ah=ab[1];ad=(ai.ttype==L||ai.ttype==K);if(af.input=="_"){ag=j(ah);if(ag.input=="^"){ah=p(ah,ag.input.length);var ac=G(ah);R(ac[0]);ah=ac[1];ae=O((ad?"munderover":"msubsup"),ae);ae.appendChild(ab[0]);ae.appendChild(ac[0]);ae=O("mrow",ae)}else{ae=O((ad?"munder":"msub"),ae);ae.appendChild(ab[0])}}else{if(af.input=="^"&&ad){ae=O("mover",ae);ae.appendChild(ab[0])}else{ae=O(af.tag,ae);ae.appendChild(ab[0])}}if(typeof ai.func!="undefined"&&ai.func){ag=j(ah);if(ag.ttype!=i&&ag.ttype!=h){ab=t(ah);ae=O("mrow",ae);ae.appendChild(ab[0]);ah=ab[1]}}}return[ae,ah]}function q(ak,aj){var ao,al,ag,ar,ah=e.createDocumentFragment();do{ak=p(ak,0);ag=t(ak);al=ag[0];ak=ag[1];ao=j(ak);if(ao.ttype==i&&ao.input=="/"){ak=p(ak,ao.input.length);ag=t(ak);if(ag[0]==null){ag[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ag[0])}ak=ag[1];R(al);al=O(ao.tag,al);al.appendChild(ag[0]);ah.appendChild(al);ao=j(ak)}else{if(al!=undefined){ah.appendChild(al)}}}while((ao.ttype!=h&&(ao.ttype!=m||aj)||F==0)&&ao!=null&&ao.output!="");if(ao.ttype==h||ao.ttype==m){var at=ah.childNodes.length;if(at>0&&ah.childNodes[at-1].nodeName=="mrow"&&ah.childNodes[at-1].lastChild&&ah.childNodes[at-1].lastChild.firstChild){var av=ah.childNodes[at-1].lastChild.firstChild.nodeValue;if(av==")"||av=="]"){var ac=ah.childNodes[at-1].firstChild.firstChild.nodeValue;if(ac=="("&&av==")"&&ao.output!="}"||ac=="["&&av=="]"){var ad=[];var ap=true;var am=ah.childNodes.length;for(ar=0;ap&&ar1){ap=ad[ar].length==ad[ar-2].length}}ap=ap&&(ad.length>1||ad[0].length>0);var af=[];if(ap){var ae,ab,ai,an,au=e.createDocumentFragment();for(ar=0;ar2){ah.removeChild(ah.firstChild);ah.removeChild(ah.firstChild)}au.appendChild(O("mtr",ae))}al=O("mtable",au);al.setAttribute("columnlines",af.join(" "));if(typeof ao.invisible=="boolean"&&ao.invisible){al.setAttribute("columnalign","left")}ah.replaceChild(al,ah.firstChild)}}}}ak=p(ak,ao.input.length);if(typeof ao.invisible!="boolean"||!ao.invisible){al=O("mo",e.createTextNode(ao.output));ah.appendChild(al)}}return[ah,ak]}function M(ad,ac){var ae,ab;F=0;ad=ad.replace(/ /g,"");ad=ad.replace(/>/g,">");ad=ad.replace(/</g,"<");ae=q(ad.replace(/^\s+/g,""),false)[0];ab=O("mstyle",ae);if(C!=""){ab.setAttribute("mathcolor",C)}if(mathfontsize!=""){ab.setAttribute("fontsize",mathfontsize);ab.setAttribute("mathsize",mathfontsize)}if(mathfontfamily!=""){ab.setAttribute("fontfamily",mathfontfamily);ab.setAttribute("mathvariant",mathfontfamily)}if(o){ab.setAttribute("displaystyle","true")}ab=O("math",ab);if(v){ab.setAttribute("title",ad.replace(/\s+/g," "))}return ab}v=false;mathfontfamily="";C="";mathfontsize="";(function(){for(var ac=0,ab=z.length;ac div":{display:"inline-block"},".mjx-svg-href":{fill:"blue",stroke:"blue"},".MathJax_SVG_Processing":{visibility:"hidden",position:"absolute",top:0,left:0,width:0,height:0,overflow:"hidden",display:"block!important"},".MathJax_SVG_Processed":{display:"none!important"},".MathJax_SVG_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_SVG_test.mjx-test-display":{display:"table!important"},".MathJax_SVG_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_SVG_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_SVG_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .MathJax_SVG_left_box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .MathJax_SVG_right_box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .MathJax_SVG_right_box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_SVG_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}}},hideProcessedMath:true,fontNames:["TeX","STIX","STIX-Web","Asana-Math","Gyre-Termes","Gyre-Pagella","Latin-Modern","Neo-Euler"],Config:function(){this.SUPER(arguments).Config.apply(this,arguments);var p=e.config.menuSettings,o=this.config,n=p.font;if(p.scale){o.scale=p.scale}if(n&&n!=="Auto"){n=n.replace(/(Local|Web|Image)$/i,"");n=n.replace(/([a-z])([A-Z])/,"$1-$2");this.fontInUse=n}else{this.fontInUse=o.font||"TeX"}if(this.fontNames.indexOf(this.fontInUse)<0){this.fontInUse="TeX"}this.fontDir+="/"+this.fontInUse;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){k=MathJax.Extension.MathEvents.Event;c=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=k.ContextMenu;this.Mousedown=k.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=g.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=g.addElement(this.hiddenDiv,"div",{id:"MathJax_SVG_Hidden"});var n=g.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;this.hiddenDiv.removeChild(n);this.textSVG=this.Element("svg");l.GLYPH.defs=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});this.TestSpan=g.Element("span",{className:"MathJax_SVG_test"},[["span",{className:"MathJax_SVG_left_box"}],["span",{className:"MathJax_SVG_ex_box"}],["span",{className:"MathJax_SVG_right_box"}]]);return j.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){var n=document.body.appendChild(this.TestSpan.cloneNode(true));n.className+=" mjx-test-inline mjx-test-default";this.defaultEx=n.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,n.lastChild.offsetLeft-n.firstChild.offsetLeft-2);document.body.removeChild(n)},preTranslate:function(s){var r=s.jax[this.id],D,z=r.length,y,G,w,C,u,E,p,F,o,v,t=false,A,q=this.config.linebreaks.automatic,x=this.config.linebreaks.width;if(q){t=(x.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(t){x=x.replace(/\s*container\s*/,"")}else{v=this.defaultWidth}if(x===""){x="100%"}}else{v=100000}for(D=0;D=s.SVGlast+s.SVGchunk){this.postTranslate(s,true);s.SVGchunk=Math.floor(s.SVGchunk*this.config.EqnChunkFactor);s.SVGdelay=true}}},postTranslate:function(t,q){var o=t.jax[this.id];if(!this.hideProcessedMath){return}for(var r=t.SVGlast,n=t.SVGeqn;r=55296&&q<56319){v++;q=(((q-55296)<<10)+(D.charCodeAt(v)-56320))+65536;if(this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(q,u);q=y.n;u=y.variant}}else{o=this.FONTDATA.RANGES;for(p=0,A=o.length;p=o[p].low&&q<=o[p].high){if(o[p].remap&&o[p].remap[q]){q=z+o[p].remap[q]}else{if(o[p].remapOnly){break}q=q-o[p].low+z;if(o[p].add){q+=o[p].add}}if(u["variant"+o[p].offset]){u=this.FONTDATA.VARIANT[u["variant"+o[p].offset]]}break}}}if(u.remap&&u.remap[q]){q=u.remap[q];if(u.remap.variant){u=this.FONTDATA.VARIANT[u.remap.variant]}}else{if(this.FONTDATA.REMAP[q]&&!u.noRemap){q=this.FONTDATA.REMAP[q]}}if(h(q)){u=this.FONTDATA.VARIANT[q[1]];q=q[0]}if(typeof(q)==="string"){D=q+D.substr(v+1);s=D.length;v=-1;continue}r=this.lookupChar(u,q);B=r[q];if(B){if((B[5]&&B[5].space)||(B[5]===""&&B[0]+B[1]===0)){x.w+=B[2]}else{B=[t,r.id+"-"+q.toString(16).toUpperCase()].concat(B);x.Add(l.GLYPH.apply(l,B),x.w,0)}}else{if(this.FONTDATA.DELIMITERS[q]){B=this.createDelimiter(q,0,1,r);x.Add(B,x.w,(this.FONTDATA.DELIMITERS[q].dir==="V"?B.d:0))}else{if(q<=65535){B=String.fromCharCode(q)}else{z=q-65536;B=String.fromCharCode((z>>10)+55296)+String.fromCharCode((z&1023)+56320)}var w=l.TEXT(t*100/a.config.scale,B,{"font-family":u.defaultFamily||a.config.undefinedFamily,"font-style":(u.italic?"italic":""),"font-weight":(u.bold?"bold":"")});if(u.h!=null){w.h=u.h}if(u.d!=null){w.d=u.d}B=l.G();B.Add(w);x.Add(B,x.w,0);e.signal.Post(["SVG Jax - unknown char",q,u])}}}if(a.isChar(D)&&r.skew&&r.skew[q]){x.skew=r.skew[q]*1000}if(x.element.childNodes.length===1&&!x.element.firstChild.getAttribute("x")){x.element=x.element.firstChild;x.removeable=false;x.scale=t}return x},lookupChar:function(r,u){var q,o;if(!r.FONTS){var t=this.FONTDATA.FONTS;var s=(r.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(s instanceof Array)){s=[s]}if(r.fonts!=s){r.fonts=s}r.FONTS=[];for(q=0,o=s.length;q=55296&&p<56319)},findBlock:function(o,s){if(o.Ranges){for(var r=0,n=o.Ranges.length;r=0;p--){if(o.Ranges[p][2]==q){o.Ranges.splice(p,1)}}this.loadFont(o.directory+"/"+q+".js")}}}},loadFont:function(n){e.RestartAfter(j.Require(this.fontDir+"/"+n))},createDelimiter:function(n,p,s,q){if(!s){s=1}var u=l.G();if(!n){u.Clean();delete u.element;u.w=u.r=this.TeX.nulldelimiterspace*s;return u}if(!(p instanceof Array)){p=[p,p]}var v=p[1];p=p[0];var o={alias:n};while(o.alias){n=o.alias;o=this.FONTDATA.DELIMITERS[n];if(!o){o={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(o.load){e.RestartAfter(j.Require(this.fontDir+"/fontdata-"+o.load+".js"))}for(var t=0,r=o.HW.length;t=p-10-a.config.blacker||(t==r-1&&!o.stretch)){if(o.HW[t][2]){s*=o.HW[t][2]}if(o.HW[t][3]){n=o.HW[t][3]}return this.createChar(s,[n,o.HW[t][1]],q).With({stretched:true})}}if(o.stretch){this["extendDelimiter"+o.dir](u,v,o.stretch,s,q)}return u},createChar:function(u,s,p){var t="",r={fonts:[s[1]],noRemap:true};if(p&&p===i.VARIANT.BOLD){r.fonts=[s[1]+"-bold",s[1]]}if(typeof(s[1])!=="string"){r=s[1]}if(s[0] instanceof Array){for(var q=0,n=s[0].length;qt){var n=this.createChar(q,o.ext,p);var r=(o.mid?2:1),x=(C-t)/r,D=(x+100)/(n.h+n.d);while(r-->0){var v=a.Element("g",{transform:"translate("+n.y+","+(z-D*n.h+50+n.y)+") scale(1,"+D+")"});v.appendChild(n.element.cloneNode(false));u.element.appendChild(v);z-=x;if(o.mid&&r){u.Add(B,0,z-B.h);z-=(B.h+B.d)}}}else{if(o.mid){z+=(t-C)/2;u.Add(B,0,z-B.h);z+=-(B.h+B.d)+(t-C)/2}else{z+=(t-C)}}u.Add(w,0,z-w.h);u.Clean();u.scale=q;u.isMultiChar=true},extendDelimiterH:function(v,q,o,t,p){var r=this.createChar(t,(o.left||o.rep),p);var E=this.createChar(t,(o.right||o.rep),p);v.Add(r,-r.l,0);var D=(r.r-r.l)+(E.r-E.l),B=r.r-r.l;if(o.mid){var C=this.createChar(t,o.mid,p);D+=C.w}if(o.min&&qD){var A=this.createChar(t,o.rep,p),n=o.fuzz||0;var u=(o.mid?2:1),z=(q-D)/u,F=(z+n)/(A.r-A.l);while(u-->0){var y=a.Element("g",{transform:"translate("+(B-n/2-F*A.l+A.x)+","+A.y+") scale("+F+",1)"});y.appendChild(A.element.cloneNode(false));v.element.appendChild(y);B+=z;if(o.mid&&u){v.Add(C,B,0);B+=C.w}}}else{if(o.mid){B-=(D-q)/2;v.Add(C,B,0);B+=C.w-(D-q)/2}else{B-=(D-q)}}v.Add(E,B-E.l,0);v.Clean();v.scale=t;v.isMultiChar=true},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:300,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,NBSP:"\u00A0"});var l=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(n){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,n)}},With:function(n){return e.Insert(this,n)},Add:function(q,w,v,n,u){if(w){q.x+=w}if(v){q.y+=v}if(q.element){if(q.removeable&&q.element.childNodes.length===1&&q.n===1){var o=q.element.firstChild,s=o.nodeName.toLowerCase();if(s==="use"||s==="rect"){q.element=o;q.scale=q.childScale;var t=q.childX,r=q.childY;q.x+=t;q.y+=r;q.h-=r;q.d+=r;q.H-=r;q.D+=r;q.w-=t;q.r-=t;q.l+=t;q.removeable=false;o.setAttribute("x",Math.floor(q.x/q.scale));o.setAttribute("y",Math.floor(q.y/q.scale))}}if(Math.abs(q.x)<1&&Math.abs(q.y)<1){q.remove=q.removeable}else{s=q.element.nodeName.toLowerCase();if(s==="g"){if(!q.element.firstChild){q.remove=q.removeable}else{q.element.setAttribute("transform","translate("+Math.floor(q.x)+","+Math.floor(q.y)+")")}}else{if(s==="line"||s==="polygon"||s==="path"||s==="a"){var p=q.element.getAttribute("transform")||"";if(p){p=" "+p}p="translate("+Math.floor(q.x)+","+Math.floor(q.y)+")"+p;q.element.setAttribute("transform",p)}else{q.element.setAttribute("x",Math.floor(q.x/q.scale));q.element.setAttribute("y",Math.floor(q.y/q.scale))}}}if(q.remove){this.n+=q.n;while(q.element.firstChild){if(u&&this.element.firstChild){this.element.insertBefore(q.element.firstChild,this.element.firstChild)}else{this.element.appendChild(q.element.firstChild)}}}else{if(u){this.element.insertBefore(q.element,this.element.firstChild)}else{this.element.appendChild(q.element)}}delete q.element}if(q.hasIndent){this.hasIndent=q.hasIndent}if(q.tw!=null){this.tw=q.tw}if(q.d-q.y>this.d){this.d=q.d-q.y;if(this.d>this.D){this.D=this.d}}if(q.y+q.h>this.h){this.h=q.y+q.h;if(this.h>this.H){this.H=this.h}}if(q.D-q.y>this.D){this.D=q.D-q.y}if(q.y+q.H>this.H){this.H=q.y+q.H}if(q.x+q.lthis.r){this.r=q.x+q.r}if(n||q.x+q.w+(q.X||0)>this.w){this.w=q.x+q.w+(q.X||0)}this.childScale=q.scale;this.childX=q.x;this.childY=q.y;this.n++;return q},Align:function(r,s,q,p,o){q=({left:q,center:(this.w-r.w)/2,right:this.w-r.w-q})[s]||0;var n=this.w;this.Add(r,q+(o||0),p);this.w=n},Clean:function(){if(this.h===-a.BIGDIMEN){this.h=this.d=this.l=0}return this}});l.ROW=l.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(o){var n=o.toSVG();this.svg.push(n);if(o.SVGcanStretch("Vertical")){n.mml=o}if(n.h+n.y>this.sh){this.sh=n.h+n.y}if(n.d-n.y>this.sd){this.sd=n.d-n.y}},Stretch:function(){for(var q=0,n=this.svg.length;qo.w&&a.isChar(r)&&!q.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGchildSVG:function(n){return(this.data[n]?this.data[n].toSVG():l())},SVGdataStretched:function(o,n,p){this.SVGdata={HW:n,D:p};if(!this.data[o]){return l()}if(p!=null){return this.data[o].SVGstretchV(n,p)}if(n!=null){return this.data[o].SVGstretchH(n)}return this.data[o].toSVG()},SVGsaveData:function(n){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=n.w,this.SVGdata.x=n.x;this.SVGdata.h=n.h,this.SVGdata.d=n.d;if(n.y){this.SVGdata.h+=n.y;this.SVGdata.d-=n.y}if(n.X!=null){this.SVGdata.X=n.X}if(n.tw!=null){this.SVGdata.tw=n.tw}if(n.skew){this.SVGdata.skew=n.skew}if(n.ic){this.SVGdata.ic=n.ic}if(this["class"]){n.removeable=false;a.Element(n.element,{"class":this["class"]})}if(this.id){n.removeable=false;a.Element(n.element,{id:this.id})}if(this.href){this.SVGaddHref(n)}if(a.config.addMMLclasses){this.SVGaddClass(n.element,"mjx-svg-"+this.type);n.removeable=false}var o=this.style;if(o&&n.element){n.element.style.cssText=o;if(n.element.style.fontSize){n.element.style.fontSize=""}n.element.style.border=n.element.style.padding="";if(n.removeable){n.removeable=(n.element.style.cssText==="")}}this.SVGaddAttributes(n)},SVGaddClass:function(p,n){var o=p.getAttribute("class");p.setAttribute("class",(o?o+" ":"")+n)},SVGaddAttributes:function(o){if(this.attrNames){var u=this.attrNames,q=i.nocopyAttributes,t=e.config.ignoreMMLattributes;var r=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var p=0,n=u.length;p600?"bold":"normal")}return o},SVGhandleSpace:function(q){if(this.hasMMLspacing()){if(this.type!=="mo"){return}var p=this.getValues("scriptlevel","lspace","rspace");if(p.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var o=this.SVGgetMu(q);p.lspace=Math.max(0,a.length2em(p.lspace,o));p.rspace=Math.max(0,a.length2em(p.rspace,o));var n=this,r=this.Parent();while(r&&r.isEmbellished()&&r.Core()===n){n=r;r=r.Parent()}if(p.lspace){q.x+=p.lspace}if(p.rspace){q.X=p.rspace}}}else{var s=this.texSpacing();this.SVGgetScale();if(s!==""){q.x+=a.length2em(s,this.scale)*this.mscale}}},SVGhandleColor:function(r){var A=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!A.color){A.color=this.styles.color}if(A.color&&!this.mathcolor){A.mathcolor=A.color}if(A.mathcolor){a.Element(r.element,{fill:A.mathcolor,stroke:A.mathcolor});r.removeable=false}var v=(this.styles||{}).border,y=(this.styles||{}).padding,w=((v||{}).left||0),t=((y||{}).left||0),n;A.background=(this.mathbackground||this.background||(this.styles||{}).background||i.COLOR.TRANSPARENT);if(w+t){var o=l();for(n in r){if(r.hasOwnProperty(n)){o[n]=r[n]}}o.x=0;o.y=0;r.element=a.Element("g");r.removeable=true;r.Add(o,w+t,0)}if(y){r.w+=y.right||0;r.h+=y.top||0;r.d+=y.bottom||0}if(v){r.w+=v.right||0;r.h+=v.top||0;r.d+=v.bottom||0}if(A.background!==i.COLOR.TRANSPARENT){var x=r.element.nodeName.toLowerCase();if(x!=="g"&&x!=="svg"){var s=a.Element("g");s.appendChild(r.element);r.element=s;r.removeable=true}r.Add(l.RECT(r.h,r.d,r.w,{fill:A.background,stroke:"none"}),0,0,false,true)}if(v){var z=5;var p={left:["V",r.h+r.d,-z,-r.d],right:["V",r.h+r.d,r.w-v.right+z,-r.d],top:["H",r.w,0,r.h-v.top+z],bottom:["H",r.w,0,-r.d-z]};for(n in p){if(p.hasOwnProperty(n)){if(v[n]){var u=p[n],q=l[u[0]+"LINE"];r.Add(q(u[1],v[n],v[n+"Style"],v[n+"Color"]),u[2],u[3])}}}}},SVGhandleVariant:function(n,p,o){return a.HandleVariant(n,p,o)},SVGgetVariant:function(){var n=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var o=n.mathvariant;if(this.variantForm){o="-"+a.fontInUse+"-variant"}n.hasVariant=this.Get("mathvariant",true);if(!n.hasVariant){n.family=n.fontfamily;n.weight=n.fontweight;n.style=n.fontstyle}if(this.styles){if(!n.style&&this.styles.fontStyle){n.style=this.styles.fontStyle}if(!n.weight&&this.styles.fontWeight){n.weight=this.styles.fontWeight}if(!n.family&&this.styles.fontFamily){n.family=this.styles.fontFamily}}if(n.family&&!n.hasVariant){if(!n.weight&&n.mathvariant.match(/bold/)){n.weight="bold"}if(!n.style&&n.mathvariant.match(/italic/)){n.style="italic"}o={forceFamily:true,font:{"font-family":n.family}};if(n.style){o.font["font-style"]=n.style}if(n.weight){o.font["font-weight"]=n.weight}return o}if(n.weight==="bold"){o={normal:i.VARIANT.BOLD,italic:i.VARIANT.BOLDITALIC,fraktur:i.VARIANT.BOLDFRAKTUR,script:i.VARIANT.BOLDSCRIPT,"sans-serif":i.VARIANT.BOLDSANSSERIF,"sans-serif-italic":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.weight==="normal"){o={bold:i.VARIANT.normal,"bold-italic":i.VARIANT.ITALIC,"bold-fraktur":i.VARIANT.FRAKTUR,"bold-script":i.VARIANT.SCRIPT,"bold-sans-serif":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.SANSSERIFITALIC}[o]||o}}if(n.style==="italic"){o={normal:i.VARIANT.ITALIC,bold:i.VARIANT.BOLDITALIC,"sans-serif":i.VARIANT.SANSSERIFITALIC,"bold-sans-serif":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.style==="normal"){o={italic:i.VARIANT.NORMAL,"bold-italic":i.VARIANT.BOLD,"sans-serif-italic":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.BOLDSANSSERIF}[o]||o}}if(!(o in a.FONTDATA.VARIANT)){o="normal"}return a.FONTDATA.VARIANT[o]},SVGgetScale:function(o){var p=1;if(this.mscale){p=this.scale}else{var n=this.getValues("scriptlevel","fontsize");n.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if((this.styles||{}).fontSize&&!n.fontsize){n.fontsize=this.styles.fontSize}if(n.fontsize&&!this.mathsize){n.mathsize=n.fontsize}if(n.scriptlevel!==0){if(n.scriptlevel>2){n.scriptlevel=2}p=Math.pow(this.Get("scriptsizemultiplier"),n.scriptlevel);n.scriptminsize=a.length2em(this.Get("scriptminsize"))/1000;if(p2){o.scriptlevel=2}n=Math.sqrt(Math.pow(o.scriptsizemultiplier,o.scriptlevel))}return n},SVGnotEmpty:function(n){while(n){if((n.type!=="mrow"&&n.type!=="texatom")||n.data.length>1){return true}n=n.data[0]}return false},SVGcanStretch:function(p){var o=false;if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){o=n.SVGcanStretch(p);if(o&&n.forceStretch){this.forceStretch=true}}}return o},SVGstretchV:function(n,o){return this.toSVG(n,o)},SVGstretchH:function(n){return this.toSVG(n)},SVGlineBreaks:function(){return false}},{SVGemptySVG:function(){var n=this.SVG();n.Clean();this.SVGsaveData(n);return n},SVGautoload:function(){this.constructor.Augment({toSVG:i.mbase.SVGautoloadFail});var n=a.autoloadDir+"/"+this.type+".js";e.RestartAfter(j.Require(n))},SVGautoloadFail:function(){throw Error("SVG can't autoload '"+this.type+"'")},SVGautoloadList:{},SVGautoloadFile:function(n){if(i.mbase.SVGautoloadList.hasOwnProperty(n)){throw Error("SVG can't autoload file '"+n+"'")}i.mbase.SVGautoloadList[n]=true;var o=a.autoloadDir+"/"+n+".js";e.RestartAfter(j.Require(o))}});i.chars.Augment({toSVG:function(o,r,n,p){var q=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.entity.Augment({toSVG:function(o,r,n,p){var q=this.toString().replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.mo.Augment({toSVG:function(o,n){this.SVGgetStyles();var v=this.svg=this.SVG();var r=this.SVGgetScale(v);this.SVGhandleSpace(v);if(this.data.length==0){v.Clean();this.SVGsaveData(v);return v}if(n!=null){return this.SVGstretchV(o,n)}else{if(o!=null){return this.SVG.strechH(o)}}var t=this.SVGgetVariant();var B=this.getValues("largeop","displaystyle");if(B.largeop){t=a.FONTDATA.VARIANT[B.displaystyle?"-largeOp":"-smallOp"]}var A=this.CoreParent(),s=(A&&A.isa(i.msubsup)&&this!==A.data[0]),p=(s?this.remapChars:null);if(a.isChar(this.data.join(""))&&A&&A.isa(i.munderover)&&a.isChar(this.CoreText(A.data[A.base]))){var w=A.data[A.over],z=A.data[A.under];if(w&&this===w.CoreMO()&&A.Get("accent")){p=a.FONTDATA.REMAPACCENT}else{if(z&&this===z.CoreMO()&&A.Get("accentunder")){p=a.FONTDATA.REMAPACCENTUNDER}}}if(s&&this.data.join("").match(/['`"\u00B4\u2032-\u2037\u2057]/)){t=a.FONTDATA.VARIANT["-"+a.fontInUse+"-variant"]}for(var u=0,q=this.data.length;u10*C.w){y+=-C.l}v.Add(C,y,0,true);if(C.skew){v.skew=C.skew}}}v.Clean();if(!a.isChar(this.data.join(""))){delete v.skew}if(B.largeop){v.y=a.TeX.axis_height-(v.h-v.d)/2/r;if(v.r>v.w){v.ic=v.r-v.w;v.w=v.r}}this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGcanStretch:function(r){if(!this.Get("stretchy")){return false}var s=this.data.join("");if(s.length>1){return false}var o=this.CoreParent();if(o&&o.isa(i.munderover)&&a.isChar(this.CoreText(o.data[o.base]))){var q=o.data[o.over],n=o.data[o.under];if(q&&this===q.CoreMO()&&o.Get("accent")){s=a.FONTDATA.REMAPACCENT[s]||s}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){s=a.FONTDATA.REMAPACCENTUNDER[s]||s}}}s=a.FONTDATA.DELIMITERS[s.charCodeAt(0)];var p=(s&&s.dir==r.substr(0,1));if(!p){delete this.svg}this.forceStretch=p&&(this.Get("minsize",true)||this.Get("maxsize",true));return p},SVGstretchV:function(s,t){var p=this.svg||this.toSVG();var o=this.getValues("symmetric","maxsize","minsize");var r=a.TeX.axis_height*p.scale,n=this.SVGgetMu(p),q;if(o.symmetric){q=2*Math.max(s-r,t+r)}else{q=s+t}o.maxsize=a.length2em(o.maxsize,n,p.h+p.d);o.minsize=a.length2em(o.minsize,n,p.h+p.d);q=Math.max(o.minsize,Math.min(o.maxsize,q));if(q!=o.minsize){q=[Math.max(q*a.TeX.delimiterfactor/1000,q-a.TeX.delimitershortfall),q]}p=a.createDelimiter(this.data.join("").charCodeAt(0),q,p.scale);if(o.symmetric){q=(p.h+p.d)/2+r}else{q=(p.h+p.d)*s/(s+t)}p.y=q-p.h;this.SVGhandleSpace(p);this.SVGhandleColor(p);delete this.svg.element;this.SVGsaveData(p);p.stretched=true;return p},SVGstretchH:function(o){var q=this.svg||this.toSVG(),n=this.SVGgetMu(q);var p=this.getValues("maxsize","minsize","mathvariant","fontweight");if((p.fontweight==="bold"||parseInt(p.fontweight)>=600)&&!this.Get("mathvariant",true)){p.mathvariant=i.VARIANT.BOLD}p.maxsize=a.length2em(p.maxsize,n,q.w);p.minsize=a.length2em(p.minsize,n,q.w);o=Math.max(p.minsize,Math.min(p.maxsize,o));q=a.createDelimiter(this.data.join("").charCodeAt(0),o,q.scale,p.mathvariant);this.SVGhandleSpace(q);this.SVGhandleColor(q);delete this.svg.element;this.SVGsaveData(q);q.stretched=true;return q}});i.mn.Augment({SVGremapMinus:function(n){return n.replace(/^-/,"\u2212")},toSVG:function(){this.SVGgetStyles();var r=this.SVGgetVariant();var o=this.SVG();this.SVGgetScale(o);this.SVGhandleSpace(o);var q=this.SVGremapMinus;for(var p=0,n=this.data.length;po.w&&a.isChar(s)&&!r.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},}),i.mtext.Augment({toSVG:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){this.SVGgetStyles();var n=this.SVG(),q=this.SVGgetScale(n);this.SVGhandleSpace(n);var o=this.SVGgetVariant(),p={direction:this.Get("dir")};if(o.bold){p["font-weight"]="bold"}if(o.italic){p["font-style"]="italic"}o=this.Get("mathvariant");if(o==="monospace"){p["class"]="MJX-monospace"}else{if(o.match(/sans-serif/)){p["class"]="MJX-sans-serif"}}n.Add(l.TEXT(q*100/a.config.scale,this.data.join(""),p));n.Clean();this.SVGhandleColor(n);this.SVGsaveData(n);return n}else{return this.SUPER(arguments).toSVG.call(this)}}});i.merror.Augment({toSVG:function(p,n){this.SVGgetStyles();var t=this.SVG(),r=a.length2em(this.styles.fontSize||1)/1000;this.SVGhandleSpace(t);var o=(r!==1?{transform:"scale("+a.Fixed(r)+")"}:{});var v=l(o);v.Add(this.SVGchildSVG(0));v.Clean();if(r!==1){v.removeable=false;var u=["w","h","d","l","r","D","H"];for(var s=0,q=u.length;st.H){t.H=t.h}if(t.d>t.D){t.D=t.d}}this.SVGhandleColor(t);this.SVGsaveData(t);return t},SVGlength2em:function(q,t,o,u,n){if(n==null){n=-a.BIGDIMEN}var r=String(t).match(/width|height|depth/);var s=(r?q[r[0].charAt(0)]:(u?q[u]:0));var p=a.length2em(t,o,s/this.mscale)*this.mscale;if(u&&String(t).match(/^\s*[-+]/)){return Math.max(n,q[u]+p)}else{return p}}});i.mrow.Augment({SVG:l.ROW,toSVG:function(q,s){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(s!=null){o.sh=q;o.sd=s}for(var p=0,n=this.data.length;pa.linebreakWidth)||this.hasNewline()},SVGmultiline:function(n){i.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(o){var p=this.SVG();this.SVGhandleSpace(p);for(var q=0,n=this.data.length;qz){n=((u.h+u.d)-(z-A))/2}w=l.RECT(A,0,r.w);z=r.h+n+A;y=this.SVGaddRoot(v,u,y,u.h+u.d-z,s);v.Add(u,y,z-u.h);v.Add(w,y+u.w,z-w.h);v.Add(r,y+u.w,0);v.Clean();v.h+=A;v.H+=A;this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGaddRoot:function(o,p,n,r,q){return n}});i.mroot.Augment({toSVG:i.msqrt.prototype.toSVG,SVGaddRoot:function(q,o,t,r,n){var v=(o.isMultiChar?0.55:0.65)*o.w;if(this.data[1]){var s=this.data[1].toSVG();s.x=0;var p=this.SVGrootHeight(o.h+o.d,n,s)-r;var u=Math.min(s.w,s.r);t=Math.max(u,v);q.Add(s,t-u,p)}else{v=t}return t-v},SVGrootHeight:function(p,o,n){return 0.45*(p-900*o)+600*o+Math.max(0,n.d-75)}});i.mfenced.Augment({SVG:l.ROW,toSVG:function(){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data.open){o.Check(this.data.open)}if(this.data[0]!=null){o.Check(this.data[0])}for(var p=1,n=this.data.length;pJ){J=N}if(!L[K]&&J>o){o=J}}}if(E==null&&G!=null){o=G}else{if(o==-a.BIGDIMEN){o=J}}for(K=J=0,H=this.data.length;KJ){J=N}}}var C=a.TeX.rule_thickness*this.mscale;var u,r,z,w,s,B,I,M=0;p=q[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,y:0,scale:O};if(p.ic){M=1.3*p.ic+0.05}for(K=0,H=this.data.length;KJ){F.skew+=(J-N-u)/2}}}else{z=a.TeX.big_op_spacing1*O;w=a.TeX.big_op_spacing3*O;I=Math.max(z,w-Math.max(0,v.d))}I=Math.max(I,1500/a.em);u+=M/2;r=p.y+p.h+v.d+I;v.h+=s;if(v.h>v.H){v.H=v.h}}else{if(K==this.under){if(A){I=3*C*O;s=0}else{z=a.TeX.big_op_spacing2*O;w=a.TeX.big_op_spacing4*O;I=Math.max(z,w-v.h)}I=Math.max(I,1500/a.em);u-=M/2;r=p.y-(p.d+v.h+I);v.d+=s;if(v.d>v.D){v.D=v.d}}}F.Add(v,u,r)}}F.Clean();this.SVGhandleColor(F);this.SVGsaveData(F);return F}});i.msubsup.Augment({toSVG:function(M,G){this.SVGgetStyles();var I=this.SVG(),Q=this.SVGgetScale(I);this.SVGhandleSpace(I);var K=this.SVGgetMu(I);var y=I.Add(this.SVGdataStretched(this.base,M,G));var w=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var O=a.TeX.x_height*Q,F=a.TeX.scriptspace*Q;var n,z;if(this.SVGnotEmpty(this.data[this.sup])){n=this.data[this.sup].toSVG();n.w+=F;n.r=Math.max(n.w,n.r)}if(this.SVGnotEmpty(this.data[this.sub])){z=this.data[this.sub].toSVG();z.w+=F;z.r=Math.max(z.w,z.r)}var J=a.TeX.sup_drop*w,H=a.TeX.sub_drop*w;var C=y.h+(y.y||0)-J,B=y.d-(y.y||0)+H,P=0,L;if(y.ic){y.w-=y.ic;P=1.3*y.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(a.isChar(this.data[this.base].data.join(""))&&y.scale===1&&!y.stretched&&!this.data[this.base].Get("largeop")){C=B=0}}var N=this.getValues("subscriptshift","superscriptshift");N.subscriptshift=(N.subscriptshift===""?0:a.length2em(N.subscriptshift,K));N.superscriptshift=(N.superscriptshift===""?0:a.length2em(N.superscriptshift,K));var A=y.w+y.x;if(!n){if(z){B=Math.max(B,a.TeX.sub1*Q,z.h-(4/5)*O,N.subscriptshift);I.Add(z,A,-B);this.data[this.sub].SVGdata.dy=-B}}else{if(!z){var o=this.getValues("displaystyle","texprimestyle");L=a.TeX[(o.displaystyle?"sup1":(o.texprimestyle?"sup3":"sup2"))];C=Math.max(C,L*Q,n.d+(1/4)*O,N.superscriptshift);I.Add(n,A+P,C);this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=C}else{B=Math.max(B,a.TeX.sub2*Q);var E=a.TeX.rule_thickness*Q;if((C-n.d)-(z.h-B)<3*E){B=3*E-C+n.d+z.h;J=(4/5)*O-(C-n.d);if(J>0){C+=J;B-=J}}I.Add(n,A+P,Math.max(C,N.superscriptshift));I.Add(z,A,-Math.max(B,N.subscriptshift));this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=Math.max(C,N.superscriptshift);this.data[this.sub].SVGdata.dy=-Math.max(B,N.subscriptshift)}}I.Clean();this.SVGhandleColor(I);this.SVGsaveData(I);return I}});i.mmultiscripts.Augment({toSVG:i.mbase.SVGautoload});i.mtable.Augment({toSVG:i.mbase.SVGautoload});i["annotation-xml"].Augment({toSVG:i.mbase.SVGautoload});i.math.Augment({SVG:l.Subclass({type:"svg",removeable:false}),toSVG:function(B,p){var F=a.config;if(this.data[0]){this.SVGgetStyles();i.mbase.prototype.displayAlign=e.config.displayAlign;i.mbase.prototype.displayIndent=e.config.displayIndent;if(String(e.config.displayIndent).match(/^0($|[a-z%])/i)){i.mbase.prototype.displayIndent="0"}var v=l.G();v.Add(this.data[0].toSVG(),0,0,true);v.Clean();this.SVGhandleColor(v);a.Element(v.element,{stroke:"currentColor",fill:"currentColor","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"});v.removeable=false;var x=this.SVG();x.element.setAttribute("xmlns:xlink",m);if(F.useFontCache&&!F.useGlobalCache){x.element.appendChild(l.GLYPH.defs)}x.Add(v);x.Clean();this.SVGsaveData(x);if(!B){x.element=x.element.firstChild;x.element.removeAttribute("transform");x.removable=true;return x}var u=Math.max(-x.l,0),o=Math.max(x.r-x.w,0);var q=x.element.style,A=a.TeX.x_height/a.ex;var E=(Math.ceil(x.H/A)+1)*A+a.HFUZZ,n=(Math.ceil(x.D/A)+1)*A+a.DFUZZ;var z=u+x.w+o;x.element.setAttribute("width",a.Ex(z));x.element.setAttribute("height",a.Ex(E+n));q.verticalAlign=a.Ex(-n);if(u){q.marginLeft=a.Ex(-u)}if(o){q.marginRight=a.Ex(-o)}x.element.setAttribute("viewBox",a.Fixed(-u,1)+" "+a.Fixed(-E,1)+" "+a.Fixed(z,1)+" "+a.Fixed(E+n,1));if(x.H>x.h){q.marginTop=a.Ex(x.h-E)}if(x.D>x.d){q.marginBottom=a.Ex(x.d-n);q.verticalAlign=a.Ex(-x.d)}if(Math.abs(z-a.cwidth)<10){q.maxWidth=a.Fixed(a.cwidth*a.em/1000*a.config.scale)+"px"}var y=this.Get("alttext");if(y&&!x.element.getAttribute("aria-label")){x.element.setAttribute("aria-label",y)}if(!x.element.getAttribute("role")){x.element.setAttribute("role","img")}x.element.setAttribute("focusable","false");B.appendChild(x.element);x.element=null;if(!this.isMultiline&&this.Get("display")==="block"&&!x.hasIndent){var C=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(C.indentalignfirst!==i.INDENTALIGN.INDENTALIGN){C.indentalign=C.indentalignfirst}if(C.indentalign===i.INDENTALIGN.AUTO){C.indentalign=this.displayAlign}if(C.indentshiftfirst!==i.INDENTSHIFT.INDENTSHIFT){C.indentshift=C.indentshiftfirst}if(C.indentshift==="auto"){C.indentshift="0"}var s=a.length2em(C.indentshift,1,a.cwidth);if(this.displayIndent!=="0"){var t=a.length2em(this.displayIndent,1,a.cwidth);s+=(C.indentalign===i.INDENTALIGN.RIGHT?-t:t)}p.style.textAlign=C.indentalign;if(s){e.Insert(q,({left:{marginLeft:a.Ex(s)},right:{marginRight:a.Ex(-s),marginLeft:a.Ex(Math.max(0,s-z))},center:{marginLeft:a.Ex(s),marginRight:a.Ex(-s)}})[C.indentalign])}}}return B}});i.TeXAtom.Augment({toSVG:function(n,q){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data[0]!=null){var p=this.SVGdataStretched(0,n,q),r=0;if(this.texClass===i.TEXCLASS.VCENTER){r=a.TeX.axis_height-(p.h+p.d)/2+p.d}o.Add(p,0,r);o.ic=p.ic;o.skew=p.skew}this.SVGhandleColor(o);this.SVGsaveData(o);return o}});i.maligngroup.Augment({toSVG:i.mbase.SVGemptySVG});i.malignmark.Augment({toSVG:i.mbase.SVGemptySVG});i.mprescripts.Augment({toSVG:i.mbase.SVGemptySVG});i.none.Augment({toSVG:i.mbase.SVGemptySVG});e.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});e.Browser.Select({Opera:function(n){a.Augment({operaZoomRefresh:true})}});e.Register.StartupHook("End Cookie",function(){if(e.config.menuSettings.zoom!=="None"){j.Require("[MathJax]/extensions/MathZoom.js")}});if(!document.createElementNS){if(!document.namespaces.svg){document.namespaces.add("svg",b)}a.Augment({Element:function(n,o){var p=(typeof(n)==="string"?document.createElement("svg:"+n):n);p.isMathJax=true;if(o){for(var q in o){if(o.hasOwnProperty(q)){p.setAttribute(q,o[q].toString())}}}return p}})}})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG); +MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,d=MathJax.OutputJax.SVG,b=d.BBOX;a.mtable.Augment({toSVG:function(aa){this.SVGgetStyles();var o=this.SVG(),ap=this.SVGgetScale(o);if(this.data.length===0){this.SVGsaveData(o);return o}var aN=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");if(aN.width.match(/%$/)){o.width=aN.width=d.Em((d.cwidth/1000)*(parseFloat(aN.width)/100))}var v=this.SVGgetMu(o);var aK=-1;var z=[],I=[],k=[],O=[],K=[],aI,aG,w=-1,aE,u,az,S,an,E,aA;var ac=d.FONTDATA.lineH*ap*aN.useHeight,ag=d.FONTDATA.lineD*ap*aN.useHeight;for(aI=0,aE=this.data.length;aIw){w=aG}K[aG]=b.G();k[aG]=-d.BIGDIMEN}an=S.data[aG-az];O[aI][aG]=an.toSVG();if(an.isEmbellished()){E=an.CoreMO();var aM=E.Get("minsize",true);if(aM){if(E.SVGcanStretch("Vertical")){aA=E.SVGdata.h+E.SVGdata.d;if(aA){aM=d.length2em(aM,v,aA);if(aM*E.SVGdata.h/aA>z[aI]){z[aI]=aM*E.SVGdata.h/aA}if(aM*E.SVGdata.d/aA>I[aI]){I[aI]=aM*E.SVGdata.d/aA}}}else{if(E.SVGcanStretch("Horizontal")){aM=d.length2em(aM,v,E.SVGdata.w);if(aM>k[aG]){k[aG]=aM}}}}}if(O[aI][aG].h>z[aI]){z[aI]=O[aI][aG].h}if(O[aI][aG].d>I[aI]){I[aI]=O[aI][aG].d}if(O[aI][aG].w>k[aG]){k[aG]=O[aI][aG].w}}}var ao=MathJax.Hub.SplitList;var am=ao(aN.columnspacing),T=ao(aN.rowspacing),ai=ao(aN.columnalign),L=ao(aN.rowalign),N=ao(aN.columnlines),h=ao(aN.rowlines),ar=ao(aN.columnwidth),aw=[];for(aI=0,aE=am.length;aIO.length){aD=O.length}}g=0;ay=-(aA+ab)+z[0];for(aI=0,aE=aD-1;aI0.98){aj=X/(V+X);at=V+X}else{at=V/(1-ax)}}else{at=Math.max(V+X,d.length2em(aN.width,v));for(aI=0,aE=Math.min(w,am.length);aI0.01){if(aJ&&at>V){at=(at-V)/aJ;for(aI=0,aE=B.length;aIq+az*ak){R.indentalign=ai[aK];ak=az*(al+az*aO);aH+=al+Math.max(0,ak)}}else{if(ai[aK]===R.indentalign){if(e<0){aO=az*e;e=0}ak+=az*e;if(al>az*ak){ak=az*al}ak+=aO;aH+=az*ak}else{ak-=az*e;if(aH-az*ak+al>d.cwidth){ak=az*(aH+al-d.cwidth);if(az*ak>0){aH=d.cwidth+az*ak;ak=0}}}}var G=o;o=this.SVG();o.hasIndent=true;o.w=o.r=Math.max(aH,d.cwidth);o.Align(K[aK],ai[aK],0,0,aO);o.Align(G,R.indentalign,0,0,ak);o.tw=aH}this.SVGsaveData(o);return o},SVGhandleSpace:function(e){if(!this.hasFrame&&!e.width){e.x=e.X=167}this.SUPER(arguments).SVGhandleSpace.call(this,e)}});a.mtd.Augment({toSVG:function(e,g){var f=this.svg=this.SVG();if(this.data[0]){f.Add(this.SVGdataStretched(0,e,g));f.Clean()}this.SVGhandleColor(f);this.SVGsaveData(f);return f}});MathJax.Hub.Startup.signal.Post("SVG mtable Ready");MathJax.Ajax.loadComplete(d.autoloadDir+"/mtable.js")}); +(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/AM_SVG-full.js"); diff --git a/revisions_report_files/mathjax-27/config/AM_SVG.js b/revisions_report_files/mathjax-27/config/AM_SVG.js new file mode 100644 index 0000000..30da269 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/AM_SVG.js @@ -0,0 +1,47 @@ +/* + * /MathJax/config/AM_SVG.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.asciimath2jax={version:"2.7.6",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(aa){var g;var X=MathJax.Object.Subclass({firstChild:null,lastChild:null,Init:function(){this.childNodes=[]},appendChild:function(ab){if(ab.parent){ab.parent.removeChild(ab)}if(this.lastChild){this.lastChild.nextSibling=ab}if(!this.firstChild){this.firstChild=ab}this.childNodes.push(ab);ab.parent=this;this.lastChild=ab;return ab},removeChild:function(ad){for(var ac=0,ab=this.childNodes.length;ac=ab-1){this.lastChild=ae}this.childNodes[ad]=ae;ae.nextSibling=ac.nextSibling;ac.nextSibling=ac.parent=null;return ac},hasChildNodes:function(ab){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var ab=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ac=ab.apply(this,arguments)||this;ac.childNodes=ac.data;ac.nodeName=ac.type;return ac},appendChild:function(af){if(af.parent){af.parent.removeChild(af)}var ad=arguments;if(af.isa(X)){ad=af.childNodes;af.data=af.childNodes=[];af.firstChild=af.lastChild=null}for(var ae=0,ac=ad.length;ae=ac-1){this.lastChild=af}this.SetData(ae,af);af.nextSibling=ad.nextSibling;ad.nextSibling=ad.parent=null;return ad},hasChildNodes:function(ac){return(this.childNodes.length>0)},setAttribute:function(ac,ad){this[ac]=ad}})};var Q={};var e={getElementById:true,createElementNS:function(ac,ab){var ad=g[ab]();if(ab==="mo"&&aa.config.useMathMLspacing){ad.useMMLspacing=128}return ad},createTextNode:function(ab){return g.chars(ab).With({nodeValue:ab})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var C="blue";var o=true;var v=true;var d=".";var f=true;var l=(J.appName.slice(0,9)=="Microsoft");function E(ab){if(l){return e.createElement(ab)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",ab)}}var W="http://www.w3.org/1998/Math/MathML";function P(ab){if(l){return e.createElement("m:"+ab)}else{return e.createElementNS(W,ab)}}function O(ab,ad){var ac;if(l){ac=e.createElement("m:"+ab)}else{ac=e.createElementNS(W,ab)}if(ad){ac.appendChild(ad)}return ac}function u(ab,ac){z.push({input:ab,tag:"mo",output:ac,tex:null,ttype:V});B()}function r(ab){z.push(ab);B()}var D=["\uD835\uDC9C","\u212C","\uD835\uDC9E","\uD835\uDC9F","\u2130","\u2131","\uD835\uDCA2","\u210B","\u2110","\uD835\uDCA5","\uD835\uDCA6","\u2112","\u2133","\uD835\uDCA9","\uD835\uDCAA","\uD835\uDCAB","\uD835\uDCAC","\u211B","\uD835\uDCAE","\uD835\uDCAF","\uD835\uDCB0","\uD835\uDCB1","\uD835\uDCB2","\uD835\uDCB3","\uD835\uDCB4","\uD835\uDCB5","\uD835\uDCB6","\uD835\uDCB7","\uD835\uDCB8","\uD835\uDCB9","\u212F","\uD835\uDCBB","\u210A","\uD835\uDCBD","\uD835\uDCBE","\uD835\uDCBF","\uD835\uDCC0","\uD835\uDCC1","\uD835\uDCC2","\uD835\uDCC3","\u2134","\uD835\uDCC5","\uD835\uDCC6","\uD835\uDCC7","\uD835\uDCC8","\uD835\uDCC9","\uD835\uDCCA","\uD835\uDCCB","\uD835\uDCCC","\uD835\uDCCD","\uD835\uDCCE","\uD835\uDCCF"];var H=["\uD835\uDD04","\uD835\uDD05","\u212D","\uD835\uDD07","\uD835\uDD08","\uD835\uDD09","\uD835\uDD0A","\u210C","\u2111","\uD835\uDD0D","\uD835\uDD0E","\uD835\uDD0F","\uD835\uDD10","\uD835\uDD11","\uD835\uDD12","\uD835\uDD13","\uD835\uDD14","\u211C","\uD835\uDD16","\uD835\uDD17","\uD835\uDD18","\uD835\uDD19","\uD835\uDD1A","\uD835\uDD1B","\uD835\uDD1C","\u2128","\uD835\uDD1E","\uD835\uDD1F","\uD835\uDD20","\uD835\uDD21","\uD835\uDD22","\uD835\uDD23","\uD835\uDD24","\uD835\uDD25","\uD835\uDD26","\uD835\uDD27","\uD835\uDD28","\uD835\uDD29","\uD835\uDD2A","\uD835\uDD2B","\uD835\uDD2C","\uD835\uDD2D","\uD835\uDD2E","\uD835\uDD2F","\uD835\uDD30","\uD835\uDD31","\uD835\uDD32","\uD835\uDD33","\uD835\uDD34","\uD835\uDD35","\uD835\uDD36","\uD835\uDD37"];var w=["\uD835\uDD38","\uD835\uDD39","\u2102","\uD835\uDD3B","\uD835\uDD3C","\uD835\uDD3D","\uD835\uDD3E","\u210D","\uD835\uDD40","\uD835\uDD41","\uD835\uDD42","\uD835\uDD43","\uD835\uDD44","\u2115","\uD835\uDD46","\u2119","\u211A","\u211D","\uD835\uDD4A","\uD835\uDD4B","\uD835\uDD4C","\uD835\uDD4D","\uD835\uDD4E","\uD835\uDD4F","\uD835\uDD50","\u2124","\uD835\uDD52","\uD835\uDD53","\uD835\uDD54","\uD835\uDD55","\uD835\uDD56","\uD835\uDD57","\uD835\uDD58","\uD835\uDD59","\uD835\uDD5A","\uD835\uDD5B","\uD835\uDD5C","\uD835\uDD5D","\uD835\uDD5E","\uD835\uDD5F","\uD835\uDD60","\uD835\uDD61","\uD835\uDD62","\uD835\uDD63","\uD835\uDD64","\uD835\uDD65","\uD835\uDD66","\uD835\uDD67","\uD835\uDD68","\uD835\uDD69","\uD835\uDD6A","\uD835\uDD6B"];var c=0,A=1,U=2,i=3,b=4,h=5,a=6,L=7,V=8,m=9,Y=10,K=15;var k={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:Y};var z=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:c},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:c},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:c},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:c},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:c},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:c},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:c},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:c},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:c},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:c},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:c},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:c},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"lamda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lamda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:c},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:c},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:c},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:c},{input:"phi",tag:"mi",output:f?"\u03D5":"\u03C6",tex:null,ttype:c},{input:"varphi",tag:"mi",output:f?"\u03C6":"\u03D5",tex:null,ttype:c},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:c},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:c},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:c},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:c},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:c},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:c},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:c},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:c},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:c},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:c},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:c},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:c},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:c},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:c},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:c},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:c},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:c},{input:"**",tag:"mo",output:"\u2217",tex:"ast",ttype:c},{input:"***",tag:"mo",output:"\u22C6",tex:"star",ttype:c},{input:"//",tag:"mo",output:"/",tex:null,ttype:c},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:c},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:c},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:c},{input:"|><",tag:"mo",output:"\u22C9",tex:"ltimes",ttype:c},{input:"><|",tag:"mo",output:"\u22CA",tex:"rtimes",ttype:c},{input:"|><|",tag:"mo",output:"\u22C8",tex:"bowtie",ttype:c},{input:"-:",tag:"mo",output:"\u00F7",tex:"div",ttype:c},{input:"divide",tag:"mo",output:"-:",tex:null,ttype:V},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:c},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:c},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:c},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:c},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:L},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:L},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:c},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:L},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:c},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:L},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:c},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:L},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:c},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:L},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:c},{input:":=",tag:"mo",output:":=",tex:null,ttype:c},{input:"lt",tag:"mo",output:"<",tex:null,ttype:c},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:c},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:c},{input:"gt",tag:"mo",output:">",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:"left(",ttype:b},{input:")",tag:"mo",output:")",tex:"right)",ttype:h},{input:"[",tag:"mo",output:"[",tex:"left[",ttype:b},{input:"]",tag:"mo",output:"]",tex:"right]",ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:m},{input:":|:",tag:"mo",output:"|",tex:null,ttype:c},{input:"|:",tag:"mo",output:"|",tex:null,ttype:b},{input:":|",tag:"mo",output:"|",tex:null,ttype:h},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:":'",tag:"mo",output:"\u2235",tex:"because",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"frown",tag:"mo",output:"\u2322",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"Sin",tag:"mo",output:"Sin",tex:null,ttype:A,func:true},{input:"Cos",tag:"mo",output:"Cos",tex:null,ttype:A,func:true},{input:"Tan",tag:"mo",output:"Tan",tex:null,ttype:A,func:true},{input:"Arcsin",tag:"mo",output:"Arcsin",tex:null,ttype:A,func:true},{input:"Arccos",tag:"mo",output:"Arccos",tex:null,ttype:A,func:true},{input:"Arctan",tag:"mo",output:"Arctan",tex:null,ttype:A,func:true},{input:"Sinh",tag:"mo",output:"Sinh",tex:null,ttype:A,func:true},{input:"Cosh",tag:"mo",output:"Cosh",tex:null,ttype:A,func:true},{input:"Tanh",tag:"mo",output:"Tanh",tex:null,ttype:A,func:true},{input:"Cot",tag:"mo",output:"Cot",tex:null,ttype:A,func:true},{input:"Sec",tag:"mo",output:"Sec",tex:null,ttype:A,func:true},{input:"Csc",tag:"mo",output:"Csc",tex:null,ttype:A,func:true},{input:"Log",tag:"mo",output:"Log",tex:null,ttype:A,func:true},{input:"Ln",tag:"mo",output:"Ln",tex:null,ttype:A,func:true},{input:"Abs",tag:"mo",output:"abs",tex:null,ttype:A,notexcopy:true,rewriteleftright:["|","|"]},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:i},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"overset",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"underset",tag:"munder",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:i},{input:"^",tag:"msup",output:"^",tex:null,ttype:i},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"overarc",tag:"mover",output:"\u23DC",tex:"overparen",ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"id",tag:"mrow",ttype:U},{input:"class",tag:"mrow",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},k,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ac,ab){if(ac.input>ab.input){return 1}else{return -1}}var S=[];function n(){var ac;var ab=z.length;for(ac=0;ac>1;if(ac[ab]=S[ab]}s=y;if(af!=""){y=z[ae].ttype;return z[ae]}y=c;ab=1;ak=ah.slice(0,1);var ai=true;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}if(ak==d){ak=ah.slice(ab,ab+1);if("0"<=ak&&ak<="9"){ai=false;ab++;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}}}if((ai&&ab>1)||ab>2){ak=ah.slice(0,ab-1);aj="mn"}else{ab=2;ak=ah.slice(0,1);aj=(("A">ak||ak>"Z")&&("a">ak||ak>"z")?"mo":"mi")}if(ak=="-"&&s==i){y=i;return{input:ak,tag:aj,output:ak,ttype:A,func:true}}return{input:ak,tag:aj,output:ak,ttype:c}}function R(ac){var ab;if(!ac.hasChildNodes()){return}if(ac.firstChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.firstChild.firstChild.nodeValue;if(ab=="("||ab=="["||ab=="{"){ac.removeChild(ac.firstChild)}}if(ac.lastChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.lastChild.firstChild.nodeValue;if(ab==")"||ab=="]"||ab=="}"){ac.removeChild(ac.lastChild)}}}var F,s,y;function G(ai){var ad,ac,al,af,ak,ag=e.createDocumentFragment();ai=p(ai,0);ad=j(ai);if(ad==null||ad.ttype==h&&F>0){return[null,ai]}if(ad.ttype==V){ai=ad.output+p(ai,ad.input.length);ad=j(ai)}switch(ad.ttype){case L:case c:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai];case b:F++;ai=p(ai,ad.input.length);al=q(ai,true);F--;if(typeof ad.invisible=="boolean"&&ad.invisible){ac=O("mrow",al[0])}else{ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0])}return[ac,al[1]];case Y:if(ad!=k){ai=p(ai,ad.input.length)}if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}else{if(ad==k){af=ai.slice(1).indexOf('"')+1}else{af=0}}}}if(af==-1){af=ai.length}ak=ai.slice(1,af);if(ak.charAt(0)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ag.appendChild(O(ad.tag,e.createTextNode(ak)));if(ak.charAt(ak.length-1)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ai=p(ai,af+1);return[O("mrow",ag),ai];case K:case A:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O(ad.tag,e.createTextNode(ad.output)),ai]}if(typeof ad.func=="boolean"&&ad.func){ak=ai.charAt(0);if(ak=="^"||ak=="_"||ak=="/"||ak=="|"||ak==","||(ad.input.length==1&&ad.input.match(/\w/)&&ak!="(")){return[O(ad.tag,e.createTextNode(ad.output)),ai]}else{ac=O("mrow",O(ad.tag,e.createTextNode(ad.output)));ac.appendChild(al[0]);return[ac,al[1]]}}R(al[0]);if(ad.input=="sqrt"){return[O(ad.tag,al[0]),al[1]]}else{if(typeof ad.rewriteleftright!="undefined"){ac=O("mrow",O("mo",e.createTextNode(ad.rewriteleftright[0])));ac.appendChild(al[0]);ac.appendChild(O("mo",e.createTextNode(ad.rewriteleftright[1])));return[ac,al[1]]}else{if(ad.input=="cancel"){ac=O(ad.tag,al[0]);ac.setAttribute("notation","updiagonalstrike");return[ac,al[1]]}else{if(typeof ad.acc=="boolean"&&ad.acc){ac=O(ad.tag,al[0]);var ah=O("mo",e.createTextNode(ad.output));if(ad.input=="vec"&&((al[0].nodeName=="mrow"&&al[0].childNodes.length==1&&al[0].firstChild.firstChild.nodeValue!==null&&al[0].firstChild.firstChild.nodeValue.length==1)||(al[0].firstChild.nodeValue!==null&&al[0].firstChild.nodeValue.length==1))){ah.setAttribute("stretchy",false)}ac.appendChild(ah);return[ac,al[1]]}else{if(!l&&typeof ad.codes!="undefined"){for(af=0;af64&&ak.charCodeAt(ae)<91){aj=aj+ad.codes[ak.charCodeAt(ae)-65]}else{if(ak.charCodeAt(ae)>96&&ak.charCodeAt(ae)<123){aj=aj+ad.codes[ak.charCodeAt(ae)-71]}else{aj=aj+ak.charAt(ae)}}}if(al[0].nodeName=="mi"){al[0]=O("mo").appendChild(e.createTextNode(aj))}else{al[0].replaceChild(O("mo").appendChild(e.createTextNode(aj)),al[0].childNodes[af])}}}}ac=O(ad.tag,al[0]);ac.setAttribute(ad.atname,ad.atval);return[ac,al[1]]}}}}case U:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(al[0]);var ab=G(al[1]);if(ab[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(ab[0]);if(["color","class","id"].indexOf(ad.input)>=0){if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}}}ak=ai.slice(1,af);ac=O(ad.tag,ab[0]);if(ad.input==="color"){ac.setAttribute("mathcolor",ak)}else{if(ad.input==="class"){ac.setAttribute("class",ak)}else{if(ad.input==="id"){ac.setAttribute("id",ak)}}}return[ac,ab[1]]}if(ad.input=="root"||ad.output=="stackrel"){ag.appendChild(ab[0])}ag.appendChild(al[0]);if(ad.input=="frac"){ag.appendChild(ab[0])}return[O(ad.tag,ag),ab[1]];case i:ai=p(ai,ad.input.length);return[O("mo",e.createTextNode(ad.output)),ai];case a:ai=p(ai,ad.input.length);ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);ag.appendChild(O(ad.tag,e.createTextNode(ad.output)));ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);return[O("mrow",ag),ai];case m:F++;ai=p(ai,ad.input.length);al=q(ai,false);F--;ak="";if(al[0].lastChild!=null){ak=al[0].lastChild.firstChild.nodeValue}if(ak=="|"&&ai.charAt(0)!==","){ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0]);return[ac,al[1]]}else{ac=O("mo",e.createTextNode("\u2223"));ac=O("mrow",ac);return[ac,ai]}default:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai]}}function t(ah){var af,ai,ag,ae,ab,ad;ah=p(ah,0);ai=j(ah);ab=G(ah);ae=ab[0];ah=ab[1];af=j(ah);if(af.ttype==i&&af.input!="/"){ah=p(ah,af.input.length);ab=G(ah);if(ab[0]==null){ab[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ab[0])}ah=ab[1];ad=(ai.ttype==L||ai.ttype==K);if(af.input=="_"){ag=j(ah);if(ag.input=="^"){ah=p(ah,ag.input.length);var ac=G(ah);R(ac[0]);ah=ac[1];ae=O((ad?"munderover":"msubsup"),ae);ae.appendChild(ab[0]);ae.appendChild(ac[0]);ae=O("mrow",ae)}else{ae=O((ad?"munder":"msub"),ae);ae.appendChild(ab[0])}}else{if(af.input=="^"&&ad){ae=O("mover",ae);ae.appendChild(ab[0])}else{ae=O(af.tag,ae);ae.appendChild(ab[0])}}if(typeof ai.func!="undefined"&&ai.func){ag=j(ah);if(ag.ttype!=i&&ag.ttype!=h){ab=t(ah);ae=O("mrow",ae);ae.appendChild(ab[0]);ah=ab[1]}}}return[ae,ah]}function q(ak,aj){var ao,al,ag,ar,ah=e.createDocumentFragment();do{ak=p(ak,0);ag=t(ak);al=ag[0];ak=ag[1];ao=j(ak);if(ao.ttype==i&&ao.input=="/"){ak=p(ak,ao.input.length);ag=t(ak);if(ag[0]==null){ag[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ag[0])}ak=ag[1];R(al);al=O(ao.tag,al);al.appendChild(ag[0]);ah.appendChild(al);ao=j(ak)}else{if(al!=undefined){ah.appendChild(al)}}}while((ao.ttype!=h&&(ao.ttype!=m||aj)||F==0)&&ao!=null&&ao.output!="");if(ao.ttype==h||ao.ttype==m){var at=ah.childNodes.length;if(at>0&&ah.childNodes[at-1].nodeName=="mrow"&&ah.childNodes[at-1].lastChild&&ah.childNodes[at-1].lastChild.firstChild){var av=ah.childNodes[at-1].lastChild.firstChild.nodeValue;if(av==")"||av=="]"){var ac=ah.childNodes[at-1].firstChild.firstChild.nodeValue;if(ac=="("&&av==")"&&ao.output!="}"||ac=="["&&av=="]"){var ad=[];var ap=true;var am=ah.childNodes.length;for(ar=0;ap&&ar1){ap=ad[ar].length==ad[ar-2].length}}ap=ap&&(ad.length>1||ad[0].length>0);var af=[];if(ap){var ae,ab,ai,an,au=e.createDocumentFragment();for(ar=0;ar2){ah.removeChild(ah.firstChild);ah.removeChild(ah.firstChild)}au.appendChild(O("mtr",ae))}al=O("mtable",au);al.setAttribute("columnlines",af.join(" "));if(typeof ao.invisible=="boolean"&&ao.invisible){al.setAttribute("columnalign","left")}ah.replaceChild(al,ah.firstChild)}}}}ak=p(ak,ao.input.length);if(typeof ao.invisible!="boolean"||!ao.invisible){al=O("mo",e.createTextNode(ao.output));ah.appendChild(al)}}return[ah,ak]}function M(ad,ac){var ae,ab;F=0;ad=ad.replace(/ /g,"");ad=ad.replace(/>/g,">");ad=ad.replace(/</g,"<");ae=q(ad.replace(/^\s+/g,""),false)[0];ab=O("mstyle",ae);if(C!=""){ab.setAttribute("mathcolor",C)}if(mathfontsize!=""){ab.setAttribute("fontsize",mathfontsize);ab.setAttribute("mathsize",mathfontsize)}if(mathfontfamily!=""){ab.setAttribute("fontfamily",mathfontfamily);ab.setAttribute("mathvariant",mathfontfamily)}if(o){ab.setAttribute("displaystyle","true")}ab=O("math",ab);if(v){ab.setAttribute("title",ad.replace(/\s+/g," "))}return ab}v=false;mathfontfamily="";C="";mathfontsize="";(function(){for(var ac=0,ab=z.length;ac/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/AM_SVG.js"); diff --git a/revisions_report_files/mathjax-27/config/MML_CHTML-full.js b/revisions_report_files/mathjax-27/config/MML_CHTML-full.js new file mode 100644 index 0000000..4e866f7 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/MML_CHTML-full.js @@ -0,0 +1,53 @@ +/* + * /MathJax/config/MML_CHTML-full.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/CommonHTML/jax.js", + "[MathJax]/jax/output/CommonHTML/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.mml2jax={version:"2.7.6",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var d,b;if(typeof(document.namespaces)!=="undefined"){try{for(d=0,b=document.namespaces.length;d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +(function(d,h,l,g,m,b,j){var p="2.7.6";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Menu_Button .MathJax_Hover_Arrow":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"4px","-webkit-border-radius":"4px","-moz-border-radius":"4px","-khtml-border-radius":"4px","font-family":"'Courier New',Courier","font-size":"9px",color:"#F0F0F0"},".MathJax_Menu_Button .MathJax_Hover_Arrow span":{display:"block","background-color":"#AAA",border:"1px solid","border-radius":"3px","line-height":0,padding:"4px"},".MathJax_Hover_Arrow:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_Hover_Arrow:hover span":{"background-color":"#CCC!important"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",KEY:{RETURN:13,ESCAPE:27,SPACE:32,LEFT:37,UP:38,RIGHT:39,DOWN:40},Mousedown:function(q){return n.Handler(q,"Mousedown",this)},Mouseup:function(q){return n.Handler(q,"Mouseup",this)},Mousemove:function(q){return n.Handler(q,"Mousemove",this)},Mouseover:function(q){return n.Handler(q,"Mouseover",this)},Mouseout:function(q){return n.Handler(q,"Mouseout",this)},Click:function(q){return n.Handler(q,"Click",this)},DblClick:function(q){return n.Handler(q,"DblClick",this)},Menu:function(q){return n.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return n.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}else{q.returnValue=false}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true}return false},Keydown:function(r,q){if(!r){r=window.event}if(r.keyCode===n.KEY.SPACE){n.ContextMenu(r,this)}},ContextMenu:function(t,E,w){var B=b[E.jaxID],v=B.getJaxFromMath(E);var F=(B.config.showMathMenu!=null?B:d).config.showMathMenu;if(!F||(k.context!=="MathJax"&&!w)){return}if(c.msieEventBug){t=window.event||t}n.ClearSelection();f.ClearHoverTimer();if(v.hover){if(v.hover.remove){clearTimeout(v.hover.remove);delete v.hover.remove}v.hover.nofade=true}var u=MathJax.Menu;var G,D;if(u){if(u.loadingDomain){return n.False(t)}G=m.loadDomain("MathMenu");if(!G){u.jax=v;var r=u.menu.Find("Show Math As").submenu;r.items[0].name=v.sourceMenuTitle;r.items[0].format=(v.sourceMenuFormat||"MathML");r.items[1].name=j[v.inputJax].sourceMenuTitle;r.items[5].disabled=!j[v.inputJax].annotationEncoding;var A=r.items[2];A.disabled=true;var q=A.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var z=0,y=q.length;z0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(c,d){var a;var b=function(e){return MathJax.Localization._.apply(MathJax.Localization,[["MathML",e]].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(f,e){this.Parse(f,e)},Parse:function(h,e){var j;if(typeof h!=="string"){j=h.parentNode}else{j=c.ParseXML(this.preProcessMath.call(this,h));if(j==null){c.Error(["ErrorParsingMathML","Error parsing MathML"])}}var g=j.getElementsByTagName("parsererror")[0];if(g){c.Error(["ParsingError","Error parsing MathML: %1",g.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")])}if(j.childNodes.length!==1){c.Error(["MathMLSingleElement","MathML must be formed by a single element"])}if(j.firstChild.nodeName.toLowerCase()==="html"){var f=j.getElementsByTagName("h1")[0];if(f&&f.textContent==="XML parsing error"&&f.nextSibling){c.Error(["ParsingError","Error parsing MathML: %1",String(f.nextSibling.nodeValue).replace(/fatal parsing error: /,"")])}}if(j.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){c.Error(["MathMLRootElement","MathML must be formed by a element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g *":{position:"absolute"},".MJXc-bevelled > *":{display:"inline-block"},".mjx-stack":{display:"inline-block"},".mjx-op":{display:"block"},".mjx-under":{display:"table-cell"},".mjx-over":{display:"block"},".mjx-over > *":{"padding-left":"0px!important","padding-right":"0px!important"},".mjx-under > *":{"padding-left":"0px!important","padding-right":"0px!important"},".mjx-stack > .mjx-sup":{display:"block"},".mjx-stack > .mjx-sub":{display:"block"},".mjx-prestack > .mjx-presup":{display:"block"},".mjx-prestack > .mjx-presub":{display:"block"},".mjx-delim-h > .mjx-char":{display:"inline-block"},".mjx-surd":{"vertical-align":"top"},".mjx-mphantom *":{visibility:"hidden"},".mjx-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"2px 3px","font-style":"normal","font-size":"90%"},".mjx-annotation-xml":{"line-height":"normal"},".mjx-menclose > svg":{fill:"none",stroke:"currentColor"},".mjx-mtr":{display:"table-row"},".mjx-mlabeledtr":{display:"table-row"},".mjx-mtd":{display:"table-cell","text-align":"center"},".mjx-label":{display:"table-row"},".mjx-box":{display:"inline-block"},".mjx-block":{display:"block"},".mjx-span":{display:"inline"},".mjx-char":{display:"block","white-space":"pre"},".mjx-itable":{display:"inline-table",width:"auto"},".mjx-row":{display:"table-row"},".mjx-cell":{display:"table-cell"},".mjx-table":{display:"table",width:"100%"},".mjx-line":{display:"block",height:0},".mjx-strut":{width:0,"padding-top":k+"em"},".mjx-vsize":{width:0},".MJXc-space1":{"margin-left":".167em"},".MJXc-space2":{"margin-left":".222em"},".MJXc-space3":{"margin-left":".278em"},".mjx-chartest":{display:"block",visibility:"hidden",position:"absolute",top:0,"line-height":"normal","font-size":"500%"},".mjx-chartest .mjx-char":{display:"inline"},".mjx-chartest .mjx-box":{"padding-top":"1000px"},".MJXc-processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MJXc-processed":{display:"none"},".mjx-test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".mjx-test.mjx-test-display":{display:"table!important"},".mjx-test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".mjx-test.mjx-test-default":{display:"block!important",clear:"both"},".mjx-ex-box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .mjx-left-box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .mjx-right-box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .mjx-right-box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_CHTML_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401,position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}};var i=1000000;var n=5;var c={},r=MathJax.Hub.config;a.Augment({settings:f.config.menuSettings,config:{styles:p},Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var s=this.settings;if(s.scale){this.config.scale=s.scale}this.require.push(this.fontDir+"/TeX/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js");c=this.config.linebreaks},Startup:function(){e=MathJax.Extension.MathEvents.Event;q=MathJax.Extension.MathEvents.Touch;h=MathJax.Extension.MathEvents.Hover;this.ContextMenu=e.ContextMenu;this.Mousedown=e.AltContextMenu;this.Mouseover=h.Mouseover;this.Mouseout=h.Mouseout;this.Mousemove=h.Mousemove;var s=a.addElement(document.body,"mjx-block",{style:{display:"block",width:"5in"}});this.pxPerInch=s.offsetWidth/5;s.parentNode.removeChild(s);this.TestSpan=a.Element("mjx-test",{style:{left:"1em"}},[["mjx-left-box"],["mjx-ex-box"],["mjx-right-box"]]);return o.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){this.getDefaultExEm();if(this.defaultEm){return}var s=MathJax.Callback();o.timer.start(o,function(t){if(t.time(s)){f.signal.Post(["CommonHTML Jax - no default em size"]);return}a.getDefaultExEm();if(a.defaultEm){s()}else{setTimeout(t,t.delay)}},this.defaultEmDelay,this.defaultEmTimeout);return s},defaultEmDelay:100,defaultEmTimeout:1000,getDefaultExEm:function(){var s=document.body.appendChild(this.TestSpan.cloneNode(true));s.className+=" mjx-test-inline mjx-test-default";this.defaultEm=this.getFontSize(s);this.defaultEx=s.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,s.lastChild.offsetLeft-s.firstChild.offsetLeft-2);document.body.removeChild(s)},getFontSize:(window.getComputedStyle?function(t){var s=window.getComputedStyle(t);return parseFloat(s.fontSize)}:function(s){return s.style.pixelLeft}),getMaxWidth:(window.getComputedStyle?function(t){var s=window.getComputedStyle(t);if(s.maxWidth!=="none"){return parseFloat(s.maxWidth)}return 0}:function(t){var s=t.currentStyle.maxWidth;if(s!=="none"){if(s.match(/\d*px/)){return parseFloat(s)}var u=t.style.left;t.style.left=s;s=t.style.pixelLeft;t.style.left=u;return s}return 0}),loadFont:function(s){f.RestartAfter(o.Require(this.fontDir+"/"+s))},fontLoaded:function(s){if(!s.match(/-|fontdata/)){s+="-Regular"}if(!s.match(/\.js$/)){s+=".js"}MathJax.Callback.Queue(["Post",f.Startup.signal,"CommonHTML - font data loaded for "+s],["loadComplete",o,this.fontDir+"/"+s])},Element:function(s,u,t){if(s.substr(0,4)==="mjx-"){if(!u){u={}}if(u.isMathJax==null){u.isMathJax=true}if(u.className){u.className=s+" "+u.className}else{u.className=s}s="span"}return this.HTMLElement(s,u,t)},addElement:function(u,s,v,t){return u.appendChild(this.Element(s,v,t))},HTMLElement:m.Element,ucMatch:m.ucMatch,setScript:m.setScript,getNode:function(x,w){var u=RegExp("\\b"+w+"\\b");var t=[];while(x){for(var v=0,s=x.childNodes.length;v=x.CHTMLlast+x.CHTMLchunk){this.postTranslate(x);x.CHTMLchunk=Math.floor(x.CHTMLchunk*this.config.EqnChunkFactor);x.CHTMLdelay=true}},initCHTML:function(t,s){},savePreview:function(s){var t=s.MathJax.preview;if(t&&t.parentNode){s.MathJax.tmpPreview=document.createElement("span");t.parentNode.replaceChild(s.MathJax.tmpPreview,t)}},restorePreview:function(s){var t=s.MathJax.tmpPreview;if(t){t.parentNode.replaceChild(s.MathJax.preview,t);delete s.MathJax.tmpPreview}},getMetrics:function(s){var t=s.CHTML;this.jax=s;this.em=t.em;this.outerEm=t.outerEm;this.scale=t.scale;this.cwidth=t.cwidth;this.linebreakWidth=t.lineWidth},postTranslate:function(x){var t=x.jax[this.id];for(var v=x.CHTMLlast,s=x.CHTMLeqn;vC.h){t.marginTop=a.Em(C.t-C.h)}if(C.b>C.d){t.marginBottom=a.Em(C.b-C.d)}if(C.l<0){t.paddingLeft=a.Em(-C.l)}if(C.r>C.w){t.marginRight=a.Em(C.r-C.w)}t.position="absolute";var z=v.offsetWidth,x=v.offsetHeight,D=A.firstChild.offsetHeight,w=A.firstChild.offsetWidth;v.style.position="";return{Y:-e.getBBox(B).h,mW:w,mH:D,zW:z,zH:x}},Remove:function(s){var t=document.getElementById(s.inputID+"-Frame");if(t&&s.CHTML.display){t=t.parentNode}if(t){t.parentNode.removeChild(t)}delete s.CHTML},ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18,thin:0.04,medium:0.06,thick:0.1,infinity:i},SPACECLASS:{thinmathspace:"MJXc-space1",mediummathspace:"MJXc-space2",thickmathspace:"MJXc-space3"},pxPerInch:96,em:16,maxStretchyParts:1000,FONTDEF:{},TEXDEF:{x_height:0.442,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.45,big_op_spacing5:0.1,surd_height:0.075,scriptspace:0.05,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},isChar:function(s){if(s.length===1){return true}if(s.length!==2){return false}var t=s.charCodeAt(0);return(t>=55296&&t<56319)},unicodeChar:function(s){if(s<65535){return String.fromCharCode(s)}s-=65536;return String.fromCharCode((s>>10)+55296)+String.fromCharCode((s&1023)+56320)},getUnicode:function(s){var t=s.text.charCodeAt(s.i);s.i++;if(t>=55296&&t<56319){t=(((t-55296)<<10)+(s.text.charCodeAt(s.i)-56320))+65536;s.i++}return t},getCharList:function(w,v){var u,z,s=w.cache,B=v;if(s[v]){return s[v]}if(v>65535&&this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(v,w);v=y.n;w=y.variant}var t=this.FONTDATA.RANGES,A=this.FONTDATA.VARIANT;if(v>=t[0].low&&v<=t[t.length-1].high){for(u=0,z=t.length;u=t[u].low&&v<=t[u].high){if(t[u].remap&&t[u].remap[v]){v=x+t[u].remap[v]}else{v=v-t[u].low+x;if(t[u].add){v+=t[u].add}}if(w["variant"+t[u].offset]){w=A[w["variant"+t[u].offset]]}break}}}s[B]=this.remapChar(w,v,0);return s[B]},remapChar:function(t,y,w){var v=[],x=this.FONTDATA.VARIANT;if(t.remap&&t.remap[y]){y=t.remap[y];if(t.remap.variant){t=x[t.remap.variant]}}else{if(this.FONTDATA.REMAP[y]&&!t.noRemap){y=this.FONTDATA.REMAP[y]}}if(g(y)){if(y[2]){w=n}t=x[y[1]];y=y[0]}if(typeof(y)==="string"){var s={text:y,i:0,length:y.length};while(s.i(B.a||0)){B.a=u.a}u.className=w.className;var t=w[D.n];if(A){var v=w;if(g(A)){v=a.FONTDATA.FONTS[A[1]];A=A[0];if(typeof(v)==="string"){a.loadFont(v)}}if(v[D.n]){a.fixChar(v[D.n],D.n)}t=a.fixChar(v[A],A);u.className=v.className}u.text+=t.c;if(B.hB.w+t[3]){B.l=B.w+t[3]}if(B.rw.a){w.a=u.a}}s=this.flushText(s,u,t.style);if(v[2]<3){s.style.width=a.Em(v[2])}},flushText:function(t,u,s){t=a.addElement(t,"mjx-charbox",{className:u.className,style:s},[u.text]);if(u.a){t.style.paddingBottom=a.Em(u.a)}u.text="";u.className=null;u.a=0;u.flushed=true;return t}},handleText:function(u,x,t,w){if(u.childNodes.length===0){a.addElement(u,"mjx-char");w=a.BBOX.empty(w)}if(typeof(t)==="string"){t=this.FONTDATA.VARIANT[t]}if(!t){t=this.FONTDATA.VARIANT[d.VARIANT.NORMAL]}var s={text:x,i:0,length:x.length},v=[];if(t.style&&s.length){v.push(this.styledText(t,x))}else{while(s.i-w.b){u.firstChild.style.paddingBottom=this.EmRounded(w.d+w.b)}return w},createDelimiter:function(x,s,u,A,v){if(!s){var B=this.BBOX.zero();B.w=B.r=this.TEX.nulldelimiterspace;a.addElement(x,"mjx-box",{style:{width:B.w}});return B}if(!(u instanceof Array)){u=[u,u]}var z=u[1];u=u[0];var t={alias:s};while(t.alias){s=t.alias;t=this.FONTDATA.DELIMITERS[s];if(!t){t={HW:[0,this.FONTDATA.VARIANT[d.VARIANT.NORMAL]]}}}if(t.load){f.RestartAfter(o.Require(this.fontDir+"/TeX/fontdata-"+t.load+".js"))}for(var y=0,w=t.HW.length;y=u-0.01||(y==w-1&&!t.stretch)){if(t.HW[y][3]){s=t.HW[y][3]}B=this.createChar(x,[s,t.HW[y][1]],(t.HW[y][2]||1),v);B.offset=0.6*B.w;if(A){B.scale=A.scale;A.rscale=A.rscale}return B}}if(!t.stretch){return B}return this["extendDelimiter"+t.dir](x,z,t.stretch,A,v)},extendDelimiterV:function(E,x,P,w,C){E=a.addElement(E,"mjx-delim-v");var N=a.Element("span");var B,A,O,v,I,t,F,y,G=1,M;I=this.createChar(N,(P.top||P.ext),1,C);B=N.removeChild(N.firstChild);t=this.createChar(N,(P.bot||P.ext),1,C);A=N.removeChild(N.firstChild);F=y=a.BBOX.zero();var J=I.h+I.d+t.h+t.d-l;E.appendChild(B);if(P.mid){F=this.createChar(N,P.mid,1,C);O=N.removeChild(N.firstChild);J+=F.h+F.d;G=2}if(P.min&&xJ){y=this.createChar(N,P.ext,1,C);v=N.removeChild(N.firstChild);var L=y.h+y.d,u=L-l;var D=Math.min(Math.ceil((x-J)/(G*u)),this.maxStretchyParts);if(P.fullExtenders){x=D*G*u+J}else{u=(x-J)/(G*D)}M=y.d+y.a-L/2;v.style.margin=v.style.padding="";v.style.lineHeight=a.Em(u);v.style.marginBottom=a.Em(M-l/2/G);v.style.marginTop=a.Em(-M-l/2/G);var K=v.textContent,z="\n"+K;while(--D>0){K+=z}v.textContent=K;E.appendChild(v);if(P.mid){E.appendChild(O);E.appendChild(v.cloneNode(true))}}else{M=(x-J-l)/G;B.style.marginBottom=a.Em(M+parseFloat(B.style.marginBottom||"0"));if(P.mid){E.appendChild(O)}A.style.marginTop=a.Em(M+parseFloat(A.style.marginTop||"0"))}E.appendChild(A);var s=a.BBOX({w:Math.max(I.w,y.w,t.w,F.w),l:Math.min(I.l,y.l,t.l,F.l),r:Math.max(I.r,y.r,t.r,F.r),h:x-t.d,d:t.d,t:x-t.d,b:t.d});s.offset=0.5*s.w;if(w){s.scale=w.scale;s.rscale=w.rscale}return s},extendDelimiterH:function(F,s,P,v,D){F=a.addElement(F,"mjx-delim-h");var N=a.Element("span");var t,M,O,u,K,C,x,G,z,H=1;C=this.createChar(N,(P.left||P.rep),1,D);t=N.removeChild(N.firstChild);x=this.createChar(N,(P.right||P.rep),1,D);M=N.removeChild(N.firstChild);z=this.createChar(N,P.rep,1,D);u=N.removeChild(N.firstChild);t.style.marginLeft=a.Em(-C.l);M.style.marginRight=a.Em(x.r-x.w);F.appendChild(t);var Q=a.BBOX.zero();Q.h=Math.max(C.h,x.h,z.h);Q.d=Math.max(C.D||C.d,x.D||x.d,z.D||z.d);var y=(C.r-C.l)+(x.r-x.l)-l;if(P.mid){G=this.createChar(N,P.mid,1,D);O=N.removeChild(N.firstChild);O.style.marginleft=a.Em(-G.l);O.style.marginRight=a.Em(G.r-G.w);y+=G.r-G.l+l;H=2;if(G.h>Q.h){Q.h=G.h}if(G.d>Q.d){Q.d=G.d}}if(P.min&&sy){var B=z.r-z.l,J=B-l;var E=Math.min(Math.ceil((s-y)/(H*J)),this.maxStretchyParts);if(P.fullExtenders){s=E*H*J+y}else{J=(s-y)/(H*E)}var L=(B-J+l/H)/2;u.style.marginLeft=a.Em(-z.l-L);u.style.marginRight=a.Em(z.r-z.w+L);u.style.letterSpacing=a.Em(-(z.w-J));t.style.marginRight=a.Em(C.r-C.w);M.style.marginleft=a.Em(-x.l);var I=u.textContent,A=I;while(--E>0){I+=A}u.textContent=I;F.appendChild(u);if(P.mid){F.appendChild(O);K=F.appendChild(u.cloneNode(true))}}else{L=(s-y-l/H)/2;t.style.marginRight=a.Em(C.r-C.w+L);if(P.mid){F.appendChild(O)}M.style.marginLeft=a.Em(-x.l+L)}F.appendChild(M);this.adjustHeights([t,u,O,K,M],[C,z,G,z,x],Q);if(v){Q.scale=v.scale;Q.rscale=v.rscale}return Q},adjustHeights:function(t,w,x){var u=x.h,y=x.d;if(x.d<0){y=-x.d;x.D=x.d;x.d=0}for(var v=0,s=t.length;v0){delete this.D}},rescale:function(s){this.w*=s;this.h*=s;this.d*=s;this.l*=s;this.r*=s;this.t*=s;this.b*=s;if(this.L){this.L*=s}if(this.R){this.R*=s}if(this.D){this.D*=s}},combine:function(t,s,v){t.X=s;t.Y=v;var u=t.rscale;if(s+u*t.r>this.r){this.r=s+u*t.r}if(s+u*t.lthis.w){this.w=s+u*(t.w+(t.L||0)+(t.R||0))}if(v+u*t.h>this.h){this.h=v+u*t.h}if(t.D&&(this.D==null||u*t.D-v>this.D)&&u*t.D>this.d){this.D=u*t.D-v}else{if(t.D==null&&this.D){delete this.D}}if(u*t.d-v>this.d){this.d=u*t.d-v}if(v+u*t.t>this.t){this.t=v+u*t.t}if(u*t.b-v>this.b){this.b=u*t.b-v}},append:function(t){var u=t.rscale;var s=this.w;if(s+u*t.r>this.r){this.r=s+u*t.r}if(s+u*t.lthis.h){this.h=u*t.h}if(t.D&&(this.D==null||u*t.D>this.D)&&u*t.D>this.d){this.D=u*t.D}else{if(t.D==null&&this.D){delete this.D}}if(u*t.d>this.d){this.d=u*t.d}if(u*t.t>this.t){this.t=u*t.t}if(u*t.b>this.b){this.b=u*t.b}},updateFrom:function(s){this.h=s.h;this.d=s.d;this.w=s.w;this.r=s.r;this.l=s.l;this.t=s.t;this.b=s.b;if(s.pwidth){this.pwidth=s.pwidth}if(s.D){this.D=s.D}else{delete this.D}},adjust:function(t,s,v,u){this[s]+=a.length2em(t,1,this.scale);if(u==null){if(this[s]>this[v]){this[v]=this[s]}}else{if(this[v]z.r){z.r=z.w}if(t.h>z.h){z.h=t.h}if(t.d>z.d){z.d=t.d}if(t.t>z.t){z.t=t.t}if(t.b>z.b){z.b=t.b}}}},CHTMLstretchChildH:function(v,s,x){var y=this.data[v];if(y){var z=this.CHTML,u=y.CHTML;if(u.stretch||(u.stretch==null&&y.CHTMLcanStretch("Horizontal",s))){var t=u.w;u=y.CHTMLstretchH(this.CHTMLchildNode(x,v),s);z.w+=u.w-t;if(z.w>z.r){z.r=z.w}if(u.h>z.h){z.h=u.h}if(u.d>z.d){z.d=u.d}if(u.t>z.t){z.t=u.t}if(u.b>z.b){z.b=u.b}}}},CHTMLupdateFrom:function(s){this.CHTML.updateFrom(s);if(this.inferRow){this.data[0].CHTML.updateFrom(s)}},CHTMLcanStretch:function(w,u,v){var t=false;if(this.isEmbellished()){var s=this.Core();if(s&&s!==this){t=s.CHTMLcanStretch(w,u,v)}}this.CHTML.stretch=t;return t},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));return this.CHTML},CHTMLstretchCoreH:function(t,s){return this.Core().CHTMLstretchH(this.CHTMLcoreNode(t),s)},CHTMLcreateNode:function(s){if(!this.CHTML){this.CHTML={}}this.CHTML=a.BBOX.zero();if(this.href){s=a.addElement(s,"a",{href:this.href,isMathJax:true})}if(!this.CHTMLnodeID){this.CHTMLnodeID=a.GetID()}var t=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+a.idPostfix;return this.CHTMLhandleAttributes(a.addElement(s,"mjx-"+this.type,{id:t}))},CHTMLnodeElement:function(){if(!this.CHTMLnodeID){return null}return document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+a.idPostfix)},CHTMLlength2em:function(t,s){return a.length2em(t,s,this.CHTML.scale)},CHTMLhandleAttributes:function(v){if(this["class"]){if(v.className){v.className+=" "+this["class"]}else{v.className=this["class"]}}if(this.attrNames){var z=this.attrNames,u=d.nocopyAttributes,y=f.config.ignoreMMLattributes;var w=(this.type==="mstyle"?d.math.prototype.defaults:this.defaults);for(var t=0,s=z.length;t2){s.scriptlevel=2}x=Math.pow(this.Get("scriptsizemultiplier"),s.scriptlevel);s.scriptminsize=a.length2em(this.Get("scriptminsize"),0.8,1);if(x600?"bold":"normal")}var t=s.mathvariant;if(this.variantForm){t="-TeX-variant"}if(s.family&&!s.hasVariant){if(!s.weight&&s.mathvariant.match(/bold/)){s.weight="bold"}if(!s.style&&s.mathvariant.match(/italic/)){s.style="italic"}this.CHTMLvariant={fonts:[],noRemap:true,cache:{},style:{"font-family":s.family,"font-weight":s.weight||"normal","font-style":s.style||"normal"}};return}if(s.weight==="bold"){t={normal:d.VARIANT.BOLD,italic:d.VARIANT.BOLDITALIC,fraktur:d.VARIANT.BOLDFRAKTUR,script:d.VARIANT.BOLDSCRIPT,"sans-serif":d.VARIANT.BOLDSANSSERIF,"sans-serif-italic":d.VARIANT.SANSSERIFBOLDITALIC}[t]||t}else{if(s.weight==="normal"){t={bold:d.VARIANT.normal,"bold-italic":d.VARIANT.ITALIC,"bold-fraktur":d.VARIANT.FRAKTUR,"bold-script":d.VARIANT.SCRIPT,"bold-sans-serif":d.VARIANT.SANSSERIF,"sans-serif-bold-italic":d.VARIANT.SANSSERIFITALIC}[t]||t}}if(s.style==="italic"){t={normal:d.VARIANT.ITALIC,bold:d.VARIANT.BOLDITALIC,"sans-serif":d.VARIANT.SANSSERIFITALIC,"bold-sans-serif":d.VARIANT.SANSSERIFBOLDITALIC}[t]||t}else{if(s.style==="normal"){t={italic:d.VARIANT.NORMAL,"bold-italic":d.VARIANT.BOLD,"sans-serif-italic":d.VARIANT.SANSSERIF,"sans-serif-bold-italic":d.VARIANT.BOLDSANSSERIF}[t]||t}}this.CHTMLvariant=a.FONTDATA.VARIANT[t]||a.FONTDATA.VARIANT[d.VARIANT.NORMAL]},CHTMLbboxFor:function(s){if(this.data[s]&&this.data[s].CHTML){return this.data[s].CHTML}return a.BBOX.zero()},CHTMLdrawBBox:function(t,u){if(!u){u=this.CHTML}var s=a.Element("mjx-box",{style:{opacity:0.25,"margin-left":a.Em(-(u.w+(u.R||0)))}},[["mjx-box",{style:{height:a.Em(u.h),width:a.Em(u.w),"background-color":"red"}}],["mjx-box",{style:{height:a.Em(u.d),width:a.Em(u.w),"margin-left":a.Em(-u.w),"vertical-align":a.Em(-u.d),"background-color":"green"}}]]);if(t.nextSibling){t.parentNode.insertBefore(s,t.nextSibling)}else{t.parentNode.appendChild(s)}},CHTMLnotEmpty:function(s){while(s&&s.data.length<2&&(s.type==="mrow"||s.type==="texatom")){s=s.data[0]}return !!s}},{CHTMLautoload:function(){this.constructor.Augment({toCommonHTML:d.mbase.CHTMLautoloadFail});var s=a.autoloadDir+"/"+this.type+".js";f.RestartAfter(o.Require(s))},CHTMLautoloadFail:function(){throw Error("CommonHTML can't autoload '"+this.type+"'")},CHTMLautoloadList:{},CHTMLautoloadFile:function(s){if(d.mbase.CHTMLautoloadList.hasOwnProperty(s)){throw Error("CommonHTML can't autoload file '"+s+"'")}d.mbase.CHTMLautoloadList[s]=true;var t=a.autoloadDir+"/"+s+".js";f.RestartAfter(o.Require(t))},CHTMLstretchV:function(s,t){this.Core().CHTMLstretchV(s,t);this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.chars.Augment({toCommonHTML:function(t,s){this.CHTML=null;if(s==null){s={}}var u=this.toString();if(s.remap){u=s.remap(u,s.remapchars)}this.CHTMLhandleText(t,u,s.variant||this.parent.CHTMLvariant)}});d.entity.Augment({toCommonHTML:function(t,s){if(s==null){s={}}var u=this.toString();if(s.remapchars){u=s.remap(u,s.remapchars)}this.CHTMLhandleText(t,u,s.variant||this.parent.CHTMLvariant)}});d.math.Augment({toCommonHTML:function(x){x=this.CHTMLdefaultNode(x);if(this.CHTML.w<0){x.parentNode.style.width="0px";x.parentNode.style.marginRight=a.Em(this.CHTML.w)}var v=this.Get("alttext");if(v&&!x.getAttribute("aria-label")){x.setAttribute("aria-label",v)}if(this.CHTML.pwidth){x.parentNode.style.minWidth=this.CHTML.mwidth||a.Em(this.CHTML.w);x.parentNode.className="mjx-full-width "+x.parentNode.className;x.style.width=this.CHTML.pwidth}else{if(!this.isMultiline&&this.Get("display")==="block"){var u=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(u.indentalignfirst!==d.INDENTALIGN.INDENTALIGN){u.indentalign=u.indentalignfirst}if(u.indentalign===d.INDENTALIGN.AUTO){u.indentalign=r.displayAlign}if(u.indentshiftfirst!==d.INDENTSHIFT.INDENTSHIFT){u.indentshift=u.indentshiftfirst}if(u.indentshift==="auto"){u.indentshift="0"}var t=this.CHTMLlength2em(u.indentshift,a.cwidth);if(r.displayIndent!=="0"){var s=this.CHTMLlength2em(r.displayIndent,a.cwidth);t+=(u.indentalign===d.INDENTALIGN.RIGHT?-s:s)}var w=x.parentNode.parentNode.style;x.parentNode.style.textAlign=w.textAlign=u.indentalign;if(t){t*=a.em/a.outerEm;f.Insert(w,({left:{marginLeft:a.Em(t)},right:{marginRight:a.Em(-t)},center:{marginLeft:a.Em(t),marginRight:a.Em(-t)}})[u.indentalign])}}}return x}});d.mi.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&!a.isChar(t)){delete u.skew}if(u.r>u.w&&a.isChar(t)&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mn.Augment({CHTMLremapMinus:function(s){return s.replace(/^-/,"\u2212")},toCommonHTML:function(s){s=this.CHTMLdefaultNode(s,{childOptions:{remap:this.CHTMLremapMinus}});var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&!a.isChar(t)){delete u.skew}if(u.r>u.w&&a.isChar(t)&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mo.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLgetVariant();this.CHTMLhandleScale(v);a.BBOX.empty(this.CHTML);var t=this.getValues("displaystyle","largeop");t.variant=this.CHTMLvariant;t.text=this.data.join("");if(t.text==""){if(this.fence){v.style.width=a.Em(a.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(t);this.CHTMLadjustVariant(t);for(var u=0,s=this.data.length;u0){if(!this.hasValue("lspace")){t.lspace=0.15}if(!this.hasValue("rspace")){t.rspace=0.15}}var s=this,u=this.Parent();while(u&&u.isEmbellished()&&u.Core()===s){s=u;u=u.Parent();v=s.CHTMLnodeElement()}if(t.lspace){v.style.paddingLeft=a.Em(t.lspace)}if(t.rspace){v.style.paddingRight=a.Em(t.rspace)}this.CHTML.L=t.lspace;this.CHTML.R=t.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(u){var t=this.CoreParent();u.parent=t;if(a.isChar(u.text)&&t&&t.isa(d.munderover)){var v=t.data[t.over],s=t.data[t.under];if(v&&this===v.CoreMO()&&t.Get("accent")){u.remapchars=a.FONTDATA.REMAPACCENT}else{if(s&&this===s.CoreMO()&&t.Get("accentunder")){u.remapchars=a.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(t){var s=t.parent,u=(s&&s.isa(d.msubsup)&&this!==s.data[s.base]);if(t.largeop){t.mathvariant=(t.displaystyle?"-largeOp":"-smallOp")}if(u){t.remapchars=this.remapChars;if(t.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){t.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(s){s=s.firstChild;var t=a.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});s.insertBefore(t,s.firstChild)},CHTMLcenterOp:function(s){var u=this.CHTML;var t=(u.h-u.d)/2-a.TEX.axis_height;if(Math.abs(t)>0.001){s.style.verticalAlign=a.Em(-t)}u.h-=t;u.d+=t;if(u.r>u.w){u.ic=u.r-u.w;u.w=u.r;s.style.paddingRight=a.Em(u.ic)}},CHTMLcanStretch:function(w,u,v){if(!this.Get("stretchy")){return false}var x=this.data.join("");if(!a.isChar(x)){return false}var t={text:x};this.CHTMLadjustAccent(t);if(t.remapchars){x=t.remapchars[x]||x}x=a.FONTDATA.DELIMITERS[x.charCodeAt(0)];var s=(x&&x.dir===w.substr(0,1));if(s){s=(this.CHTML.h!==u||this.CHTML.d!==v||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(s){this.CHTML.stretch=true}}return s},CHTMLstretchV:function(v,y){var w=this.CHTMLnodeElement(),x=this.CHTML;var t=this.getValues("symmetric","maxsize","minsize");var u,s=a.TEX.axis_height;if(t.symmetric){u=2*Math.max(v-s,y+s)}else{u=v+y}t.maxsize=this.CHTMLlength2em(t.maxsize,x.h+x.d);t.minsize=this.CHTMLlength2em(t.minsize,x.h+x.d);u=Math.max(t.minsize,Math.min(t.maxsize,u));if(u!==x.sH){if(u!=t.minsize){u=[Math.max(u*a.TEX.delimiterfactor/1000,u-a.TEX.delimitershortfall),u]}while(w.firstChild){w.removeChild(w.firstChild)}this.CHTML=x=a.createDelimiter(w,this.data.join("").charCodeAt(0),u,x);x.sH=(u instanceof Array?u[1]:u);if(t.symmetric){u=(x.h+x.d)/2+s}else{u=(x.h+x.d)*v/(v+y)}u-=x.h;if(Math.abs(u)>0.05){w.style.verticalAlign=a.Em(u);x.h+=u;x.d-=u;x.t+=u;x.b-=u}}return this.CHTML},CHTMLstretchH:function(u,s){var v=this.CHTML;var t=this.getValues("maxsize","minsize","mathvariant","fontweight");if((t.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(t.fontweight)>=600)&&!this.Get("mathvariant",true)){t.mathvariant=d.VARIANT.BOLD}t.maxsize=this.CHTMLlength2em(t.maxsize,v.w);t.minsize=this.CHTMLlength2em(t.minsize,v.w);s=Math.max(t.minsize,Math.min(t.maxsize,s));if(s!==v.sW){while(u.firstChild){u.removeChild(u.firstChild)}this.CHTML=v=a.createDelimiter(u,this.data.join("").charCodeAt(0),s,v,t.mathvariant);v.sW=s}return this.CHTML}});d.mtext.Augment({CHTMLgetVariant:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){var u=(a.config.scale/100)/a.scale;var t={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:u,style:{"font-size":a.Percent(u)}};var s=this.Get("mathvariant");if(s.match(/bold/)){t.style["font-weight"]="bold"}if(s.match(/italic|-tex-mathit/)){t.style["font-style"]="italic"}if(s==="monospace"){t.className+=" MJXc-monospace-font"}if(s==="double-struck"){t.className+=" MJXc-double-struck-font"}if(s.match(/fraktur/)){t.className+=" MJXc-fraktur-font"}if(s.match(/sans-serif/)){t.className+=" MJXc-sans-serif-font"}if(s.match(/script/)){t.className+=" MJXc-script-font"}this.CHTMLvariant=t}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});d.merror.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var t=this.CHTML;t.rescale(0.9);t.h+=3/a.em;if(t.h>t.t){t.t=t.h}t.d+=3/a.em;if(t.d>t.b){t.b=t.d}t.w+=8/a.em;t.r=t.w;t.l=0;return s}});d.mspace.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);var t=this.getValues("height","depth","width");var s=this.CHTMLlength2em(t.width),u=this.CHTMLlength2em(t.height),y=this.CHTMLlength2em(t.depth);var x=this.CHTML;x.w=x.r=s;x.h=x.t=u;x.d=x.b=y;x.l=0;if(s<0){v.style.marginRight=a.Em(s);s=0}v.style.width=a.Em(s);v.style.height=a.Em(Math.max(0,u+y));if(y){v.style.verticalAlign=a.Em(-y)}this.CHTMLhandleBBox(v);this.CHTMLhandleColor(v);return v}});d.mpadded.Augment({toCommonHTML:function(t,F){var s;if(F&&F.stretch){t=t.firstChild;s=t.firstChild}else{t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:true});s=t.firstChild;t=a.addElement(t,"mjx-block");t.appendChild(s);a.addElement(t,"mjx-strut")}var z=this.CHTMLbboxFor(0);var D=this.getValues("width","height","depth","lspace","voffset");var B=0,A=0,C=z.w,u=z.h,v=z.d;s.style.width=0;s.style.margin=a.Em(-u)+" 0 "+a.Em(-v);if(D.width!==""){C=this.CHTMLdimen(D.width,"w",C,0)}if(D.height!==""){u=this.CHTMLdimen(D.height,"h",u,0)}if(D.depth!==""){v=this.CHTMLdimen(D.depth,"d",v,0)}if(D.voffset!==""){A=this.CHTMLdimen(D.voffset);if(A){s.style.position="relative";s.style.top=a.Em(-A)}}if(D.lspace!==""){B=this.CHTMLdimen(D.lspace);if(B){s.style.position="relative";s.style.left=a.Em(B)}}t.style.width=0;t.style.marginTop=a.Em(u-k);t.style.padding="0 "+a.Em(C)+" "+a.Em(v)+" 0";var E=a.BBOX({w:C,h:u,d:v,l:0,r:C,t:u,b:v,scale:this.CHTML.scale,rscale:this.CHTML.rscale});E.combine(z,B,A);E.w=C;E.h=u;E.d=v;this.CHTML=E;return t.parentNode},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLdimen:function(w,y,x,s){if(s==null){s=-i}w=String(w);var t=w.match(/width|height|depth/);var u=(t?this.CHTML[t[0].charAt(0)]:(y?this.CHTML[y]:0));var v=(this.CHTMLlength2em(w,u)||0);if(w.match(/^[-+]/)&&x!=null){v+=x}if(s!=null){v=Math.max(s,v)}return v}});d.munderover.Augment({toCommonHTML:function(w,G){var E=this.getValues("displaystyle","accent","accentunder","align");var u=this.data[this.base];if(!E.displaystyle&&u!=null&&(u.movablelimits||u.CoreMO().Get("movablelimits"))){return d.msubsup.prototype.toCommonHTML.call(this,w,t)}var B,z,s=[],t=false;if(G&&G.stretch){if(this.data[this.base]){u=a.getNode(w,"mjx-op")}if(this.data[this.under]){B=a.getNode(w,"mjx-under")}if(this.data[this.over]){z=a.getNode(w,"mjx-over")}s[0]=u;s[1]=B||z;s[2]=z;t=true}else{var y=["mjx-op","mjx-under","mjx-over"];if(this.over===1){y[1]=y[2]}w=this.CHTMLdefaultNode(w,{childNodes:y,noBBox:true,forceChild:true,minChildren:2});s[0]=u=w.removeChild(w.firstChild);s[1]=B=z=w.removeChild(w.firstChild);if(w.firstChild){s[2]=z=w.removeChild(w.firstChild)}}var x=[],v=this.CHTMLgetBBoxes(x,s,E);var F=x[this.base],C=this.CHTML;C.w=v;C.h=F.h;C.d=F.d;if(F.h<0.35){u.style.marginTop=a.Em(F.h-0.35)}if(E.accent&&F.hu){u=s}}if(u===-i){u=s}for(y=0;yD.w){D.skew+=(D.w-(A.x+u*A.w))/2}}}else{y=a.TEX.big_op_spacing1;x=a.TEX.big_op_spacing3;v=Math.max(y,x-Math.max(0,u*A.d))}A.x+=E/2;A.y=D.h+v+w+u*A.d;if(v){B.style.paddingBottom=a.Em(v/u)}if(w){B.style.paddingTop=a.Em(w/u)}return C},CHTMLaddUnderscript:function(B,z,E,D,t,A,s){var C=this.CHTML;var y,x,w=a.TEX.big_op_spacing5,v;var F=z[this.under],u=F.rscale;if(!s){a.addElement(t,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);t.firstChild.firstChild.firstChild.appendChild(A);t.firstChild.lastChild.appendChild(B)}if(F.D){F.d=F.D}if(F.d<0){B.firstChild.style.verticalAlign="top";t.firstChild.style.marginBottom=a.Em(F.d)}if(E.accentunder){v=2*a.TEX.rule_thickness;w=0}else{y=a.TEX.big_op_spacing2;x=a.TEX.big_op_spacing4;v=Math.max(y,x-u*F.h)}F.x=-D/2;F.y=-(C.d+v+w+u*F.h);if(v){B.style.paddingTop=a.Em(v/u)}if(w){B.style.paddingBottom=a.Em(w/u)}},CHTMLplaceBoxes:function(s,B,A,E,z){var t=this.CHTML.w,y,v=z.length,x;var D=a.BBOX.zero();D.scale=this.CHTML.scale;D.rscale=this.CHTML.rscale;z[this.base].x=z[this.base].y=0;var F=i;for(y=0;y0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=a.Em(N/B);z.style.paddingBottom=a.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=a.Em(Y/w);z.style.paddingRight=a.Em(N/w);E.style.verticalAlign=a.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.mfrac.Augment({toCommonHTML:function(N){N=this.CHTMLdefaultNode(N,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var x=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var O=x.displaystyle;var D=N.firstChild,w=N.lastChild;var y=a.addElement(N,"mjx-box");y.appendChild(D);y.appendChild(w);N.appendChild(y);if(x.numalign!=="center"){D.style.textAlign=x.numalign}if(x.denomalign!=="center"){w.style.textAlign=x.denomalign}var P=this.CHTMLbboxFor(0),B=this.CHTMLbboxFor(1),C=a.BBOX.empty(this.CHTML),F=P.rscale,z=B.rscale;x.linethickness=Math.max(0,a.thickness2em(x.linethickness||"0",C.scale));var M=a.TEX.min_rule_thickness/a.em,T=a.TEX.axis_height;var J=x.linethickness,L,K,I,G;if(x.bevelled){y.className+=" MJXc-bevelled";var S=(O?0.4:0.15);var E=Math.max(F*(P.h+P.d),z*(B.h+B.d))+2*S;var R=a.Element("mjx-bevel");y.insertBefore(R,w);var s=a.createDelimiter(R,47,E);I=F*(P.d-P.h)/2+T+S;G=z*(B.d-B.h)/2+T-S;if(I){D.style.verticalAlign=a.Em(I/F)}if(G){w.style.verticalAlign=a.Em(G/z)}R.style.marginLeft=R.style.marginRight=a.Em(-S/2);C.combine(P,0,I);C.combine(s,F*P.w-S/2,0);C.combine(B,F*P.w+s.w-S,G);C.clean()}else{y.className+=" MJXc-stacked";if(O){I=a.TEX.num1;G=a.TEX.denom1}else{I=(J===0?a.TEX.num3:a.TEX.num2);G=a.TEX.denom2}if(J===0){L=Math.max((O?7:3)*a.TEX.rule_thickness,2*M);K=(I-P.d*F)-(B.h*z-G);if(KD){s=((A.h+A.d)-(D-G))/2}D=F.h+s+G;var B=this.CHTMLaddRoot(w,A,A.h+A.d-D);v.style.paddingTop=a.Em(s);v.style.borderTop=a.Px(y*F.scale,1)+" solid";E.style.paddingTop=a.Em(2*G-y);F.h+=s+2*G;C.combine(A,B,D-A.h);C.combine(F,B+A.w,0);C.clean();return w},CHTMLaddRoot:function(){return 0},CHTMLhandleBBox:function(s){var t=this.CHTMLbboxFor(0);delete t.pwidth;this.SUPER(arguments).CHTMLhandleBBox.apply(this,arguments)}});d.mroot.Augment({toCommonHTML:d.msqrt.prototype.toCommonHTML,CHTMLhandleBBox:d.msqrt.prototype.CHTMLhandleBBox,CHTMLaddRoot:function(A,u,v){if(!this.data[1]){return}var z=this.CHTML,B=this.data[1].CHTML,x=A.firstChild;var s=B.rscale;var t=this.CHTMLrootHeight(B,u,s)-v;var y=Math.min(B.w,B.r);var C=Math.max(y,u.offset/s);if(t){x.style.verticalAlign=a.Em(t/s)}if(C>y){x.firstChild.style.paddingLeft=a.Em(C-y)}C-=u.offset/s;x.style.width=a.Em(C);z.combine(B,0,t);return C*s},CHTMLrootHeight:function(u,s,t){return 0.45*(s.h+s.d-0.9)+s.offset+Math.max(0,u.d-0.075)}});d.mfenced.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);this.CHTMLaddChild(v,"open",{});for(var u=0,s=this.data.length;ua.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(s,t){this.CHTMLstretchChildV(this.CoreIndex(),s,t);return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLstretchChildH(this.CoreIndex(),s,t);return this.CHTML}});d.TeXAtom.Augment({toCommonHTML:function(x,w){if(!w||!w.stretch){x=this.CHTMLdefaultNode(x)}if(this.texClass===d.TEXCLASS.VCENTER){var s=a.TEX.axis_height,u=this.CHTML;var t=s-(u.h+u.d)/2+u.d;if(Math.abs(t)>0.001){x.style.verticalAlign=a.Em(t);u.h+=t;u.t+=t;u.d-=t;u.b-=t}}return x},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.semantics.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);if(this.data[0]){this.data[0].toCommonHTML(s);this.CHTMLupdateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(s)}return s}});d.annotation.Augment({toCommonHTML:function(s){return this.CHTMLcreateNode(s)}});d["annotation-xml"].Augment({toCommonHTML:d.mbase.CHTMLautoload});d.ms.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mglyph.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.menclose.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.maction.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mmultiscripts.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mtable.Augment({toCommonHTML:d.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(f.config.menuSettings.zoom!=="None"){o.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML); +MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var g="2.7.6";var b=MathJax.ElementJax.mml,a=MathJax.Hub.config,e=MathJax.OutputJax.CommonHTML,d=MathJax.Hub.SplitList;var c=-1,f=1000000;b.mtable.Augment({toCommonHTML:function(l){var m={rows:[],labels:[],labeled:false};l=this.CHTMLdefaultNode(l,{noBBox:true,childOptions:m});var k=e.Element("mjx-table");while(l.firstChild){k.appendChild(l.firstChild)}l.appendChild(k);var h=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width","side","minlabelspacing","useHeight");var j=e.TEX.min_rule_thickness/e.em;m.t=e.Px(j*this.CHTML.scale,1);this.CHTMLgetBoxSizes(h,m);this.CHTMLgetAttributes(h,m);this.CHTMLadjustCells(h,m);if(h.frame){k.style.border=m.t+" "+h.frame}this.CHTMLalignV(h,m,l);this.CHTMLcolumnWidths(h,m,l);this.CHTMLstretchCells(h,m);if(m.labeled){this.CHTMLaddLabels(h,m,l,k)}var i=this.CHTML;i.w=i.r=m.R;i.h=i.t=m.T-m.B;i.d=i.b=m.B;if(!h.frame&&!i.pwidth){l.style.padding="0 "+e.Em(1/6);i.L=i.R=1/6}this.CHTMLhandleSpace(l);this.CHTMLhandleBBox(l);this.CHTMLhandleColor(l);return l},CHTMLgetBoxSizes:function(z,k){var r=e.FONTDATA.lineH*z.useHeight,t=e.FONTDATA.lineD*z.useHeight;var y=[],h=[],l=[],w=-1,q,n;for(q=0,n=this.data.length;qw){w=p}}var u=B.data[p-A].CHTML;if(u.h>y[q]){y[q]=u.h}if(u.d>h[q]){h[q]=u.d}if(u.w>l[p]){l[p]=u.w}}}if(z.equalrows){k.HD=true;var x=Math.max.apply(Math,y);var o=Math.max.apply(Math,h);for(q=0,n=y.length;qt||m<=0){m=null}}else{w.align=this.defaults.align}var p=0,l=0,u=e.TEX.axis_height;if(w.fspace){p+=k.FSPACE[1]}if(w.frame){p+=2/e.em;l+=1/e.em}for(var q=0;q=m){l+=r+s+x[q]}}}if(!m){l=({top:p,bottom:0,center:p/2,baseline:p/2,axis:p/2-u})[w.align]}if(l){o.style.verticalAlign=e.Em(-l)}k.T=p;k.B=l},CHTMLcolumnWidths:function(l,r,A){var I=r.CWIDTH,K=r.CSPACE,u=r.J,F;var G=0,n=false,y=l.width.match(/%$/);var H,B,v;if(l.width!=="auto"&&!y){G=Math.max(0,this.CHTMLlength2em(l.width,r.R));n=true}if(l.equalcolumns){if(y){var z=e.Percent(1/(u+1));for(F=0;F<=u;F++){I[F]=z}}else{v=Math.max.apply(Math,r.W);if(l.width!=="auto"){var q=(l.fspace?r.FSPACE[0]+(l.frame?2/e.em:0):0);for(F=0;F<=u;F++){q+=K[F]}v=Math.max((G-q)/(u+1),v)}v=e.Em(v);for(F=0;F<=u;F++){I[F]=v}}n=true}var E=0;if(l.fspace){E=r.FSPACE[0]}var s=[],D=[],h=[],o=[];var t=r.rows[0];for(F=0;F<=u;F++){o[F]=r.W[F];if(I[F]==="auto"){s.push(F)}else{if(I[F]==="fit"){D.push(F)}else{if(I[F].match(/%$/)){h.push(F)}else{o[F]=this.CHTMLlength2em(I[F],o[F])}}}E+=o[F]+K[F];if(t[F]){t[F].style.width=e.Em(o[F])}}if(l.frame){E+=2/e.em}var C=(D.length>0);if(n){if(y){for(F=0;F<=u;F++){cell=t[F].style;if(I[F]==="auto"&&!C){cell.width=""}else{if(I[F]==="fit"){cell.width=""}else{if(I[F].match(/%$/)){cell.width=I[F]}else{cell.minWidth=cell.maxWidth=cell.width}}}}}else{if(G>E){var k=0;for(H=0,B=h.length;HE&&D.length){var x=(G-E)/D.length;for(H=0,B=D.length;Ht*z){z=t*p}z+=y;z*=t;D+=z}else{D+=p-t*z+n;z-=t*n;z*=-t}}var o=e.addElement(w,"mjx-box",{style:{width:"100%","text-align":q.indentalign}});o.appendChild(B);var C=e.Element("mjx-itable");B.style.display="inline-table";if(!B.style.width){B.style.width="auto"}C.style.verticalAlign="top";B.style.verticalAlign=e.Em(k.T-k.B-k.H[0]);w.style.verticalAlign="";if(z){if(q.indentalign===b.INDENTALIGN.CENTER){B.style.marginLeft=e.Em(z);B.style.marginRight=e.Em(-z)}else{var u="margin"+(q.indentalign===b.INDENTALIGN.RIGHT?"Right":"Left");B.style[u]=e.Em(z)}}if(k.CALIGN[c]==="left"){w.insertBefore(C,o);C.style.marginRight=e.Em(-k.W[c]-y);if(y){C.style.marginLeft=e.Em(y)}}else{w.appendChild(C);C.style.marginLeft=e.Em(-k.W[c]+y)}var l=k.labels,j=0;if(h.fspace){j=k.FSPACE[0]+(h.frame?1/e.em:0)}for(var x=0,v=l.length;x1){h.h*=k;h.d*=k}}}else{h.w=Math.max(h.w,this.CHTMLlength2em(j,h.w))}}}}return l}});MathJax.Hub.Startup.signal.Post("CommonHTML mtable Ready");MathJax.Ajax.loadComplete(e.autoloadDir+"/mtable.js")}); +(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/MML_CHTML-full.js"); diff --git a/revisions_report_files/mathjax-27/config/MML_CHTML.js b/revisions_report_files/mathjax-27/config/MML_CHTML.js new file mode 100644 index 0000000..c4b85cc --- /dev/null +++ b/revisions_report_files/mathjax-27/config/MML_CHTML.js @@ -0,0 +1,49 @@ +/* + * /MathJax/config/MML_CHTML.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.mml2jax={version:"2.7.6",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var d,b;if(typeof(document.namespaces)!=="undefined"){try{for(d=0,b=document.namespaces.length;d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +(function(d,h,l,g,m,b,j){var p="2.7.6";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Menu_Button .MathJax_Hover_Arrow":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"4px","-webkit-border-radius":"4px","-moz-border-radius":"4px","-khtml-border-radius":"4px","font-family":"'Courier New',Courier","font-size":"9px",color:"#F0F0F0"},".MathJax_Menu_Button .MathJax_Hover_Arrow span":{display:"block","background-color":"#AAA",border:"1px solid","border-radius":"3px","line-height":0,padding:"4px"},".MathJax_Hover_Arrow:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_Hover_Arrow:hover span":{"background-color":"#CCC!important"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",KEY:{RETURN:13,ESCAPE:27,SPACE:32,LEFT:37,UP:38,RIGHT:39,DOWN:40},Mousedown:function(q){return n.Handler(q,"Mousedown",this)},Mouseup:function(q){return n.Handler(q,"Mouseup",this)},Mousemove:function(q){return n.Handler(q,"Mousemove",this)},Mouseover:function(q){return n.Handler(q,"Mouseover",this)},Mouseout:function(q){return n.Handler(q,"Mouseout",this)},Click:function(q){return n.Handler(q,"Click",this)},DblClick:function(q){return n.Handler(q,"DblClick",this)},Menu:function(q){return n.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return n.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}else{q.returnValue=false}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true}return false},Keydown:function(r,q){if(!r){r=window.event}if(r.keyCode===n.KEY.SPACE){n.ContextMenu(r,this)}},ContextMenu:function(t,E,w){var B=b[E.jaxID],v=B.getJaxFromMath(E);var F=(B.config.showMathMenu!=null?B:d).config.showMathMenu;if(!F||(k.context!=="MathJax"&&!w)){return}if(c.msieEventBug){t=window.event||t}n.ClearSelection();f.ClearHoverTimer();if(v.hover){if(v.hover.remove){clearTimeout(v.hover.remove);delete v.hover.remove}v.hover.nofade=true}var u=MathJax.Menu;var G,D;if(u){if(u.loadingDomain){return n.False(t)}G=m.loadDomain("MathMenu");if(!G){u.jax=v;var r=u.menu.Find("Show Math As").submenu;r.items[0].name=v.sourceMenuTitle;r.items[0].format=(v.sourceMenuFormat||"MathML");r.items[1].name=j[v.inputJax].sourceMenuTitle;r.items[5].disabled=!j[v.inputJax].annotationEncoding;var A=r.items[2];A.disabled=true;var q=A.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var z=0,y=q.length;z0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(c,d){var a;var b=function(e){return MathJax.Localization._.apply(MathJax.Localization,[["MathML",e]].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(f,e){this.Parse(f,e)},Parse:function(h,e){var j;if(typeof h!=="string"){j=h.parentNode}else{j=c.ParseXML(this.preProcessMath.call(this,h));if(j==null){c.Error(["ErrorParsingMathML","Error parsing MathML"])}}var g=j.getElementsByTagName("parsererror")[0];if(g){c.Error(["ParsingError","Error parsing MathML: %1",g.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")])}if(j.childNodes.length!==1){c.Error(["MathMLSingleElement","MathML must be formed by a single element"])}if(j.firstChild.nodeName.toLowerCase()==="html"){var f=j.getElementsByTagName("h1")[0];if(f&&f.textContent==="XML parsing error"&&f.nextSibling){c.Error(["ParsingError","Error parsing MathML: %1",String(f.nextSibling.nodeValue).replace(/fatal parsing error: /,"")])}}if(j.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){c.Error(["MathMLRootElement","MathML must be formed by a element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/MML_CHTML.js"); diff --git a/revisions_report_files/mathjax-27/config/MML_SVG-full.js b/revisions_report_files/mathjax-27/config/MML_SVG-full.js new file mode 100644 index 0000000..96eca17 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/MML_SVG-full.js @@ -0,0 +1,53 @@ +/* + * /MathJax/config/MML_SVG-full.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/SVG/jax.js", + "[MathJax]/jax/output/SVG/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.mml2jax={version:"2.7.6",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var d,b;if(typeof(document.namespaces)!=="undefined"){try{for(d=0,b=document.namespaces.length;d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +(function(d,h,l,g,m,b,j){var p="2.7.6";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Menu_Button .MathJax_Hover_Arrow":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"4px","-webkit-border-radius":"4px","-moz-border-radius":"4px","-khtml-border-radius":"4px","font-family":"'Courier New',Courier","font-size":"9px",color:"#F0F0F0"},".MathJax_Menu_Button .MathJax_Hover_Arrow span":{display:"block","background-color":"#AAA",border:"1px solid","border-radius":"3px","line-height":0,padding:"4px"},".MathJax_Hover_Arrow:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_Hover_Arrow:hover span":{"background-color":"#CCC!important"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",KEY:{RETURN:13,ESCAPE:27,SPACE:32,LEFT:37,UP:38,RIGHT:39,DOWN:40},Mousedown:function(q){return n.Handler(q,"Mousedown",this)},Mouseup:function(q){return n.Handler(q,"Mouseup",this)},Mousemove:function(q){return n.Handler(q,"Mousemove",this)},Mouseover:function(q){return n.Handler(q,"Mouseover",this)},Mouseout:function(q){return n.Handler(q,"Mouseout",this)},Click:function(q){return n.Handler(q,"Click",this)},DblClick:function(q){return n.Handler(q,"DblClick",this)},Menu:function(q){return n.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return n.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}else{q.returnValue=false}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true}return false},Keydown:function(r,q){if(!r){r=window.event}if(r.keyCode===n.KEY.SPACE){n.ContextMenu(r,this)}},ContextMenu:function(t,E,w){var B=b[E.jaxID],v=B.getJaxFromMath(E);var F=(B.config.showMathMenu!=null?B:d).config.showMathMenu;if(!F||(k.context!=="MathJax"&&!w)){return}if(c.msieEventBug){t=window.event||t}n.ClearSelection();f.ClearHoverTimer();if(v.hover){if(v.hover.remove){clearTimeout(v.hover.remove);delete v.hover.remove}v.hover.nofade=true}var u=MathJax.Menu;var G,D;if(u){if(u.loadingDomain){return n.False(t)}G=m.loadDomain("MathMenu");if(!G){u.jax=v;var r=u.menu.Find("Show Math As").submenu;r.items[0].name=v.sourceMenuTitle;r.items[0].format=(v.sourceMenuFormat||"MathML");r.items[1].name=j[v.inputJax].sourceMenuTitle;r.items[5].disabled=!j[v.inputJax].annotationEncoding;var A=r.items[2];A.disabled=true;var q=A.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var z=0,y=q.length;z0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(c,d){var a;var b=function(e){return MathJax.Localization._.apply(MathJax.Localization,[["MathML",e]].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(f,e){this.Parse(f,e)},Parse:function(h,e){var j;if(typeof h!=="string"){j=h.parentNode}else{j=c.ParseXML(this.preProcessMath.call(this,h));if(j==null){c.Error(["ErrorParsingMathML","Error parsing MathML"])}}var g=j.getElementsByTagName("parsererror")[0];if(g){c.Error(["ParsingError","Error parsing MathML: %1",g.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")])}if(j.childNodes.length!==1){c.Error(["MathMLSingleElement","MathML must be formed by a single element"])}if(j.firstChild.nodeName.toLowerCase()==="html"){var f=j.getElementsByTagName("h1")[0];if(f&&f.textContent==="XML parsing error"&&f.nextSibling){c.Error(["ParsingError","Error parsing MathML: %1",String(f.nextSibling.nodeValue).replace(/fatal parsing error: /,"")])}}if(j.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){c.Error(["MathMLRootElement","MathML must be formed by a element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g div":{display:"inline-block"},".mjx-svg-href":{fill:"blue",stroke:"blue"},".MathJax_SVG_Processing":{visibility:"hidden",position:"absolute",top:0,left:0,width:0,height:0,overflow:"hidden",display:"block!important"},".MathJax_SVG_Processed":{display:"none!important"},".MathJax_SVG_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_SVG_test.mjx-test-display":{display:"table!important"},".MathJax_SVG_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_SVG_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_SVG_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .MathJax_SVG_left_box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .MathJax_SVG_right_box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .MathJax_SVG_right_box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_SVG_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}}},hideProcessedMath:true,fontNames:["TeX","STIX","STIX-Web","Asana-Math","Gyre-Termes","Gyre-Pagella","Latin-Modern","Neo-Euler"],Config:function(){this.SUPER(arguments).Config.apply(this,arguments);var p=e.config.menuSettings,o=this.config,n=p.font;if(p.scale){o.scale=p.scale}if(n&&n!=="Auto"){n=n.replace(/(Local|Web|Image)$/i,"");n=n.replace(/([a-z])([A-Z])/,"$1-$2");this.fontInUse=n}else{this.fontInUse=o.font||"TeX"}if(this.fontNames.indexOf(this.fontInUse)<0){this.fontInUse="TeX"}this.fontDir+="/"+this.fontInUse;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){k=MathJax.Extension.MathEvents.Event;c=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=k.ContextMenu;this.Mousedown=k.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=g.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=g.addElement(this.hiddenDiv,"div",{id:"MathJax_SVG_Hidden"});var n=g.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;this.hiddenDiv.removeChild(n);this.textSVG=this.Element("svg");l.GLYPH.defs=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});this.TestSpan=g.Element("span",{className:"MathJax_SVG_test"},[["span",{className:"MathJax_SVG_left_box"}],["span",{className:"MathJax_SVG_ex_box"}],["span",{className:"MathJax_SVG_right_box"}]]);return j.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){var n=document.body.appendChild(this.TestSpan.cloneNode(true));n.className+=" mjx-test-inline mjx-test-default";this.defaultEx=n.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,n.lastChild.offsetLeft-n.firstChild.offsetLeft-2);document.body.removeChild(n)},preTranslate:function(s){var r=s.jax[this.id],D,z=r.length,y,G,w,C,u,E,p,F,o,v,t=false,A,q=this.config.linebreaks.automatic,x=this.config.linebreaks.width;if(q){t=(x.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(t){x=x.replace(/\s*container\s*/,"")}else{v=this.defaultWidth}if(x===""){x="100%"}}else{v=100000}for(D=0;D=s.SVGlast+s.SVGchunk){this.postTranslate(s,true);s.SVGchunk=Math.floor(s.SVGchunk*this.config.EqnChunkFactor);s.SVGdelay=true}}},postTranslate:function(t,q){var o=t.jax[this.id];if(!this.hideProcessedMath){return}for(var r=t.SVGlast,n=t.SVGeqn;r=55296&&q<56319){v++;q=(((q-55296)<<10)+(D.charCodeAt(v)-56320))+65536;if(this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(q,u);q=y.n;u=y.variant}}else{o=this.FONTDATA.RANGES;for(p=0,A=o.length;p=o[p].low&&q<=o[p].high){if(o[p].remap&&o[p].remap[q]){q=z+o[p].remap[q]}else{if(o[p].remapOnly){break}q=q-o[p].low+z;if(o[p].add){q+=o[p].add}}if(u["variant"+o[p].offset]){u=this.FONTDATA.VARIANT[u["variant"+o[p].offset]]}break}}}if(u.remap&&u.remap[q]){q=u.remap[q];if(u.remap.variant){u=this.FONTDATA.VARIANT[u.remap.variant]}}else{if(this.FONTDATA.REMAP[q]&&!u.noRemap){q=this.FONTDATA.REMAP[q]}}if(h(q)){u=this.FONTDATA.VARIANT[q[1]];q=q[0]}if(typeof(q)==="string"){D=q+D.substr(v+1);s=D.length;v=-1;continue}r=this.lookupChar(u,q);B=r[q];if(B){if((B[5]&&B[5].space)||(B[5]===""&&B[0]+B[1]===0)){x.w+=B[2]}else{B=[t,r.id+"-"+q.toString(16).toUpperCase()].concat(B);x.Add(l.GLYPH.apply(l,B),x.w,0)}}else{if(this.FONTDATA.DELIMITERS[q]){B=this.createDelimiter(q,0,1,r);x.Add(B,x.w,(this.FONTDATA.DELIMITERS[q].dir==="V"?B.d:0))}else{if(q<=65535){B=String.fromCharCode(q)}else{z=q-65536;B=String.fromCharCode((z>>10)+55296)+String.fromCharCode((z&1023)+56320)}var w=l.TEXT(t*100/a.config.scale,B,{"font-family":u.defaultFamily||a.config.undefinedFamily,"font-style":(u.italic?"italic":""),"font-weight":(u.bold?"bold":"")});if(u.h!=null){w.h=u.h}if(u.d!=null){w.d=u.d}B=l.G();B.Add(w);x.Add(B,x.w,0);e.signal.Post(["SVG Jax - unknown char",q,u])}}}if(a.isChar(D)&&r.skew&&r.skew[q]){x.skew=r.skew[q]*1000}if(x.element.childNodes.length===1&&!x.element.firstChild.getAttribute("x")){x.element=x.element.firstChild;x.removeable=false;x.scale=t}return x},lookupChar:function(r,u){var q,o;if(!r.FONTS){var t=this.FONTDATA.FONTS;var s=(r.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(s instanceof Array)){s=[s]}if(r.fonts!=s){r.fonts=s}r.FONTS=[];for(q=0,o=s.length;q=55296&&p<56319)},findBlock:function(o,s){if(o.Ranges){for(var r=0,n=o.Ranges.length;r=0;p--){if(o.Ranges[p][2]==q){o.Ranges.splice(p,1)}}this.loadFont(o.directory+"/"+q+".js")}}}},loadFont:function(n){e.RestartAfter(j.Require(this.fontDir+"/"+n))},createDelimiter:function(n,p,s,q){if(!s){s=1}var u=l.G();if(!n){u.Clean();delete u.element;u.w=u.r=this.TeX.nulldelimiterspace*s;return u}if(!(p instanceof Array)){p=[p,p]}var v=p[1];p=p[0];var o={alias:n};while(o.alias){n=o.alias;o=this.FONTDATA.DELIMITERS[n];if(!o){o={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(o.load){e.RestartAfter(j.Require(this.fontDir+"/fontdata-"+o.load+".js"))}for(var t=0,r=o.HW.length;t=p-10-a.config.blacker||(t==r-1&&!o.stretch)){if(o.HW[t][2]){s*=o.HW[t][2]}if(o.HW[t][3]){n=o.HW[t][3]}return this.createChar(s,[n,o.HW[t][1]],q).With({stretched:true})}}if(o.stretch){this["extendDelimiter"+o.dir](u,v,o.stretch,s,q)}return u},createChar:function(u,s,p){var t="",r={fonts:[s[1]],noRemap:true};if(p&&p===i.VARIANT.BOLD){r.fonts=[s[1]+"-bold",s[1]]}if(typeof(s[1])!=="string"){r=s[1]}if(s[0] instanceof Array){for(var q=0,n=s[0].length;qt){var n=this.createChar(q,o.ext,p);var r=(o.mid?2:1),x=(C-t)/r,D=(x+100)/(n.h+n.d);while(r-->0){var v=a.Element("g",{transform:"translate("+n.y+","+(z-D*n.h+50+n.y)+") scale(1,"+D+")"});v.appendChild(n.element.cloneNode(false));u.element.appendChild(v);z-=x;if(o.mid&&r){u.Add(B,0,z-B.h);z-=(B.h+B.d)}}}else{if(o.mid){z+=(t-C)/2;u.Add(B,0,z-B.h);z+=-(B.h+B.d)+(t-C)/2}else{z+=(t-C)}}u.Add(w,0,z-w.h);u.Clean();u.scale=q;u.isMultiChar=true},extendDelimiterH:function(v,q,o,t,p){var r=this.createChar(t,(o.left||o.rep),p);var E=this.createChar(t,(o.right||o.rep),p);v.Add(r,-r.l,0);var D=(r.r-r.l)+(E.r-E.l),B=r.r-r.l;if(o.mid){var C=this.createChar(t,o.mid,p);D+=C.w}if(o.min&&qD){var A=this.createChar(t,o.rep,p),n=o.fuzz||0;var u=(o.mid?2:1),z=(q-D)/u,F=(z+n)/(A.r-A.l);while(u-->0){var y=a.Element("g",{transform:"translate("+(B-n/2-F*A.l+A.x)+","+A.y+") scale("+F+",1)"});y.appendChild(A.element.cloneNode(false));v.element.appendChild(y);B+=z;if(o.mid&&u){v.Add(C,B,0);B+=C.w}}}else{if(o.mid){B-=(D-q)/2;v.Add(C,B,0);B+=C.w-(D-q)/2}else{B-=(D-q)}}v.Add(E,B-E.l,0);v.Clean();v.scale=t;v.isMultiChar=true},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:300,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,NBSP:"\u00A0"});var l=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(n){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,n)}},With:function(n){return e.Insert(this,n)},Add:function(q,w,v,n,u){if(w){q.x+=w}if(v){q.y+=v}if(q.element){if(q.removeable&&q.element.childNodes.length===1&&q.n===1){var o=q.element.firstChild,s=o.nodeName.toLowerCase();if(s==="use"||s==="rect"){q.element=o;q.scale=q.childScale;var t=q.childX,r=q.childY;q.x+=t;q.y+=r;q.h-=r;q.d+=r;q.H-=r;q.D+=r;q.w-=t;q.r-=t;q.l+=t;q.removeable=false;o.setAttribute("x",Math.floor(q.x/q.scale));o.setAttribute("y",Math.floor(q.y/q.scale))}}if(Math.abs(q.x)<1&&Math.abs(q.y)<1){q.remove=q.removeable}else{s=q.element.nodeName.toLowerCase();if(s==="g"){if(!q.element.firstChild){q.remove=q.removeable}else{q.element.setAttribute("transform","translate("+Math.floor(q.x)+","+Math.floor(q.y)+")")}}else{if(s==="line"||s==="polygon"||s==="path"||s==="a"){var p=q.element.getAttribute("transform")||"";if(p){p=" "+p}p="translate("+Math.floor(q.x)+","+Math.floor(q.y)+")"+p;q.element.setAttribute("transform",p)}else{q.element.setAttribute("x",Math.floor(q.x/q.scale));q.element.setAttribute("y",Math.floor(q.y/q.scale))}}}if(q.remove){this.n+=q.n;while(q.element.firstChild){if(u&&this.element.firstChild){this.element.insertBefore(q.element.firstChild,this.element.firstChild)}else{this.element.appendChild(q.element.firstChild)}}}else{if(u){this.element.insertBefore(q.element,this.element.firstChild)}else{this.element.appendChild(q.element)}}delete q.element}if(q.hasIndent){this.hasIndent=q.hasIndent}if(q.tw!=null){this.tw=q.tw}if(q.d-q.y>this.d){this.d=q.d-q.y;if(this.d>this.D){this.D=this.d}}if(q.y+q.h>this.h){this.h=q.y+q.h;if(this.h>this.H){this.H=this.h}}if(q.D-q.y>this.D){this.D=q.D-q.y}if(q.y+q.H>this.H){this.H=q.y+q.H}if(q.x+q.lthis.r){this.r=q.x+q.r}if(n||q.x+q.w+(q.X||0)>this.w){this.w=q.x+q.w+(q.X||0)}this.childScale=q.scale;this.childX=q.x;this.childY=q.y;this.n++;return q},Align:function(r,s,q,p,o){q=({left:q,center:(this.w-r.w)/2,right:this.w-r.w-q})[s]||0;var n=this.w;this.Add(r,q+(o||0),p);this.w=n},Clean:function(){if(this.h===-a.BIGDIMEN){this.h=this.d=this.l=0}return this}});l.ROW=l.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(o){var n=o.toSVG();this.svg.push(n);if(o.SVGcanStretch("Vertical")){n.mml=o}if(n.h+n.y>this.sh){this.sh=n.h+n.y}if(n.d-n.y>this.sd){this.sd=n.d-n.y}},Stretch:function(){for(var q=0,n=this.svg.length;qo.w&&a.isChar(r)&&!q.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGchildSVG:function(n){return(this.data[n]?this.data[n].toSVG():l())},SVGdataStretched:function(o,n,p){this.SVGdata={HW:n,D:p};if(!this.data[o]){return l()}if(p!=null){return this.data[o].SVGstretchV(n,p)}if(n!=null){return this.data[o].SVGstretchH(n)}return this.data[o].toSVG()},SVGsaveData:function(n){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=n.w,this.SVGdata.x=n.x;this.SVGdata.h=n.h,this.SVGdata.d=n.d;if(n.y){this.SVGdata.h+=n.y;this.SVGdata.d-=n.y}if(n.X!=null){this.SVGdata.X=n.X}if(n.tw!=null){this.SVGdata.tw=n.tw}if(n.skew){this.SVGdata.skew=n.skew}if(n.ic){this.SVGdata.ic=n.ic}if(this["class"]){n.removeable=false;a.Element(n.element,{"class":this["class"]})}if(this.id){n.removeable=false;a.Element(n.element,{id:this.id})}if(this.href){this.SVGaddHref(n)}if(a.config.addMMLclasses){this.SVGaddClass(n.element,"mjx-svg-"+this.type);n.removeable=false}var o=this.style;if(o&&n.element){n.element.style.cssText=o;if(n.element.style.fontSize){n.element.style.fontSize=""}n.element.style.border=n.element.style.padding="";if(n.removeable){n.removeable=(n.element.style.cssText==="")}}this.SVGaddAttributes(n)},SVGaddClass:function(p,n){var o=p.getAttribute("class");p.setAttribute("class",(o?o+" ":"")+n)},SVGaddAttributes:function(o){if(this.attrNames){var u=this.attrNames,q=i.nocopyAttributes,t=e.config.ignoreMMLattributes;var r=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var p=0,n=u.length;p600?"bold":"normal")}return o},SVGhandleSpace:function(q){if(this.hasMMLspacing()){if(this.type!=="mo"){return}var p=this.getValues("scriptlevel","lspace","rspace");if(p.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var o=this.SVGgetMu(q);p.lspace=Math.max(0,a.length2em(p.lspace,o));p.rspace=Math.max(0,a.length2em(p.rspace,o));var n=this,r=this.Parent();while(r&&r.isEmbellished()&&r.Core()===n){n=r;r=r.Parent()}if(p.lspace){q.x+=p.lspace}if(p.rspace){q.X=p.rspace}}}else{var s=this.texSpacing();this.SVGgetScale();if(s!==""){q.x+=a.length2em(s,this.scale)*this.mscale}}},SVGhandleColor:function(r){var A=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!A.color){A.color=this.styles.color}if(A.color&&!this.mathcolor){A.mathcolor=A.color}if(A.mathcolor){a.Element(r.element,{fill:A.mathcolor,stroke:A.mathcolor});r.removeable=false}var v=(this.styles||{}).border,y=(this.styles||{}).padding,w=((v||{}).left||0),t=((y||{}).left||0),n;A.background=(this.mathbackground||this.background||(this.styles||{}).background||i.COLOR.TRANSPARENT);if(w+t){var o=l();for(n in r){if(r.hasOwnProperty(n)){o[n]=r[n]}}o.x=0;o.y=0;r.element=a.Element("g");r.removeable=true;r.Add(o,w+t,0)}if(y){r.w+=y.right||0;r.h+=y.top||0;r.d+=y.bottom||0}if(v){r.w+=v.right||0;r.h+=v.top||0;r.d+=v.bottom||0}if(A.background!==i.COLOR.TRANSPARENT){var x=r.element.nodeName.toLowerCase();if(x!=="g"&&x!=="svg"){var s=a.Element("g");s.appendChild(r.element);r.element=s;r.removeable=true}r.Add(l.RECT(r.h,r.d,r.w,{fill:A.background,stroke:"none"}),0,0,false,true)}if(v){var z=5;var p={left:["V",r.h+r.d,-z,-r.d],right:["V",r.h+r.d,r.w-v.right+z,-r.d],top:["H",r.w,0,r.h-v.top+z],bottom:["H",r.w,0,-r.d-z]};for(n in p){if(p.hasOwnProperty(n)){if(v[n]){var u=p[n],q=l[u[0]+"LINE"];r.Add(q(u[1],v[n],v[n+"Style"],v[n+"Color"]),u[2],u[3])}}}}},SVGhandleVariant:function(n,p,o){return a.HandleVariant(n,p,o)},SVGgetVariant:function(){var n=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var o=n.mathvariant;if(this.variantForm){o="-"+a.fontInUse+"-variant"}n.hasVariant=this.Get("mathvariant",true);if(!n.hasVariant){n.family=n.fontfamily;n.weight=n.fontweight;n.style=n.fontstyle}if(this.styles){if(!n.style&&this.styles.fontStyle){n.style=this.styles.fontStyle}if(!n.weight&&this.styles.fontWeight){n.weight=this.styles.fontWeight}if(!n.family&&this.styles.fontFamily){n.family=this.styles.fontFamily}}if(n.family&&!n.hasVariant){if(!n.weight&&n.mathvariant.match(/bold/)){n.weight="bold"}if(!n.style&&n.mathvariant.match(/italic/)){n.style="italic"}o={forceFamily:true,font:{"font-family":n.family}};if(n.style){o.font["font-style"]=n.style}if(n.weight){o.font["font-weight"]=n.weight}return o}if(n.weight==="bold"){o={normal:i.VARIANT.BOLD,italic:i.VARIANT.BOLDITALIC,fraktur:i.VARIANT.BOLDFRAKTUR,script:i.VARIANT.BOLDSCRIPT,"sans-serif":i.VARIANT.BOLDSANSSERIF,"sans-serif-italic":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.weight==="normal"){o={bold:i.VARIANT.normal,"bold-italic":i.VARIANT.ITALIC,"bold-fraktur":i.VARIANT.FRAKTUR,"bold-script":i.VARIANT.SCRIPT,"bold-sans-serif":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.SANSSERIFITALIC}[o]||o}}if(n.style==="italic"){o={normal:i.VARIANT.ITALIC,bold:i.VARIANT.BOLDITALIC,"sans-serif":i.VARIANT.SANSSERIFITALIC,"bold-sans-serif":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.style==="normal"){o={italic:i.VARIANT.NORMAL,"bold-italic":i.VARIANT.BOLD,"sans-serif-italic":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.BOLDSANSSERIF}[o]||o}}if(!(o in a.FONTDATA.VARIANT)){o="normal"}return a.FONTDATA.VARIANT[o]},SVGgetScale:function(o){var p=1;if(this.mscale){p=this.scale}else{var n=this.getValues("scriptlevel","fontsize");n.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if((this.styles||{}).fontSize&&!n.fontsize){n.fontsize=this.styles.fontSize}if(n.fontsize&&!this.mathsize){n.mathsize=n.fontsize}if(n.scriptlevel!==0){if(n.scriptlevel>2){n.scriptlevel=2}p=Math.pow(this.Get("scriptsizemultiplier"),n.scriptlevel);n.scriptminsize=a.length2em(this.Get("scriptminsize"))/1000;if(p2){o.scriptlevel=2}n=Math.sqrt(Math.pow(o.scriptsizemultiplier,o.scriptlevel))}return n},SVGnotEmpty:function(n){while(n){if((n.type!=="mrow"&&n.type!=="texatom")||n.data.length>1){return true}n=n.data[0]}return false},SVGcanStretch:function(p){var o=false;if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){o=n.SVGcanStretch(p);if(o&&n.forceStretch){this.forceStretch=true}}}return o},SVGstretchV:function(n,o){return this.toSVG(n,o)},SVGstretchH:function(n){return this.toSVG(n)},SVGlineBreaks:function(){return false}},{SVGemptySVG:function(){var n=this.SVG();n.Clean();this.SVGsaveData(n);return n},SVGautoload:function(){this.constructor.Augment({toSVG:i.mbase.SVGautoloadFail});var n=a.autoloadDir+"/"+this.type+".js";e.RestartAfter(j.Require(n))},SVGautoloadFail:function(){throw Error("SVG can't autoload '"+this.type+"'")},SVGautoloadList:{},SVGautoloadFile:function(n){if(i.mbase.SVGautoloadList.hasOwnProperty(n)){throw Error("SVG can't autoload file '"+n+"'")}i.mbase.SVGautoloadList[n]=true;var o=a.autoloadDir+"/"+n+".js";e.RestartAfter(j.Require(o))}});i.chars.Augment({toSVG:function(o,r,n,p){var q=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.entity.Augment({toSVG:function(o,r,n,p){var q=this.toString().replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.mo.Augment({toSVG:function(o,n){this.SVGgetStyles();var v=this.svg=this.SVG();var r=this.SVGgetScale(v);this.SVGhandleSpace(v);if(this.data.length==0){v.Clean();this.SVGsaveData(v);return v}if(n!=null){return this.SVGstretchV(o,n)}else{if(o!=null){return this.SVG.strechH(o)}}var t=this.SVGgetVariant();var B=this.getValues("largeop","displaystyle");if(B.largeop){t=a.FONTDATA.VARIANT[B.displaystyle?"-largeOp":"-smallOp"]}var A=this.CoreParent(),s=(A&&A.isa(i.msubsup)&&this!==A.data[0]),p=(s?this.remapChars:null);if(a.isChar(this.data.join(""))&&A&&A.isa(i.munderover)&&a.isChar(this.CoreText(A.data[A.base]))){var w=A.data[A.over],z=A.data[A.under];if(w&&this===w.CoreMO()&&A.Get("accent")){p=a.FONTDATA.REMAPACCENT}else{if(z&&this===z.CoreMO()&&A.Get("accentunder")){p=a.FONTDATA.REMAPACCENTUNDER}}}if(s&&this.data.join("").match(/['`"\u00B4\u2032-\u2037\u2057]/)){t=a.FONTDATA.VARIANT["-"+a.fontInUse+"-variant"]}for(var u=0,q=this.data.length;u10*C.w){y+=-C.l}v.Add(C,y,0,true);if(C.skew){v.skew=C.skew}}}v.Clean();if(!a.isChar(this.data.join(""))){delete v.skew}if(B.largeop){v.y=a.TeX.axis_height-(v.h-v.d)/2/r;if(v.r>v.w){v.ic=v.r-v.w;v.w=v.r}}this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGcanStretch:function(r){if(!this.Get("stretchy")){return false}var s=this.data.join("");if(s.length>1){return false}var o=this.CoreParent();if(o&&o.isa(i.munderover)&&a.isChar(this.CoreText(o.data[o.base]))){var q=o.data[o.over],n=o.data[o.under];if(q&&this===q.CoreMO()&&o.Get("accent")){s=a.FONTDATA.REMAPACCENT[s]||s}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){s=a.FONTDATA.REMAPACCENTUNDER[s]||s}}}s=a.FONTDATA.DELIMITERS[s.charCodeAt(0)];var p=(s&&s.dir==r.substr(0,1));if(!p){delete this.svg}this.forceStretch=p&&(this.Get("minsize",true)||this.Get("maxsize",true));return p},SVGstretchV:function(s,t){var p=this.svg||this.toSVG();var o=this.getValues("symmetric","maxsize","minsize");var r=a.TeX.axis_height*p.scale,n=this.SVGgetMu(p),q;if(o.symmetric){q=2*Math.max(s-r,t+r)}else{q=s+t}o.maxsize=a.length2em(o.maxsize,n,p.h+p.d);o.minsize=a.length2em(o.minsize,n,p.h+p.d);q=Math.max(o.minsize,Math.min(o.maxsize,q));if(q!=o.minsize){q=[Math.max(q*a.TeX.delimiterfactor/1000,q-a.TeX.delimitershortfall),q]}p=a.createDelimiter(this.data.join("").charCodeAt(0),q,p.scale);if(o.symmetric){q=(p.h+p.d)/2+r}else{q=(p.h+p.d)*s/(s+t)}p.y=q-p.h;this.SVGhandleSpace(p);this.SVGhandleColor(p);delete this.svg.element;this.SVGsaveData(p);p.stretched=true;return p},SVGstretchH:function(o){var q=this.svg||this.toSVG(),n=this.SVGgetMu(q);var p=this.getValues("maxsize","minsize","mathvariant","fontweight");if((p.fontweight==="bold"||parseInt(p.fontweight)>=600)&&!this.Get("mathvariant",true)){p.mathvariant=i.VARIANT.BOLD}p.maxsize=a.length2em(p.maxsize,n,q.w);p.minsize=a.length2em(p.minsize,n,q.w);o=Math.max(p.minsize,Math.min(p.maxsize,o));q=a.createDelimiter(this.data.join("").charCodeAt(0),o,q.scale,p.mathvariant);this.SVGhandleSpace(q);this.SVGhandleColor(q);delete this.svg.element;this.SVGsaveData(q);q.stretched=true;return q}});i.mn.Augment({SVGremapMinus:function(n){return n.replace(/^-/,"\u2212")},toSVG:function(){this.SVGgetStyles();var r=this.SVGgetVariant();var o=this.SVG();this.SVGgetScale(o);this.SVGhandleSpace(o);var q=this.SVGremapMinus;for(var p=0,n=this.data.length;po.w&&a.isChar(s)&&!r.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},}),i.mtext.Augment({toSVG:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){this.SVGgetStyles();var n=this.SVG(),q=this.SVGgetScale(n);this.SVGhandleSpace(n);var o=this.SVGgetVariant(),p={direction:this.Get("dir")};if(o.bold){p["font-weight"]="bold"}if(o.italic){p["font-style"]="italic"}o=this.Get("mathvariant");if(o==="monospace"){p["class"]="MJX-monospace"}else{if(o.match(/sans-serif/)){p["class"]="MJX-sans-serif"}}n.Add(l.TEXT(q*100/a.config.scale,this.data.join(""),p));n.Clean();this.SVGhandleColor(n);this.SVGsaveData(n);return n}else{return this.SUPER(arguments).toSVG.call(this)}}});i.merror.Augment({toSVG:function(p,n){this.SVGgetStyles();var t=this.SVG(),r=a.length2em(this.styles.fontSize||1)/1000;this.SVGhandleSpace(t);var o=(r!==1?{transform:"scale("+a.Fixed(r)+")"}:{});var v=l(o);v.Add(this.SVGchildSVG(0));v.Clean();if(r!==1){v.removeable=false;var u=["w","h","d","l","r","D","H"];for(var s=0,q=u.length;st.H){t.H=t.h}if(t.d>t.D){t.D=t.d}}this.SVGhandleColor(t);this.SVGsaveData(t);return t},SVGlength2em:function(q,t,o,u,n){if(n==null){n=-a.BIGDIMEN}var r=String(t).match(/width|height|depth/);var s=(r?q[r[0].charAt(0)]:(u?q[u]:0));var p=a.length2em(t,o,s/this.mscale)*this.mscale;if(u&&String(t).match(/^\s*[-+]/)){return Math.max(n,q[u]+p)}else{return p}}});i.mrow.Augment({SVG:l.ROW,toSVG:function(q,s){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(s!=null){o.sh=q;o.sd=s}for(var p=0,n=this.data.length;pa.linebreakWidth)||this.hasNewline()},SVGmultiline:function(n){i.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(o){var p=this.SVG();this.SVGhandleSpace(p);for(var q=0,n=this.data.length;qz){n=((u.h+u.d)-(z-A))/2}w=l.RECT(A,0,r.w);z=r.h+n+A;y=this.SVGaddRoot(v,u,y,u.h+u.d-z,s);v.Add(u,y,z-u.h);v.Add(w,y+u.w,z-w.h);v.Add(r,y+u.w,0);v.Clean();v.h+=A;v.H+=A;this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGaddRoot:function(o,p,n,r,q){return n}});i.mroot.Augment({toSVG:i.msqrt.prototype.toSVG,SVGaddRoot:function(q,o,t,r,n){var v=(o.isMultiChar?0.55:0.65)*o.w;if(this.data[1]){var s=this.data[1].toSVG();s.x=0;var p=this.SVGrootHeight(o.h+o.d,n,s)-r;var u=Math.min(s.w,s.r);t=Math.max(u,v);q.Add(s,t-u,p)}else{v=t}return t-v},SVGrootHeight:function(p,o,n){return 0.45*(p-900*o)+600*o+Math.max(0,n.d-75)}});i.mfenced.Augment({SVG:l.ROW,toSVG:function(){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data.open){o.Check(this.data.open)}if(this.data[0]!=null){o.Check(this.data[0])}for(var p=1,n=this.data.length;pJ){J=N}if(!L[K]&&J>o){o=J}}}if(E==null&&G!=null){o=G}else{if(o==-a.BIGDIMEN){o=J}}for(K=J=0,H=this.data.length;KJ){J=N}}}var C=a.TeX.rule_thickness*this.mscale;var u,r,z,w,s,B,I,M=0;p=q[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,y:0,scale:O};if(p.ic){M=1.3*p.ic+0.05}for(K=0,H=this.data.length;KJ){F.skew+=(J-N-u)/2}}}else{z=a.TeX.big_op_spacing1*O;w=a.TeX.big_op_spacing3*O;I=Math.max(z,w-Math.max(0,v.d))}I=Math.max(I,1500/a.em);u+=M/2;r=p.y+p.h+v.d+I;v.h+=s;if(v.h>v.H){v.H=v.h}}else{if(K==this.under){if(A){I=3*C*O;s=0}else{z=a.TeX.big_op_spacing2*O;w=a.TeX.big_op_spacing4*O;I=Math.max(z,w-v.h)}I=Math.max(I,1500/a.em);u-=M/2;r=p.y-(p.d+v.h+I);v.d+=s;if(v.d>v.D){v.D=v.d}}}F.Add(v,u,r)}}F.Clean();this.SVGhandleColor(F);this.SVGsaveData(F);return F}});i.msubsup.Augment({toSVG:function(M,G){this.SVGgetStyles();var I=this.SVG(),Q=this.SVGgetScale(I);this.SVGhandleSpace(I);var K=this.SVGgetMu(I);var y=I.Add(this.SVGdataStretched(this.base,M,G));var w=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var O=a.TeX.x_height*Q,F=a.TeX.scriptspace*Q;var n,z;if(this.SVGnotEmpty(this.data[this.sup])){n=this.data[this.sup].toSVG();n.w+=F;n.r=Math.max(n.w,n.r)}if(this.SVGnotEmpty(this.data[this.sub])){z=this.data[this.sub].toSVG();z.w+=F;z.r=Math.max(z.w,z.r)}var J=a.TeX.sup_drop*w,H=a.TeX.sub_drop*w;var C=y.h+(y.y||0)-J,B=y.d-(y.y||0)+H,P=0,L;if(y.ic){y.w-=y.ic;P=1.3*y.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(a.isChar(this.data[this.base].data.join(""))&&y.scale===1&&!y.stretched&&!this.data[this.base].Get("largeop")){C=B=0}}var N=this.getValues("subscriptshift","superscriptshift");N.subscriptshift=(N.subscriptshift===""?0:a.length2em(N.subscriptshift,K));N.superscriptshift=(N.superscriptshift===""?0:a.length2em(N.superscriptshift,K));var A=y.w+y.x;if(!n){if(z){B=Math.max(B,a.TeX.sub1*Q,z.h-(4/5)*O,N.subscriptshift);I.Add(z,A,-B);this.data[this.sub].SVGdata.dy=-B}}else{if(!z){var o=this.getValues("displaystyle","texprimestyle");L=a.TeX[(o.displaystyle?"sup1":(o.texprimestyle?"sup3":"sup2"))];C=Math.max(C,L*Q,n.d+(1/4)*O,N.superscriptshift);I.Add(n,A+P,C);this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=C}else{B=Math.max(B,a.TeX.sub2*Q);var E=a.TeX.rule_thickness*Q;if((C-n.d)-(z.h-B)<3*E){B=3*E-C+n.d+z.h;J=(4/5)*O-(C-n.d);if(J>0){C+=J;B-=J}}I.Add(n,A+P,Math.max(C,N.superscriptshift));I.Add(z,A,-Math.max(B,N.subscriptshift));this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=Math.max(C,N.superscriptshift);this.data[this.sub].SVGdata.dy=-Math.max(B,N.subscriptshift)}}I.Clean();this.SVGhandleColor(I);this.SVGsaveData(I);return I}});i.mmultiscripts.Augment({toSVG:i.mbase.SVGautoload});i.mtable.Augment({toSVG:i.mbase.SVGautoload});i["annotation-xml"].Augment({toSVG:i.mbase.SVGautoload});i.math.Augment({SVG:l.Subclass({type:"svg",removeable:false}),toSVG:function(B,p){var F=a.config;if(this.data[0]){this.SVGgetStyles();i.mbase.prototype.displayAlign=e.config.displayAlign;i.mbase.prototype.displayIndent=e.config.displayIndent;if(String(e.config.displayIndent).match(/^0($|[a-z%])/i)){i.mbase.prototype.displayIndent="0"}var v=l.G();v.Add(this.data[0].toSVG(),0,0,true);v.Clean();this.SVGhandleColor(v);a.Element(v.element,{stroke:"currentColor",fill:"currentColor","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"});v.removeable=false;var x=this.SVG();x.element.setAttribute("xmlns:xlink",m);if(F.useFontCache&&!F.useGlobalCache){x.element.appendChild(l.GLYPH.defs)}x.Add(v);x.Clean();this.SVGsaveData(x);if(!B){x.element=x.element.firstChild;x.element.removeAttribute("transform");x.removable=true;return x}var u=Math.max(-x.l,0),o=Math.max(x.r-x.w,0);var q=x.element.style,A=a.TeX.x_height/a.ex;var E=(Math.ceil(x.H/A)+1)*A+a.HFUZZ,n=(Math.ceil(x.D/A)+1)*A+a.DFUZZ;var z=u+x.w+o;x.element.setAttribute("width",a.Ex(z));x.element.setAttribute("height",a.Ex(E+n));q.verticalAlign=a.Ex(-n);if(u){q.marginLeft=a.Ex(-u)}if(o){q.marginRight=a.Ex(-o)}x.element.setAttribute("viewBox",a.Fixed(-u,1)+" "+a.Fixed(-E,1)+" "+a.Fixed(z,1)+" "+a.Fixed(E+n,1));if(x.H>x.h){q.marginTop=a.Ex(x.h-E)}if(x.D>x.d){q.marginBottom=a.Ex(x.d-n);q.verticalAlign=a.Ex(-x.d)}if(Math.abs(z-a.cwidth)<10){q.maxWidth=a.Fixed(a.cwidth*a.em/1000*a.config.scale)+"px"}var y=this.Get("alttext");if(y&&!x.element.getAttribute("aria-label")){x.element.setAttribute("aria-label",y)}if(!x.element.getAttribute("role")){x.element.setAttribute("role","img")}x.element.setAttribute("focusable","false");B.appendChild(x.element);x.element=null;if(!this.isMultiline&&this.Get("display")==="block"&&!x.hasIndent){var C=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(C.indentalignfirst!==i.INDENTALIGN.INDENTALIGN){C.indentalign=C.indentalignfirst}if(C.indentalign===i.INDENTALIGN.AUTO){C.indentalign=this.displayAlign}if(C.indentshiftfirst!==i.INDENTSHIFT.INDENTSHIFT){C.indentshift=C.indentshiftfirst}if(C.indentshift==="auto"){C.indentshift="0"}var s=a.length2em(C.indentshift,1,a.cwidth);if(this.displayIndent!=="0"){var t=a.length2em(this.displayIndent,1,a.cwidth);s+=(C.indentalign===i.INDENTALIGN.RIGHT?-t:t)}p.style.textAlign=C.indentalign;if(s){e.Insert(q,({left:{marginLeft:a.Ex(s)},right:{marginRight:a.Ex(-s),marginLeft:a.Ex(Math.max(0,s-z))},center:{marginLeft:a.Ex(s),marginRight:a.Ex(-s)}})[C.indentalign])}}}return B}});i.TeXAtom.Augment({toSVG:function(n,q){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data[0]!=null){var p=this.SVGdataStretched(0,n,q),r=0;if(this.texClass===i.TEXCLASS.VCENTER){r=a.TeX.axis_height-(p.h+p.d)/2+p.d}o.Add(p,0,r);o.ic=p.ic;o.skew=p.skew}this.SVGhandleColor(o);this.SVGsaveData(o);return o}});i.maligngroup.Augment({toSVG:i.mbase.SVGemptySVG});i.malignmark.Augment({toSVG:i.mbase.SVGemptySVG});i.mprescripts.Augment({toSVG:i.mbase.SVGemptySVG});i.none.Augment({toSVG:i.mbase.SVGemptySVG});e.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});e.Browser.Select({Opera:function(n){a.Augment({operaZoomRefresh:true})}});e.Register.StartupHook("End Cookie",function(){if(e.config.menuSettings.zoom!=="None"){j.Require("[MathJax]/extensions/MathZoom.js")}});if(!document.createElementNS){if(!document.namespaces.svg){document.namespaces.add("svg",b)}a.Augment({Element:function(n,o){var p=(typeof(n)==="string"?document.createElement("svg:"+n):n);p.isMathJax=true;if(o){for(var q in o){if(o.hasOwnProperty(q)){p.setAttribute(q,o[q].toString())}}}return p}})}})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG); +MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,d=MathJax.OutputJax.SVG,b=d.BBOX;a.mtable.Augment({toSVG:function(aa){this.SVGgetStyles();var o=this.SVG(),ap=this.SVGgetScale(o);if(this.data.length===0){this.SVGsaveData(o);return o}var aN=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");if(aN.width.match(/%$/)){o.width=aN.width=d.Em((d.cwidth/1000)*(parseFloat(aN.width)/100))}var v=this.SVGgetMu(o);var aK=-1;var z=[],I=[],k=[],O=[],K=[],aI,aG,w=-1,aE,u,az,S,an,E,aA;var ac=d.FONTDATA.lineH*ap*aN.useHeight,ag=d.FONTDATA.lineD*ap*aN.useHeight;for(aI=0,aE=this.data.length;aIw){w=aG}K[aG]=b.G();k[aG]=-d.BIGDIMEN}an=S.data[aG-az];O[aI][aG]=an.toSVG();if(an.isEmbellished()){E=an.CoreMO();var aM=E.Get("minsize",true);if(aM){if(E.SVGcanStretch("Vertical")){aA=E.SVGdata.h+E.SVGdata.d;if(aA){aM=d.length2em(aM,v,aA);if(aM*E.SVGdata.h/aA>z[aI]){z[aI]=aM*E.SVGdata.h/aA}if(aM*E.SVGdata.d/aA>I[aI]){I[aI]=aM*E.SVGdata.d/aA}}}else{if(E.SVGcanStretch("Horizontal")){aM=d.length2em(aM,v,E.SVGdata.w);if(aM>k[aG]){k[aG]=aM}}}}}if(O[aI][aG].h>z[aI]){z[aI]=O[aI][aG].h}if(O[aI][aG].d>I[aI]){I[aI]=O[aI][aG].d}if(O[aI][aG].w>k[aG]){k[aG]=O[aI][aG].w}}}var ao=MathJax.Hub.SplitList;var am=ao(aN.columnspacing),T=ao(aN.rowspacing),ai=ao(aN.columnalign),L=ao(aN.rowalign),N=ao(aN.columnlines),h=ao(aN.rowlines),ar=ao(aN.columnwidth),aw=[];for(aI=0,aE=am.length;aIO.length){aD=O.length}}g=0;ay=-(aA+ab)+z[0];for(aI=0,aE=aD-1;aI0.98){aj=X/(V+X);at=V+X}else{at=V/(1-ax)}}else{at=Math.max(V+X,d.length2em(aN.width,v));for(aI=0,aE=Math.min(w,am.length);aI0.01){if(aJ&&at>V){at=(at-V)/aJ;for(aI=0,aE=B.length;aIq+az*ak){R.indentalign=ai[aK];ak=az*(al+az*aO);aH+=al+Math.max(0,ak)}}else{if(ai[aK]===R.indentalign){if(e<0){aO=az*e;e=0}ak+=az*e;if(al>az*ak){ak=az*al}ak+=aO;aH+=az*ak}else{ak-=az*e;if(aH-az*ak+al>d.cwidth){ak=az*(aH+al-d.cwidth);if(az*ak>0){aH=d.cwidth+az*ak;ak=0}}}}var G=o;o=this.SVG();o.hasIndent=true;o.w=o.r=Math.max(aH,d.cwidth);o.Align(K[aK],ai[aK],0,0,aO);o.Align(G,R.indentalign,0,0,ak);o.tw=aH}this.SVGsaveData(o);return o},SVGhandleSpace:function(e){if(!this.hasFrame&&!e.width){e.x=e.X=167}this.SUPER(arguments).SVGhandleSpace.call(this,e)}});a.mtd.Augment({toSVG:function(e,g){var f=this.svg=this.SVG();if(this.data[0]){f.Add(this.SVGdataStretched(0,e,g));f.Clean()}this.SVGhandleColor(f);this.SVGsaveData(f);return f}});MathJax.Hub.Startup.signal.Post("SVG mtable Ready");MathJax.Ajax.loadComplete(d.autoloadDir+"/mtable.js")}); +(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/MML_SVG-full.js"); diff --git a/revisions_report_files/mathjax-27/config/MML_SVG.js b/revisions_report_files/mathjax-27/config/MML_SVG.js new file mode 100644 index 0000000..372de95 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/MML_SVG.js @@ -0,0 +1,49 @@ +/* + * /MathJax/config/MML_SVG.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.mml2jax={version:"2.7.6",config:{preview:"mathml"},MMLnamespace:"http://www.w3.org/1998/Math/MathML",PreProcess:function(e){if(!this.configured){this.config=MathJax.Hub.CombineConfig("mml2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.InitBrowser();this.configured=true}if(typeof(e)==="string"){e=document.getElementById(e)}if(!e){e=document.body}var h=[];this.PushMathElements(h,e,"math");this.PushMathElements(h,e,"math",this.MMLnamespace);var d,b;if(typeof(document.namespaces)!=="undefined"){try{for(d=0,b=document.namespaces.length;d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +(function(d,h,l,g,m,b,j){var p="2.7.6";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Menu_Button .MathJax_Hover_Arrow":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"4px","-webkit-border-radius":"4px","-moz-border-radius":"4px","-khtml-border-radius":"4px","font-family":"'Courier New',Courier","font-size":"9px",color:"#F0F0F0"},".MathJax_Menu_Button .MathJax_Hover_Arrow span":{display:"block","background-color":"#AAA",border:"1px solid","border-radius":"3px","line-height":0,padding:"4px"},".MathJax_Hover_Arrow:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_Hover_Arrow:hover span":{"background-color":"#CCC!important"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",KEY:{RETURN:13,ESCAPE:27,SPACE:32,LEFT:37,UP:38,RIGHT:39,DOWN:40},Mousedown:function(q){return n.Handler(q,"Mousedown",this)},Mouseup:function(q){return n.Handler(q,"Mouseup",this)},Mousemove:function(q){return n.Handler(q,"Mousemove",this)},Mouseover:function(q){return n.Handler(q,"Mouseover",this)},Mouseout:function(q){return n.Handler(q,"Mouseout",this)},Click:function(q){return n.Handler(q,"Click",this)},DblClick:function(q){return n.Handler(q,"DblClick",this)},Menu:function(q){return n.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return n.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}else{q.returnValue=false}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true}return false},Keydown:function(r,q){if(!r){r=window.event}if(r.keyCode===n.KEY.SPACE){n.ContextMenu(r,this)}},ContextMenu:function(t,E,w){var B=b[E.jaxID],v=B.getJaxFromMath(E);var F=(B.config.showMathMenu!=null?B:d).config.showMathMenu;if(!F||(k.context!=="MathJax"&&!w)){return}if(c.msieEventBug){t=window.event||t}n.ClearSelection();f.ClearHoverTimer();if(v.hover){if(v.hover.remove){clearTimeout(v.hover.remove);delete v.hover.remove}v.hover.nofade=true}var u=MathJax.Menu;var G,D;if(u){if(u.loadingDomain){return n.False(t)}G=m.loadDomain("MathMenu");if(!G){u.jax=v;var r=u.menu.Find("Show Math As").submenu;r.items[0].name=v.sourceMenuTitle;r.items[0].format=(v.sourceMenuFormat||"MathML");r.items[1].name=j[v.inputJax].sourceMenuTitle;r.items[5].disabled=!j[v.inputJax].annotationEncoding;var A=r.items[2];A.disabled=true;var q=A.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var z=0,y=q.length;z0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(c,d){var a;var b=function(e){return MathJax.Localization._.apply(MathJax.Localization,[["MathML",e]].concat([].slice.call(arguments,1)))};c.Parse=MathJax.Object.Subclass({Init:function(f,e){this.Parse(f,e)},Parse:function(h,e){var j;if(typeof h!=="string"){j=h.parentNode}else{j=c.ParseXML(this.preProcessMath.call(this,h));if(j==null){c.Error(["ErrorParsingMathML","Error parsing MathML"])}}var g=j.getElementsByTagName("parsererror")[0];if(g){c.Error(["ParsingError","Error parsing MathML: %1",g.textContent.replace(/This page.*?errors:|XML Parsing Error: |Below is a rendering of the page.*/g,"")])}if(j.childNodes.length!==1){c.Error(["MathMLSingleElement","MathML must be formed by a single element"])}if(j.firstChild.nodeName.toLowerCase()==="html"){var f=j.getElementsByTagName("h1")[0];if(f&&f.textContent==="XML parsing error"&&f.nextSibling){c.Error(["ParsingError","Error parsing MathML: %1",String(f.nextSibling.nodeValue).replace(/fatal parsing error: /,"")])}}if(j.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")!=="math"){c.Error(["MathMLRootElement","MathML must be formed by a element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/MML_SVG.js"); diff --git a/revisions_report_files/mathjax-27/config/MMLorHTML.js b/revisions_report_files/mathjax-27/config/MMLorHTML.js new file mode 100644 index 0000000..727861e --- /dev/null +++ b/revisions_report_files/mathjax-27/config/MMLorHTML.js @@ -0,0 +1,19 @@ +/* + * /MathJax/config/MMLorHTML.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +(function(c,g){var f="2.7.0";var a=MathJax.Hub.CombineConfig("MMLorHTML",{prefer:{MSIE:"MML",Firefox:"HTML",Opera:"HTML",Chrome:"HTML",Safari:"HTML",other:"HTML"}});var e={Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4};var b=(g.version==="0.0"||g.versionAtLeast(e[g]||0));var d=(g.isFirefox&&g.versionAtLeast("1.5"))||(g.isMSIE&&g.hasMathPlayer)||(g.isSafari&&g.versionAtLeast("5.0"))||(g.isOpera&&g.versionAtLeast("9.52"));c.Register.StartupHook("End Config",function(){var h=(a.prefer&&typeof(a.prefer)==="object"?a.prefer[MathJax.Hub.Browser]||a.prefer.other||"HTML":a.prefer);if(b||d){if(d&&(h==="MML"||!b)){if(MathJax.OutputJax.NativeMML){MathJax.OutputJax.NativeMML.Register("jax/mml")}else{c.config.jax.unshift("output/NativeMML")}c.Startup.signal.Post("NativeMML output selected")}else{if(MathJax.OutputJax["HTML-CSS"]){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}else{c.config.jax.unshift("output/HTML-CSS")}c.Startup.signal.Post("HTML-CSS output selected")}}else{c.PreProcess.disabled=true;c.prepareScripts.disabled=true;MathJax.Message.Set(["MathJaxNotSupported","Your browser does not support MathJax"],null,4000);c.Startup.signal.Post("MathJax not supported")}})})(MathJax.Hub,MathJax.Hub.Browser);MathJax.Ajax.loadComplete("[MathJax]/config/MMLorHTML.js"); diff --git a/revisions_report_files/mathjax-27/config/Safe.js b/revisions_report_files/mathjax-27/config/Safe.js new file mode 100644 index 0000000..a76efe4 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/Safe.js @@ -0,0 +1,19 @@ +/* + * /MathJax/config/Safe.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Hub.Register.StartupHook("End Config",function(){if(!MathJax.Hub.config.extensions){MathJax.Hub.config.extensions=[]}MathJax.Hub.config.extensions.push("Safe.js")});MathJax.Ajax.loadComplete("[MathJax]/config/Safe.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-AMS-MML_HTMLorMML.js b/revisions_report_files/mathjax-27/config/TeX-AMS-MML_HTMLorMML.js new file mode 100644 index 0000000..c8507f5 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-AMS-MML_HTMLorMML.js @@ -0,0 +1,69 @@ +/* + * /MathJax/config/TeX-AMS-MML_HTMLorMML.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Hub.Config({delayJaxRegistration: true}); + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/HTML-CSS/config.js", + "[MathJax]/jax/output/NativeMML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/config/MMLorHTML.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.OutputJax["HTML-CSS"]=MathJax.OutputJax({id:"HTML-CSS",version:"2.7.6",directory:MathJax.OutputJax.directory+"/HTML-CSS",extensionDir:MathJax.OutputJax.extensionDir+"/HTML-CSS",autoloadDir:MathJax.OutputJax.directory+"/HTML-CSS/autoload",fontDir:MathJax.OutputJax.directory+"/HTML-CSS/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{noReflows:true,matchFontHeight:true,scale:100,minScaleAdjust:50,availableFonts:["STIX","TeX"],preferredFont:"TeX",webFont:"TeX",imageFont:"TeX",undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",mtextFontInherit:false,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},styles:{".MathJax_Display":{"text-align":"center",margin:"1em 0em"},".MathJax .merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"},".MathJax .MJX-monospace":{"font-family":"monospace"},".MathJax .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')",padding:"3px 4px","z-index":401}}}});if(MathJax.Hub.Browser.isMSIE&&document.documentMode>=9){delete MathJax.OutputJax["HTML-CSS"].config.styles["#MathJax_Tooltip"].filter}if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax["HTML-CSS"].Register("jax/mml")}MathJax.Hub.Register.StartupHook("End Config",[function(b,c){var a=b.Insert({minBrowserVersion:{Firefox:3,Opera:9.52,MSIE:6,Chrome:0.3,Safari:2,Konqueror:4},inlineMathDelimiters:["$","$"],displayMathDelimiters:["$$","$$"],multilineDisplay:true,minBrowserTranslate:function(f){var e=b.getJaxFor(f),k=["[Math]"],j;var h=document.createElement("span",{className:"MathJax_Preview"});if(e.inputJax==="TeX"){if(e.root.Get("displaystyle")){j=a.displayMathDelimiters;k=[j[0]+e.originalText+j[1]];if(a.multilineDisplay){k=k[0].split(/\n/)}}else{j=a.inlineMathDelimiters;k=[j[0]+e.originalText.replace(/^\s+/,"").replace(/\s+$/,"")+j[1]]}}for(var g=0,d=k.length;g0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +(function(d,h,l,g,m,b,j){var p="2.7.6";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Menu_Button .MathJax_Hover_Arrow":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"4px","-webkit-border-radius":"4px","-moz-border-radius":"4px","-khtml-border-radius":"4px","font-family":"'Courier New',Courier","font-size":"9px",color:"#F0F0F0"},".MathJax_Menu_Button .MathJax_Hover_Arrow span":{display:"block","background-color":"#AAA",border:"1px solid","border-radius":"3px","line-height":0,padding:"4px"},".MathJax_Hover_Arrow:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_Hover_Arrow:hover span":{"background-color":"#CCC!important"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",KEY:{RETURN:13,ESCAPE:27,SPACE:32,LEFT:37,UP:38,RIGHT:39,DOWN:40},Mousedown:function(q){return n.Handler(q,"Mousedown",this)},Mouseup:function(q){return n.Handler(q,"Mouseup",this)},Mousemove:function(q){return n.Handler(q,"Mousemove",this)},Mouseover:function(q){return n.Handler(q,"Mouseover",this)},Mouseout:function(q){return n.Handler(q,"Mouseout",this)},Click:function(q){return n.Handler(q,"Click",this)},DblClick:function(q){return n.Handler(q,"DblClick",this)},Menu:function(q){return n.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return n.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}else{q.returnValue=false}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true}return false},Keydown:function(r,q){if(!r){r=window.event}if(r.keyCode===n.KEY.SPACE){n.ContextMenu(r,this)}},ContextMenu:function(t,E,w){var B=b[E.jaxID],v=B.getJaxFromMath(E);var F=(B.config.showMathMenu!=null?B:d).config.showMathMenu;if(!F||(k.context!=="MathJax"&&!w)){return}if(c.msieEventBug){t=window.event||t}n.ClearSelection();f.ClearHoverTimer();if(v.hover){if(v.hover.remove){clearTimeout(v.hover.remove);delete v.hover.remove}v.hover.nofade=true}var u=MathJax.Menu;var G,D;if(u){if(u.loadingDomain){return n.False(t)}G=m.loadDomain("MathMenu");if(!G){u.jax=v;var r=u.menu.Find("Show Math As").submenu;r.items[0].name=v.sourceMenuTitle;r.items[0].format=(v.sourceMenuFormat||"MathML");r.items[1].name=j[v.inputJax].sourceMenuTitle;r.items[5].disabled=!j[v.inputJax].annotationEncoding;var A=r.items[2];A.disabled=true;var q=A.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var z=0,y=q.length;z0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS-MML_HTMLorMML.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-AMS-MML_SVG-full.js b/revisions_report_files/mathjax-27/config/TeX-AMS-MML_SVG-full.js new file mode 100644 index 0000000..cb5488d --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-AMS-MML_SVG-full.js @@ -0,0 +1,67 @@ +/* + * /MathJax/config/TeX-AMS-MML_SVG-full.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/SVG/jax.js", + "[MathJax]/jax/output/SVG/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +(function(d,h,l,g,m,b,j){var p="2.7.6";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Menu_Button .MathJax_Hover_Arrow":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"4px","-webkit-border-radius":"4px","-moz-border-radius":"4px","-khtml-border-radius":"4px","font-family":"'Courier New',Courier","font-size":"9px",color:"#F0F0F0"},".MathJax_Menu_Button .MathJax_Hover_Arrow span":{display:"block","background-color":"#AAA",border:"1px solid","border-radius":"3px","line-height":0,padding:"4px"},".MathJax_Hover_Arrow:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_Hover_Arrow:hover span":{"background-color":"#CCC!important"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",KEY:{RETURN:13,ESCAPE:27,SPACE:32,LEFT:37,UP:38,RIGHT:39,DOWN:40},Mousedown:function(q){return n.Handler(q,"Mousedown",this)},Mouseup:function(q){return n.Handler(q,"Mouseup",this)},Mousemove:function(q){return n.Handler(q,"Mousemove",this)},Mouseover:function(q){return n.Handler(q,"Mouseover",this)},Mouseout:function(q){return n.Handler(q,"Mouseout",this)},Click:function(q){return n.Handler(q,"Click",this)},DblClick:function(q){return n.Handler(q,"DblClick",this)},Menu:function(q){return n.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return n.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}else{q.returnValue=false}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true}return false},Keydown:function(r,q){if(!r){r=window.event}if(r.keyCode===n.KEY.SPACE){n.ContextMenu(r,this)}},ContextMenu:function(t,E,w){var B=b[E.jaxID],v=B.getJaxFromMath(E);var F=(B.config.showMathMenu!=null?B:d).config.showMathMenu;if(!F||(k.context!=="MathJax"&&!w)){return}if(c.msieEventBug){t=window.event||t}n.ClearSelection();f.ClearHoverTimer();if(v.hover){if(v.hover.remove){clearTimeout(v.hover.remove);delete v.hover.remove}v.hover.nofade=true}var u=MathJax.Menu;var G,D;if(u){if(u.loadingDomain){return n.False(t)}G=m.loadDomain("MathMenu");if(!G){u.jax=v;var r=u.menu.Find("Show Math As").submenu;r.items[0].name=v.sourceMenuTitle;r.items[0].format=(v.sourceMenuFormat||"MathML");r.items[1].name=j[v.inputJax].sourceMenuTitle;r.items[5].disabled=!j[v.inputJax].annotationEncoding;var A=r.items[2];A.disabled=true;var q=A.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var z=0,y=q.length;z0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g div":{display:"inline-block"},".mjx-svg-href":{fill:"blue",stroke:"blue"},".MathJax_SVG_Processing":{visibility:"hidden",position:"absolute",top:0,left:0,width:0,height:0,overflow:"hidden",display:"block!important"},".MathJax_SVG_Processed":{display:"none!important"},".MathJax_SVG_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_SVG_test.mjx-test-display":{display:"table!important"},".MathJax_SVG_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_SVG_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_SVG_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .MathJax_SVG_left_box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .MathJax_SVG_right_box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .MathJax_SVG_right_box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_SVG_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}}},hideProcessedMath:true,fontNames:["TeX","STIX","STIX-Web","Asana-Math","Gyre-Termes","Gyre-Pagella","Latin-Modern","Neo-Euler"],Config:function(){this.SUPER(arguments).Config.apply(this,arguments);var p=e.config.menuSettings,o=this.config,n=p.font;if(p.scale){o.scale=p.scale}if(n&&n!=="Auto"){n=n.replace(/(Local|Web|Image)$/i,"");n=n.replace(/([a-z])([A-Z])/,"$1-$2");this.fontInUse=n}else{this.fontInUse=o.font||"TeX"}if(this.fontNames.indexOf(this.fontInUse)<0){this.fontInUse="TeX"}this.fontDir+="/"+this.fontInUse;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){k=MathJax.Extension.MathEvents.Event;c=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=k.ContextMenu;this.Mousedown=k.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=g.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=g.addElement(this.hiddenDiv,"div",{id:"MathJax_SVG_Hidden"});var n=g.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;this.hiddenDiv.removeChild(n);this.textSVG=this.Element("svg");l.GLYPH.defs=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});this.TestSpan=g.Element("span",{className:"MathJax_SVG_test"},[["span",{className:"MathJax_SVG_left_box"}],["span",{className:"MathJax_SVG_ex_box"}],["span",{className:"MathJax_SVG_right_box"}]]);return j.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){var n=document.body.appendChild(this.TestSpan.cloneNode(true));n.className+=" mjx-test-inline mjx-test-default";this.defaultEx=n.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,n.lastChild.offsetLeft-n.firstChild.offsetLeft-2);document.body.removeChild(n)},preTranslate:function(s){var r=s.jax[this.id],D,z=r.length,y,G,w,C,u,E,p,F,o,v,t=false,A,q=this.config.linebreaks.automatic,x=this.config.linebreaks.width;if(q){t=(x.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(t){x=x.replace(/\s*container\s*/,"")}else{v=this.defaultWidth}if(x===""){x="100%"}}else{v=100000}for(D=0;D=s.SVGlast+s.SVGchunk){this.postTranslate(s,true);s.SVGchunk=Math.floor(s.SVGchunk*this.config.EqnChunkFactor);s.SVGdelay=true}}},postTranslate:function(t,q){var o=t.jax[this.id];if(!this.hideProcessedMath){return}for(var r=t.SVGlast,n=t.SVGeqn;r=55296&&q<56319){v++;q=(((q-55296)<<10)+(D.charCodeAt(v)-56320))+65536;if(this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(q,u);q=y.n;u=y.variant}}else{o=this.FONTDATA.RANGES;for(p=0,A=o.length;p=o[p].low&&q<=o[p].high){if(o[p].remap&&o[p].remap[q]){q=z+o[p].remap[q]}else{if(o[p].remapOnly){break}q=q-o[p].low+z;if(o[p].add){q+=o[p].add}}if(u["variant"+o[p].offset]){u=this.FONTDATA.VARIANT[u["variant"+o[p].offset]]}break}}}if(u.remap&&u.remap[q]){q=u.remap[q];if(u.remap.variant){u=this.FONTDATA.VARIANT[u.remap.variant]}}else{if(this.FONTDATA.REMAP[q]&&!u.noRemap){q=this.FONTDATA.REMAP[q]}}if(h(q)){u=this.FONTDATA.VARIANT[q[1]];q=q[0]}if(typeof(q)==="string"){D=q+D.substr(v+1);s=D.length;v=-1;continue}r=this.lookupChar(u,q);B=r[q];if(B){if((B[5]&&B[5].space)||(B[5]===""&&B[0]+B[1]===0)){x.w+=B[2]}else{B=[t,r.id+"-"+q.toString(16).toUpperCase()].concat(B);x.Add(l.GLYPH.apply(l,B),x.w,0)}}else{if(this.FONTDATA.DELIMITERS[q]){B=this.createDelimiter(q,0,1,r);x.Add(B,x.w,(this.FONTDATA.DELIMITERS[q].dir==="V"?B.d:0))}else{if(q<=65535){B=String.fromCharCode(q)}else{z=q-65536;B=String.fromCharCode((z>>10)+55296)+String.fromCharCode((z&1023)+56320)}var w=l.TEXT(t*100/a.config.scale,B,{"font-family":u.defaultFamily||a.config.undefinedFamily,"font-style":(u.italic?"italic":""),"font-weight":(u.bold?"bold":"")});if(u.h!=null){w.h=u.h}if(u.d!=null){w.d=u.d}B=l.G();B.Add(w);x.Add(B,x.w,0);e.signal.Post(["SVG Jax - unknown char",q,u])}}}if(a.isChar(D)&&r.skew&&r.skew[q]){x.skew=r.skew[q]*1000}if(x.element.childNodes.length===1&&!x.element.firstChild.getAttribute("x")){x.element=x.element.firstChild;x.removeable=false;x.scale=t}return x},lookupChar:function(r,u){var q,o;if(!r.FONTS){var t=this.FONTDATA.FONTS;var s=(r.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(s instanceof Array)){s=[s]}if(r.fonts!=s){r.fonts=s}r.FONTS=[];for(q=0,o=s.length;q=55296&&p<56319)},findBlock:function(o,s){if(o.Ranges){for(var r=0,n=o.Ranges.length;r=0;p--){if(o.Ranges[p][2]==q){o.Ranges.splice(p,1)}}this.loadFont(o.directory+"/"+q+".js")}}}},loadFont:function(n){e.RestartAfter(j.Require(this.fontDir+"/"+n))},createDelimiter:function(n,p,s,q){if(!s){s=1}var u=l.G();if(!n){u.Clean();delete u.element;u.w=u.r=this.TeX.nulldelimiterspace*s;return u}if(!(p instanceof Array)){p=[p,p]}var v=p[1];p=p[0];var o={alias:n};while(o.alias){n=o.alias;o=this.FONTDATA.DELIMITERS[n];if(!o){o={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(o.load){e.RestartAfter(j.Require(this.fontDir+"/fontdata-"+o.load+".js"))}for(var t=0,r=o.HW.length;t=p-10-a.config.blacker||(t==r-1&&!o.stretch)){if(o.HW[t][2]){s*=o.HW[t][2]}if(o.HW[t][3]){n=o.HW[t][3]}return this.createChar(s,[n,o.HW[t][1]],q).With({stretched:true})}}if(o.stretch){this["extendDelimiter"+o.dir](u,v,o.stretch,s,q)}return u},createChar:function(u,s,p){var t="",r={fonts:[s[1]],noRemap:true};if(p&&p===i.VARIANT.BOLD){r.fonts=[s[1]+"-bold",s[1]]}if(typeof(s[1])!=="string"){r=s[1]}if(s[0] instanceof Array){for(var q=0,n=s[0].length;qt){var n=this.createChar(q,o.ext,p);var r=(o.mid?2:1),x=(C-t)/r,D=(x+100)/(n.h+n.d);while(r-->0){var v=a.Element("g",{transform:"translate("+n.y+","+(z-D*n.h+50+n.y)+") scale(1,"+D+")"});v.appendChild(n.element.cloneNode(false));u.element.appendChild(v);z-=x;if(o.mid&&r){u.Add(B,0,z-B.h);z-=(B.h+B.d)}}}else{if(o.mid){z+=(t-C)/2;u.Add(B,0,z-B.h);z+=-(B.h+B.d)+(t-C)/2}else{z+=(t-C)}}u.Add(w,0,z-w.h);u.Clean();u.scale=q;u.isMultiChar=true},extendDelimiterH:function(v,q,o,t,p){var r=this.createChar(t,(o.left||o.rep),p);var E=this.createChar(t,(o.right||o.rep),p);v.Add(r,-r.l,0);var D=(r.r-r.l)+(E.r-E.l),B=r.r-r.l;if(o.mid){var C=this.createChar(t,o.mid,p);D+=C.w}if(o.min&&qD){var A=this.createChar(t,o.rep,p),n=o.fuzz||0;var u=(o.mid?2:1),z=(q-D)/u,F=(z+n)/(A.r-A.l);while(u-->0){var y=a.Element("g",{transform:"translate("+(B-n/2-F*A.l+A.x)+","+A.y+") scale("+F+",1)"});y.appendChild(A.element.cloneNode(false));v.element.appendChild(y);B+=z;if(o.mid&&u){v.Add(C,B,0);B+=C.w}}}else{if(o.mid){B-=(D-q)/2;v.Add(C,B,0);B+=C.w-(D-q)/2}else{B-=(D-q)}}v.Add(E,B-E.l,0);v.Clean();v.scale=t;v.isMultiChar=true},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:300,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,NBSP:"\u00A0"});var l=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(n){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,n)}},With:function(n){return e.Insert(this,n)},Add:function(q,w,v,n,u){if(w){q.x+=w}if(v){q.y+=v}if(q.element){if(q.removeable&&q.element.childNodes.length===1&&q.n===1){var o=q.element.firstChild,s=o.nodeName.toLowerCase();if(s==="use"||s==="rect"){q.element=o;q.scale=q.childScale;var t=q.childX,r=q.childY;q.x+=t;q.y+=r;q.h-=r;q.d+=r;q.H-=r;q.D+=r;q.w-=t;q.r-=t;q.l+=t;q.removeable=false;o.setAttribute("x",Math.floor(q.x/q.scale));o.setAttribute("y",Math.floor(q.y/q.scale))}}if(Math.abs(q.x)<1&&Math.abs(q.y)<1){q.remove=q.removeable}else{s=q.element.nodeName.toLowerCase();if(s==="g"){if(!q.element.firstChild){q.remove=q.removeable}else{q.element.setAttribute("transform","translate("+Math.floor(q.x)+","+Math.floor(q.y)+")")}}else{if(s==="line"||s==="polygon"||s==="path"||s==="a"){var p=q.element.getAttribute("transform")||"";if(p){p=" "+p}p="translate("+Math.floor(q.x)+","+Math.floor(q.y)+")"+p;q.element.setAttribute("transform",p)}else{q.element.setAttribute("x",Math.floor(q.x/q.scale));q.element.setAttribute("y",Math.floor(q.y/q.scale))}}}if(q.remove){this.n+=q.n;while(q.element.firstChild){if(u&&this.element.firstChild){this.element.insertBefore(q.element.firstChild,this.element.firstChild)}else{this.element.appendChild(q.element.firstChild)}}}else{if(u){this.element.insertBefore(q.element,this.element.firstChild)}else{this.element.appendChild(q.element)}}delete q.element}if(q.hasIndent){this.hasIndent=q.hasIndent}if(q.tw!=null){this.tw=q.tw}if(q.d-q.y>this.d){this.d=q.d-q.y;if(this.d>this.D){this.D=this.d}}if(q.y+q.h>this.h){this.h=q.y+q.h;if(this.h>this.H){this.H=this.h}}if(q.D-q.y>this.D){this.D=q.D-q.y}if(q.y+q.H>this.H){this.H=q.y+q.H}if(q.x+q.lthis.r){this.r=q.x+q.r}if(n||q.x+q.w+(q.X||0)>this.w){this.w=q.x+q.w+(q.X||0)}this.childScale=q.scale;this.childX=q.x;this.childY=q.y;this.n++;return q},Align:function(r,s,q,p,o){q=({left:q,center:(this.w-r.w)/2,right:this.w-r.w-q})[s]||0;var n=this.w;this.Add(r,q+(o||0),p);this.w=n},Clean:function(){if(this.h===-a.BIGDIMEN){this.h=this.d=this.l=0}return this}});l.ROW=l.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(o){var n=o.toSVG();this.svg.push(n);if(o.SVGcanStretch("Vertical")){n.mml=o}if(n.h+n.y>this.sh){this.sh=n.h+n.y}if(n.d-n.y>this.sd){this.sd=n.d-n.y}},Stretch:function(){for(var q=0,n=this.svg.length;qo.w&&a.isChar(r)&&!q.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGchildSVG:function(n){return(this.data[n]?this.data[n].toSVG():l())},SVGdataStretched:function(o,n,p){this.SVGdata={HW:n,D:p};if(!this.data[o]){return l()}if(p!=null){return this.data[o].SVGstretchV(n,p)}if(n!=null){return this.data[o].SVGstretchH(n)}return this.data[o].toSVG()},SVGsaveData:function(n){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=n.w,this.SVGdata.x=n.x;this.SVGdata.h=n.h,this.SVGdata.d=n.d;if(n.y){this.SVGdata.h+=n.y;this.SVGdata.d-=n.y}if(n.X!=null){this.SVGdata.X=n.X}if(n.tw!=null){this.SVGdata.tw=n.tw}if(n.skew){this.SVGdata.skew=n.skew}if(n.ic){this.SVGdata.ic=n.ic}if(this["class"]){n.removeable=false;a.Element(n.element,{"class":this["class"]})}if(this.id){n.removeable=false;a.Element(n.element,{id:this.id})}if(this.href){this.SVGaddHref(n)}if(a.config.addMMLclasses){this.SVGaddClass(n.element,"mjx-svg-"+this.type);n.removeable=false}var o=this.style;if(o&&n.element){n.element.style.cssText=o;if(n.element.style.fontSize){n.element.style.fontSize=""}n.element.style.border=n.element.style.padding="";if(n.removeable){n.removeable=(n.element.style.cssText==="")}}this.SVGaddAttributes(n)},SVGaddClass:function(p,n){var o=p.getAttribute("class");p.setAttribute("class",(o?o+" ":"")+n)},SVGaddAttributes:function(o){if(this.attrNames){var u=this.attrNames,q=i.nocopyAttributes,t=e.config.ignoreMMLattributes;var r=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var p=0,n=u.length;p600?"bold":"normal")}return o},SVGhandleSpace:function(q){if(this.hasMMLspacing()){if(this.type!=="mo"){return}var p=this.getValues("scriptlevel","lspace","rspace");if(p.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var o=this.SVGgetMu(q);p.lspace=Math.max(0,a.length2em(p.lspace,o));p.rspace=Math.max(0,a.length2em(p.rspace,o));var n=this,r=this.Parent();while(r&&r.isEmbellished()&&r.Core()===n){n=r;r=r.Parent()}if(p.lspace){q.x+=p.lspace}if(p.rspace){q.X=p.rspace}}}else{var s=this.texSpacing();this.SVGgetScale();if(s!==""){q.x+=a.length2em(s,this.scale)*this.mscale}}},SVGhandleColor:function(r){var A=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!A.color){A.color=this.styles.color}if(A.color&&!this.mathcolor){A.mathcolor=A.color}if(A.mathcolor){a.Element(r.element,{fill:A.mathcolor,stroke:A.mathcolor});r.removeable=false}var v=(this.styles||{}).border,y=(this.styles||{}).padding,w=((v||{}).left||0),t=((y||{}).left||0),n;A.background=(this.mathbackground||this.background||(this.styles||{}).background||i.COLOR.TRANSPARENT);if(w+t){var o=l();for(n in r){if(r.hasOwnProperty(n)){o[n]=r[n]}}o.x=0;o.y=0;r.element=a.Element("g");r.removeable=true;r.Add(o,w+t,0)}if(y){r.w+=y.right||0;r.h+=y.top||0;r.d+=y.bottom||0}if(v){r.w+=v.right||0;r.h+=v.top||0;r.d+=v.bottom||0}if(A.background!==i.COLOR.TRANSPARENT){var x=r.element.nodeName.toLowerCase();if(x!=="g"&&x!=="svg"){var s=a.Element("g");s.appendChild(r.element);r.element=s;r.removeable=true}r.Add(l.RECT(r.h,r.d,r.w,{fill:A.background,stroke:"none"}),0,0,false,true)}if(v){var z=5;var p={left:["V",r.h+r.d,-z,-r.d],right:["V",r.h+r.d,r.w-v.right+z,-r.d],top:["H",r.w,0,r.h-v.top+z],bottom:["H",r.w,0,-r.d-z]};for(n in p){if(p.hasOwnProperty(n)){if(v[n]){var u=p[n],q=l[u[0]+"LINE"];r.Add(q(u[1],v[n],v[n+"Style"],v[n+"Color"]),u[2],u[3])}}}}},SVGhandleVariant:function(n,p,o){return a.HandleVariant(n,p,o)},SVGgetVariant:function(){var n=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var o=n.mathvariant;if(this.variantForm){o="-"+a.fontInUse+"-variant"}n.hasVariant=this.Get("mathvariant",true);if(!n.hasVariant){n.family=n.fontfamily;n.weight=n.fontweight;n.style=n.fontstyle}if(this.styles){if(!n.style&&this.styles.fontStyle){n.style=this.styles.fontStyle}if(!n.weight&&this.styles.fontWeight){n.weight=this.styles.fontWeight}if(!n.family&&this.styles.fontFamily){n.family=this.styles.fontFamily}}if(n.family&&!n.hasVariant){if(!n.weight&&n.mathvariant.match(/bold/)){n.weight="bold"}if(!n.style&&n.mathvariant.match(/italic/)){n.style="italic"}o={forceFamily:true,font:{"font-family":n.family}};if(n.style){o.font["font-style"]=n.style}if(n.weight){o.font["font-weight"]=n.weight}return o}if(n.weight==="bold"){o={normal:i.VARIANT.BOLD,italic:i.VARIANT.BOLDITALIC,fraktur:i.VARIANT.BOLDFRAKTUR,script:i.VARIANT.BOLDSCRIPT,"sans-serif":i.VARIANT.BOLDSANSSERIF,"sans-serif-italic":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.weight==="normal"){o={bold:i.VARIANT.normal,"bold-italic":i.VARIANT.ITALIC,"bold-fraktur":i.VARIANT.FRAKTUR,"bold-script":i.VARIANT.SCRIPT,"bold-sans-serif":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.SANSSERIFITALIC}[o]||o}}if(n.style==="italic"){o={normal:i.VARIANT.ITALIC,bold:i.VARIANT.BOLDITALIC,"sans-serif":i.VARIANT.SANSSERIFITALIC,"bold-sans-serif":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.style==="normal"){o={italic:i.VARIANT.NORMAL,"bold-italic":i.VARIANT.BOLD,"sans-serif-italic":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.BOLDSANSSERIF}[o]||o}}if(!(o in a.FONTDATA.VARIANT)){o="normal"}return a.FONTDATA.VARIANT[o]},SVGgetScale:function(o){var p=1;if(this.mscale){p=this.scale}else{var n=this.getValues("scriptlevel","fontsize");n.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if((this.styles||{}).fontSize&&!n.fontsize){n.fontsize=this.styles.fontSize}if(n.fontsize&&!this.mathsize){n.mathsize=n.fontsize}if(n.scriptlevel!==0){if(n.scriptlevel>2){n.scriptlevel=2}p=Math.pow(this.Get("scriptsizemultiplier"),n.scriptlevel);n.scriptminsize=a.length2em(this.Get("scriptminsize"))/1000;if(p2){o.scriptlevel=2}n=Math.sqrt(Math.pow(o.scriptsizemultiplier,o.scriptlevel))}return n},SVGnotEmpty:function(n){while(n){if((n.type!=="mrow"&&n.type!=="texatom")||n.data.length>1){return true}n=n.data[0]}return false},SVGcanStretch:function(p){var o=false;if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){o=n.SVGcanStretch(p);if(o&&n.forceStretch){this.forceStretch=true}}}return o},SVGstretchV:function(n,o){return this.toSVG(n,o)},SVGstretchH:function(n){return this.toSVG(n)},SVGlineBreaks:function(){return false}},{SVGemptySVG:function(){var n=this.SVG();n.Clean();this.SVGsaveData(n);return n},SVGautoload:function(){this.constructor.Augment({toSVG:i.mbase.SVGautoloadFail});var n=a.autoloadDir+"/"+this.type+".js";e.RestartAfter(j.Require(n))},SVGautoloadFail:function(){throw Error("SVG can't autoload '"+this.type+"'")},SVGautoloadList:{},SVGautoloadFile:function(n){if(i.mbase.SVGautoloadList.hasOwnProperty(n)){throw Error("SVG can't autoload file '"+n+"'")}i.mbase.SVGautoloadList[n]=true;var o=a.autoloadDir+"/"+n+".js";e.RestartAfter(j.Require(o))}});i.chars.Augment({toSVG:function(o,r,n,p){var q=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.entity.Augment({toSVG:function(o,r,n,p){var q=this.toString().replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.mo.Augment({toSVG:function(o,n){this.SVGgetStyles();var v=this.svg=this.SVG();var r=this.SVGgetScale(v);this.SVGhandleSpace(v);if(this.data.length==0){v.Clean();this.SVGsaveData(v);return v}if(n!=null){return this.SVGstretchV(o,n)}else{if(o!=null){return this.SVG.strechH(o)}}var t=this.SVGgetVariant();var B=this.getValues("largeop","displaystyle");if(B.largeop){t=a.FONTDATA.VARIANT[B.displaystyle?"-largeOp":"-smallOp"]}var A=this.CoreParent(),s=(A&&A.isa(i.msubsup)&&this!==A.data[0]),p=(s?this.remapChars:null);if(a.isChar(this.data.join(""))&&A&&A.isa(i.munderover)&&a.isChar(this.CoreText(A.data[A.base]))){var w=A.data[A.over],z=A.data[A.under];if(w&&this===w.CoreMO()&&A.Get("accent")){p=a.FONTDATA.REMAPACCENT}else{if(z&&this===z.CoreMO()&&A.Get("accentunder")){p=a.FONTDATA.REMAPACCENTUNDER}}}if(s&&this.data.join("").match(/['`"\u00B4\u2032-\u2037\u2057]/)){t=a.FONTDATA.VARIANT["-"+a.fontInUse+"-variant"]}for(var u=0,q=this.data.length;u10*C.w){y+=-C.l}v.Add(C,y,0,true);if(C.skew){v.skew=C.skew}}}v.Clean();if(!a.isChar(this.data.join(""))){delete v.skew}if(B.largeop){v.y=a.TeX.axis_height-(v.h-v.d)/2/r;if(v.r>v.w){v.ic=v.r-v.w;v.w=v.r}}this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGcanStretch:function(r){if(!this.Get("stretchy")){return false}var s=this.data.join("");if(s.length>1){return false}var o=this.CoreParent();if(o&&o.isa(i.munderover)&&a.isChar(this.CoreText(o.data[o.base]))){var q=o.data[o.over],n=o.data[o.under];if(q&&this===q.CoreMO()&&o.Get("accent")){s=a.FONTDATA.REMAPACCENT[s]||s}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){s=a.FONTDATA.REMAPACCENTUNDER[s]||s}}}s=a.FONTDATA.DELIMITERS[s.charCodeAt(0)];var p=(s&&s.dir==r.substr(0,1));if(!p){delete this.svg}this.forceStretch=p&&(this.Get("minsize",true)||this.Get("maxsize",true));return p},SVGstretchV:function(s,t){var p=this.svg||this.toSVG();var o=this.getValues("symmetric","maxsize","minsize");var r=a.TeX.axis_height*p.scale,n=this.SVGgetMu(p),q;if(o.symmetric){q=2*Math.max(s-r,t+r)}else{q=s+t}o.maxsize=a.length2em(o.maxsize,n,p.h+p.d);o.minsize=a.length2em(o.minsize,n,p.h+p.d);q=Math.max(o.minsize,Math.min(o.maxsize,q));if(q!=o.minsize){q=[Math.max(q*a.TeX.delimiterfactor/1000,q-a.TeX.delimitershortfall),q]}p=a.createDelimiter(this.data.join("").charCodeAt(0),q,p.scale);if(o.symmetric){q=(p.h+p.d)/2+r}else{q=(p.h+p.d)*s/(s+t)}p.y=q-p.h;this.SVGhandleSpace(p);this.SVGhandleColor(p);delete this.svg.element;this.SVGsaveData(p);p.stretched=true;return p},SVGstretchH:function(o){var q=this.svg||this.toSVG(),n=this.SVGgetMu(q);var p=this.getValues("maxsize","minsize","mathvariant","fontweight");if((p.fontweight==="bold"||parseInt(p.fontweight)>=600)&&!this.Get("mathvariant",true)){p.mathvariant=i.VARIANT.BOLD}p.maxsize=a.length2em(p.maxsize,n,q.w);p.minsize=a.length2em(p.minsize,n,q.w);o=Math.max(p.minsize,Math.min(p.maxsize,o));q=a.createDelimiter(this.data.join("").charCodeAt(0),o,q.scale,p.mathvariant);this.SVGhandleSpace(q);this.SVGhandleColor(q);delete this.svg.element;this.SVGsaveData(q);q.stretched=true;return q}});i.mn.Augment({SVGremapMinus:function(n){return n.replace(/^-/,"\u2212")},toSVG:function(){this.SVGgetStyles();var r=this.SVGgetVariant();var o=this.SVG();this.SVGgetScale(o);this.SVGhandleSpace(o);var q=this.SVGremapMinus;for(var p=0,n=this.data.length;po.w&&a.isChar(s)&&!r.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},}),i.mtext.Augment({toSVG:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){this.SVGgetStyles();var n=this.SVG(),q=this.SVGgetScale(n);this.SVGhandleSpace(n);var o=this.SVGgetVariant(),p={direction:this.Get("dir")};if(o.bold){p["font-weight"]="bold"}if(o.italic){p["font-style"]="italic"}o=this.Get("mathvariant");if(o==="monospace"){p["class"]="MJX-monospace"}else{if(o.match(/sans-serif/)){p["class"]="MJX-sans-serif"}}n.Add(l.TEXT(q*100/a.config.scale,this.data.join(""),p));n.Clean();this.SVGhandleColor(n);this.SVGsaveData(n);return n}else{return this.SUPER(arguments).toSVG.call(this)}}});i.merror.Augment({toSVG:function(p,n){this.SVGgetStyles();var t=this.SVG(),r=a.length2em(this.styles.fontSize||1)/1000;this.SVGhandleSpace(t);var o=(r!==1?{transform:"scale("+a.Fixed(r)+")"}:{});var v=l(o);v.Add(this.SVGchildSVG(0));v.Clean();if(r!==1){v.removeable=false;var u=["w","h","d","l","r","D","H"];for(var s=0,q=u.length;st.H){t.H=t.h}if(t.d>t.D){t.D=t.d}}this.SVGhandleColor(t);this.SVGsaveData(t);return t},SVGlength2em:function(q,t,o,u,n){if(n==null){n=-a.BIGDIMEN}var r=String(t).match(/width|height|depth/);var s=(r?q[r[0].charAt(0)]:(u?q[u]:0));var p=a.length2em(t,o,s/this.mscale)*this.mscale;if(u&&String(t).match(/^\s*[-+]/)){return Math.max(n,q[u]+p)}else{return p}}});i.mrow.Augment({SVG:l.ROW,toSVG:function(q,s){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(s!=null){o.sh=q;o.sd=s}for(var p=0,n=this.data.length;pa.linebreakWidth)||this.hasNewline()},SVGmultiline:function(n){i.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(o){var p=this.SVG();this.SVGhandleSpace(p);for(var q=0,n=this.data.length;qz){n=((u.h+u.d)-(z-A))/2}w=l.RECT(A,0,r.w);z=r.h+n+A;y=this.SVGaddRoot(v,u,y,u.h+u.d-z,s);v.Add(u,y,z-u.h);v.Add(w,y+u.w,z-w.h);v.Add(r,y+u.w,0);v.Clean();v.h+=A;v.H+=A;this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGaddRoot:function(o,p,n,r,q){return n}});i.mroot.Augment({toSVG:i.msqrt.prototype.toSVG,SVGaddRoot:function(q,o,t,r,n){var v=(o.isMultiChar?0.55:0.65)*o.w;if(this.data[1]){var s=this.data[1].toSVG();s.x=0;var p=this.SVGrootHeight(o.h+o.d,n,s)-r;var u=Math.min(s.w,s.r);t=Math.max(u,v);q.Add(s,t-u,p)}else{v=t}return t-v},SVGrootHeight:function(p,o,n){return 0.45*(p-900*o)+600*o+Math.max(0,n.d-75)}});i.mfenced.Augment({SVG:l.ROW,toSVG:function(){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data.open){o.Check(this.data.open)}if(this.data[0]!=null){o.Check(this.data[0])}for(var p=1,n=this.data.length;pJ){J=N}if(!L[K]&&J>o){o=J}}}if(E==null&&G!=null){o=G}else{if(o==-a.BIGDIMEN){o=J}}for(K=J=0,H=this.data.length;KJ){J=N}}}var C=a.TeX.rule_thickness*this.mscale;var u,r,z,w,s,B,I,M=0;p=q[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,y:0,scale:O};if(p.ic){M=1.3*p.ic+0.05}for(K=0,H=this.data.length;KJ){F.skew+=(J-N-u)/2}}}else{z=a.TeX.big_op_spacing1*O;w=a.TeX.big_op_spacing3*O;I=Math.max(z,w-Math.max(0,v.d))}I=Math.max(I,1500/a.em);u+=M/2;r=p.y+p.h+v.d+I;v.h+=s;if(v.h>v.H){v.H=v.h}}else{if(K==this.under){if(A){I=3*C*O;s=0}else{z=a.TeX.big_op_spacing2*O;w=a.TeX.big_op_spacing4*O;I=Math.max(z,w-v.h)}I=Math.max(I,1500/a.em);u-=M/2;r=p.y-(p.d+v.h+I);v.d+=s;if(v.d>v.D){v.D=v.d}}}F.Add(v,u,r)}}F.Clean();this.SVGhandleColor(F);this.SVGsaveData(F);return F}});i.msubsup.Augment({toSVG:function(M,G){this.SVGgetStyles();var I=this.SVG(),Q=this.SVGgetScale(I);this.SVGhandleSpace(I);var K=this.SVGgetMu(I);var y=I.Add(this.SVGdataStretched(this.base,M,G));var w=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var O=a.TeX.x_height*Q,F=a.TeX.scriptspace*Q;var n,z;if(this.SVGnotEmpty(this.data[this.sup])){n=this.data[this.sup].toSVG();n.w+=F;n.r=Math.max(n.w,n.r)}if(this.SVGnotEmpty(this.data[this.sub])){z=this.data[this.sub].toSVG();z.w+=F;z.r=Math.max(z.w,z.r)}var J=a.TeX.sup_drop*w,H=a.TeX.sub_drop*w;var C=y.h+(y.y||0)-J,B=y.d-(y.y||0)+H,P=0,L;if(y.ic){y.w-=y.ic;P=1.3*y.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(a.isChar(this.data[this.base].data.join(""))&&y.scale===1&&!y.stretched&&!this.data[this.base].Get("largeop")){C=B=0}}var N=this.getValues("subscriptshift","superscriptshift");N.subscriptshift=(N.subscriptshift===""?0:a.length2em(N.subscriptshift,K));N.superscriptshift=(N.superscriptshift===""?0:a.length2em(N.superscriptshift,K));var A=y.w+y.x;if(!n){if(z){B=Math.max(B,a.TeX.sub1*Q,z.h-(4/5)*O,N.subscriptshift);I.Add(z,A,-B);this.data[this.sub].SVGdata.dy=-B}}else{if(!z){var o=this.getValues("displaystyle","texprimestyle");L=a.TeX[(o.displaystyle?"sup1":(o.texprimestyle?"sup3":"sup2"))];C=Math.max(C,L*Q,n.d+(1/4)*O,N.superscriptshift);I.Add(n,A+P,C);this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=C}else{B=Math.max(B,a.TeX.sub2*Q);var E=a.TeX.rule_thickness*Q;if((C-n.d)-(z.h-B)<3*E){B=3*E-C+n.d+z.h;J=(4/5)*O-(C-n.d);if(J>0){C+=J;B-=J}}I.Add(n,A+P,Math.max(C,N.superscriptshift));I.Add(z,A,-Math.max(B,N.subscriptshift));this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=Math.max(C,N.superscriptshift);this.data[this.sub].SVGdata.dy=-Math.max(B,N.subscriptshift)}}I.Clean();this.SVGhandleColor(I);this.SVGsaveData(I);return I}});i.mmultiscripts.Augment({toSVG:i.mbase.SVGautoload});i.mtable.Augment({toSVG:i.mbase.SVGautoload});i["annotation-xml"].Augment({toSVG:i.mbase.SVGautoload});i.math.Augment({SVG:l.Subclass({type:"svg",removeable:false}),toSVG:function(B,p){var F=a.config;if(this.data[0]){this.SVGgetStyles();i.mbase.prototype.displayAlign=e.config.displayAlign;i.mbase.prototype.displayIndent=e.config.displayIndent;if(String(e.config.displayIndent).match(/^0($|[a-z%])/i)){i.mbase.prototype.displayIndent="0"}var v=l.G();v.Add(this.data[0].toSVG(),0,0,true);v.Clean();this.SVGhandleColor(v);a.Element(v.element,{stroke:"currentColor",fill:"currentColor","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"});v.removeable=false;var x=this.SVG();x.element.setAttribute("xmlns:xlink",m);if(F.useFontCache&&!F.useGlobalCache){x.element.appendChild(l.GLYPH.defs)}x.Add(v);x.Clean();this.SVGsaveData(x);if(!B){x.element=x.element.firstChild;x.element.removeAttribute("transform");x.removable=true;return x}var u=Math.max(-x.l,0),o=Math.max(x.r-x.w,0);var q=x.element.style,A=a.TeX.x_height/a.ex;var E=(Math.ceil(x.H/A)+1)*A+a.HFUZZ,n=(Math.ceil(x.D/A)+1)*A+a.DFUZZ;var z=u+x.w+o;x.element.setAttribute("width",a.Ex(z));x.element.setAttribute("height",a.Ex(E+n));q.verticalAlign=a.Ex(-n);if(u){q.marginLeft=a.Ex(-u)}if(o){q.marginRight=a.Ex(-o)}x.element.setAttribute("viewBox",a.Fixed(-u,1)+" "+a.Fixed(-E,1)+" "+a.Fixed(z,1)+" "+a.Fixed(E+n,1));if(x.H>x.h){q.marginTop=a.Ex(x.h-E)}if(x.D>x.d){q.marginBottom=a.Ex(x.d-n);q.verticalAlign=a.Ex(-x.d)}if(Math.abs(z-a.cwidth)<10){q.maxWidth=a.Fixed(a.cwidth*a.em/1000*a.config.scale)+"px"}var y=this.Get("alttext");if(y&&!x.element.getAttribute("aria-label")){x.element.setAttribute("aria-label",y)}if(!x.element.getAttribute("role")){x.element.setAttribute("role","img")}x.element.setAttribute("focusable","false");B.appendChild(x.element);x.element=null;if(!this.isMultiline&&this.Get("display")==="block"&&!x.hasIndent){var C=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(C.indentalignfirst!==i.INDENTALIGN.INDENTALIGN){C.indentalign=C.indentalignfirst}if(C.indentalign===i.INDENTALIGN.AUTO){C.indentalign=this.displayAlign}if(C.indentshiftfirst!==i.INDENTSHIFT.INDENTSHIFT){C.indentshift=C.indentshiftfirst}if(C.indentshift==="auto"){C.indentshift="0"}var s=a.length2em(C.indentshift,1,a.cwidth);if(this.displayIndent!=="0"){var t=a.length2em(this.displayIndent,1,a.cwidth);s+=(C.indentalign===i.INDENTALIGN.RIGHT?-t:t)}p.style.textAlign=C.indentalign;if(s){e.Insert(q,({left:{marginLeft:a.Ex(s)},right:{marginRight:a.Ex(-s),marginLeft:a.Ex(Math.max(0,s-z))},center:{marginLeft:a.Ex(s),marginRight:a.Ex(-s)}})[C.indentalign])}}}return B}});i.TeXAtom.Augment({toSVG:function(n,q){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data[0]!=null){var p=this.SVGdataStretched(0,n,q),r=0;if(this.texClass===i.TEXCLASS.VCENTER){r=a.TeX.axis_height-(p.h+p.d)/2+p.d}o.Add(p,0,r);o.ic=p.ic;o.skew=p.skew}this.SVGhandleColor(o);this.SVGsaveData(o);return o}});i.maligngroup.Augment({toSVG:i.mbase.SVGemptySVG});i.malignmark.Augment({toSVG:i.mbase.SVGemptySVG});i.mprescripts.Augment({toSVG:i.mbase.SVGemptySVG});i.none.Augment({toSVG:i.mbase.SVGemptySVG});e.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});e.Browser.Select({Opera:function(n){a.Augment({operaZoomRefresh:true})}});e.Register.StartupHook("End Cookie",function(){if(e.config.menuSettings.zoom!=="None"){j.Require("[MathJax]/extensions/MathZoom.js")}});if(!document.createElementNS){if(!document.namespaces.svg){document.namespaces.add("svg",b)}a.Augment({Element:function(n,o){var p=(typeof(n)==="string"?document.createElement("svg:"+n):n);p.isMathJax=true;if(o){for(var q in o){if(o.hasOwnProperty(q)){p.setAttribute(q,o[q].toString())}}}return p}})}})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG); +MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,d=MathJax.OutputJax.SVG,b=d.BBOX;a.mtable.Augment({toSVG:function(aa){this.SVGgetStyles();var o=this.SVG(),ap=this.SVGgetScale(o);if(this.data.length===0){this.SVGsaveData(o);return o}var aN=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");if(aN.width.match(/%$/)){o.width=aN.width=d.Em((d.cwidth/1000)*(parseFloat(aN.width)/100))}var v=this.SVGgetMu(o);var aK=-1;var z=[],I=[],k=[],O=[],K=[],aI,aG,w=-1,aE,u,az,S,an,E,aA;var ac=d.FONTDATA.lineH*ap*aN.useHeight,ag=d.FONTDATA.lineD*ap*aN.useHeight;for(aI=0,aE=this.data.length;aIw){w=aG}K[aG]=b.G();k[aG]=-d.BIGDIMEN}an=S.data[aG-az];O[aI][aG]=an.toSVG();if(an.isEmbellished()){E=an.CoreMO();var aM=E.Get("minsize",true);if(aM){if(E.SVGcanStretch("Vertical")){aA=E.SVGdata.h+E.SVGdata.d;if(aA){aM=d.length2em(aM,v,aA);if(aM*E.SVGdata.h/aA>z[aI]){z[aI]=aM*E.SVGdata.h/aA}if(aM*E.SVGdata.d/aA>I[aI]){I[aI]=aM*E.SVGdata.d/aA}}}else{if(E.SVGcanStretch("Horizontal")){aM=d.length2em(aM,v,E.SVGdata.w);if(aM>k[aG]){k[aG]=aM}}}}}if(O[aI][aG].h>z[aI]){z[aI]=O[aI][aG].h}if(O[aI][aG].d>I[aI]){I[aI]=O[aI][aG].d}if(O[aI][aG].w>k[aG]){k[aG]=O[aI][aG].w}}}var ao=MathJax.Hub.SplitList;var am=ao(aN.columnspacing),T=ao(aN.rowspacing),ai=ao(aN.columnalign),L=ao(aN.rowalign),N=ao(aN.columnlines),h=ao(aN.rowlines),ar=ao(aN.columnwidth),aw=[];for(aI=0,aE=am.length;aIO.length){aD=O.length}}g=0;ay=-(aA+ab)+z[0];for(aI=0,aE=aD-1;aI0.98){aj=X/(V+X);at=V+X}else{at=V/(1-ax)}}else{at=Math.max(V+X,d.length2em(aN.width,v));for(aI=0,aE=Math.min(w,am.length);aI0.01){if(aJ&&at>V){at=(at-V)/aJ;for(aI=0,aE=B.length;aIq+az*ak){R.indentalign=ai[aK];ak=az*(al+az*aO);aH+=al+Math.max(0,ak)}}else{if(ai[aK]===R.indentalign){if(e<0){aO=az*e;e=0}ak+=az*e;if(al>az*ak){ak=az*al}ak+=aO;aH+=az*ak}else{ak-=az*e;if(aH-az*ak+al>d.cwidth){ak=az*(aH+al-d.cwidth);if(az*ak>0){aH=d.cwidth+az*ak;ak=0}}}}var G=o;o=this.SVG();o.hasIndent=true;o.w=o.r=Math.max(aH,d.cwidth);o.Align(K[aK],ai[aK],0,0,aO);o.Align(G,R.indentalign,0,0,ak);o.tw=aH}this.SVGsaveData(o);return o},SVGhandleSpace:function(e){if(!this.hasFrame&&!e.width){e.x=e.X=167}this.SUPER(arguments).SVGhandleSpace.call(this,e)}});a.mtd.Augment({toSVG:function(e,g){var f=this.svg=this.SVG();if(this.data[0]){f.Add(this.SVGdataStretched(0,e,g));f.Clean()}this.SVGhandleColor(f);this.SVGsaveData(f);return f}});MathJax.Hub.Startup.signal.Post("SVG mtable Ready");MathJax.Ajax.loadComplete(d.autoloadDir+"/mtable.js")}); +(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS-MML_SVG-full.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-AMS-MML_SVG.js b/revisions_report_files/mathjax-27/config/TeX-AMS-MML_SVG.js new file mode 100644 index 0000000..14f31e7 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-AMS-MML_SVG.js @@ -0,0 +1,63 @@ +/* + * /MathJax/config/TeX-AMS-MML_SVG.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +(function(d,h,l,g,m,b,j){var p="2.7.6";var i=MathJax.Extension;var c=i.MathEvents={version:p};var k=d.config.menuSettings;var o={hover:500,frame:{x:3.5,y:5,bwidth:1,bcolor:"#A6D",hwidth:"15px",hcolor:"#83A"},button:{x:-6,y:-3,wx:-2},fadeinInc:0.2,fadeoutInc:0.05,fadeDelay:50,fadeoutStart:400,fadeoutDelay:15*1000,styles:{".MathJax_Hover_Frame":{"border-radius":".25em","-webkit-border-radius":".25em","-moz-border-radius":".25em","-khtml-border-radius":".25em","box-shadow":"0px 0px 15px #83A","-webkit-box-shadow":"0px 0px 15px #83A","-moz-box-shadow":"0px 0px 15px #83A","-khtml-box-shadow":"0px 0px 15px #83A",border:"1px solid #A6D ! important",display:"inline-block",position:"absolute"},".MathJax_Menu_Button .MathJax_Hover_Arrow":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"4px","-webkit-border-radius":"4px","-moz-border-radius":"4px","-khtml-border-radius":"4px","font-family":"'Courier New',Courier","font-size":"9px",color:"#F0F0F0"},".MathJax_Menu_Button .MathJax_Hover_Arrow span":{display:"block","background-color":"#AAA",border:"1px solid","border-radius":"3px","line-height":0,padding:"4px"},".MathJax_Hover_Arrow:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_Hover_Arrow:hover span":{"background-color":"#CCC!important"}}};var n=c.Event={LEFTBUTTON:0,RIGHTBUTTON:2,MENUKEY:"altKey",KEY:{RETURN:13,ESCAPE:27,SPACE:32,LEFT:37,UP:38,RIGHT:39,DOWN:40},Mousedown:function(q){return n.Handler(q,"Mousedown",this)},Mouseup:function(q){return n.Handler(q,"Mouseup",this)},Mousemove:function(q){return n.Handler(q,"Mousemove",this)},Mouseover:function(q){return n.Handler(q,"Mouseover",this)},Mouseout:function(q){return n.Handler(q,"Mouseout",this)},Click:function(q){return n.Handler(q,"Click",this)},DblClick:function(q){return n.Handler(q,"DblClick",this)},Menu:function(q){return n.Handler(q,"ContextMenu",this)},Handler:function(t,r,s){if(l.loadingMathMenu){return n.False(t)}var q=b[s.jaxID];if(!t){t=window.event}t.isContextMenu=(r==="ContextMenu");if(q[r]){return q[r](t,s)}if(i.MathZoom){return i.MathZoom.HandleEvent(t,r,s)}},False:function(q){if(!q){q=window.event}if(q){if(q.preventDefault){q.preventDefault()}else{q.returnValue=false}if(q.stopPropagation){q.stopPropagation()}q.cancelBubble=true}return false},Keydown:function(r,q){if(!r){r=window.event}if(r.keyCode===n.KEY.SPACE){n.ContextMenu(r,this)}},ContextMenu:function(t,E,w){var B=b[E.jaxID],v=B.getJaxFromMath(E);var F=(B.config.showMathMenu!=null?B:d).config.showMathMenu;if(!F||(k.context!=="MathJax"&&!w)){return}if(c.msieEventBug){t=window.event||t}n.ClearSelection();f.ClearHoverTimer();if(v.hover){if(v.hover.remove){clearTimeout(v.hover.remove);delete v.hover.remove}v.hover.nofade=true}var u=MathJax.Menu;var G,D;if(u){if(u.loadingDomain){return n.False(t)}G=m.loadDomain("MathMenu");if(!G){u.jax=v;var r=u.menu.Find("Show Math As").submenu;r.items[0].name=v.sourceMenuTitle;r.items[0].format=(v.sourceMenuFormat||"MathML");r.items[1].name=j[v.inputJax].sourceMenuTitle;r.items[5].disabled=!j[v.inputJax].annotationEncoding;var A=r.items[2];A.disabled=true;var q=A.submenu.items;annotationList=MathJax.Hub.Config.semanticsAnnotations;for(var z=0,y=q.length;z0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS-MML_SVG.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-AMS_CHTML-full.js b/revisions_report_files/mathjax-27/config/TeX-AMS_CHTML-full.js new file mode 100644 index 0000000..8679837 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-AMS_CHTML-full.js @@ -0,0 +1,61 @@ +/* + * /MathJax/config/TeX-AMS_CHTML-full.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/output/CommonHTML/jax.js", + "[MathJax]/jax/output/CommonHTML/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k *":{position:"absolute"},".MJXc-bevelled > *":{display:"inline-block"},".mjx-stack":{display:"inline-block"},".mjx-op":{display:"block"},".mjx-under":{display:"table-cell"},".mjx-over":{display:"block"},".mjx-over > *":{"padding-left":"0px!important","padding-right":"0px!important"},".mjx-under > *":{"padding-left":"0px!important","padding-right":"0px!important"},".mjx-stack > .mjx-sup":{display:"block"},".mjx-stack > .mjx-sub":{display:"block"},".mjx-prestack > .mjx-presup":{display:"block"},".mjx-prestack > .mjx-presub":{display:"block"},".mjx-delim-h > .mjx-char":{display:"inline-block"},".mjx-surd":{"vertical-align":"top"},".mjx-mphantom *":{visibility:"hidden"},".mjx-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"2px 3px","font-style":"normal","font-size":"90%"},".mjx-annotation-xml":{"line-height":"normal"},".mjx-menclose > svg":{fill:"none",stroke:"currentColor"},".mjx-mtr":{display:"table-row"},".mjx-mlabeledtr":{display:"table-row"},".mjx-mtd":{display:"table-cell","text-align":"center"},".mjx-label":{display:"table-row"},".mjx-box":{display:"inline-block"},".mjx-block":{display:"block"},".mjx-span":{display:"inline"},".mjx-char":{display:"block","white-space":"pre"},".mjx-itable":{display:"inline-table",width:"auto"},".mjx-row":{display:"table-row"},".mjx-cell":{display:"table-cell"},".mjx-table":{display:"table",width:"100%"},".mjx-line":{display:"block",height:0},".mjx-strut":{width:0,"padding-top":k+"em"},".mjx-vsize":{width:0},".MJXc-space1":{"margin-left":".167em"},".MJXc-space2":{"margin-left":".222em"},".MJXc-space3":{"margin-left":".278em"},".mjx-chartest":{display:"block",visibility:"hidden",position:"absolute",top:0,"line-height":"normal","font-size":"500%"},".mjx-chartest .mjx-char":{display:"inline"},".mjx-chartest .mjx-box":{"padding-top":"1000px"},".MJXc-processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MJXc-processed":{display:"none"},".mjx-test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".mjx-test.mjx-test-display":{display:"table!important"},".mjx-test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".mjx-test.mjx-test-default":{display:"block!important",clear:"both"},".mjx-ex-box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .mjx-left-box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .mjx-right-box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .mjx-right-box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_CHTML_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401,position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}};var i=1000000;var n=5;var c={},r=MathJax.Hub.config;a.Augment({settings:f.config.menuSettings,config:{styles:p},Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var s=this.settings;if(s.scale){this.config.scale=s.scale}this.require.push(this.fontDir+"/TeX/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js");c=this.config.linebreaks},Startup:function(){e=MathJax.Extension.MathEvents.Event;q=MathJax.Extension.MathEvents.Touch;h=MathJax.Extension.MathEvents.Hover;this.ContextMenu=e.ContextMenu;this.Mousedown=e.AltContextMenu;this.Mouseover=h.Mouseover;this.Mouseout=h.Mouseout;this.Mousemove=h.Mousemove;var s=a.addElement(document.body,"mjx-block",{style:{display:"block",width:"5in"}});this.pxPerInch=s.offsetWidth/5;s.parentNode.removeChild(s);this.TestSpan=a.Element("mjx-test",{style:{left:"1em"}},[["mjx-left-box"],["mjx-ex-box"],["mjx-right-box"]]);return o.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){this.getDefaultExEm();if(this.defaultEm){return}var s=MathJax.Callback();o.timer.start(o,function(t){if(t.time(s)){f.signal.Post(["CommonHTML Jax - no default em size"]);return}a.getDefaultExEm();if(a.defaultEm){s()}else{setTimeout(t,t.delay)}},this.defaultEmDelay,this.defaultEmTimeout);return s},defaultEmDelay:100,defaultEmTimeout:1000,getDefaultExEm:function(){var s=document.body.appendChild(this.TestSpan.cloneNode(true));s.className+=" mjx-test-inline mjx-test-default";this.defaultEm=this.getFontSize(s);this.defaultEx=s.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,s.lastChild.offsetLeft-s.firstChild.offsetLeft-2);document.body.removeChild(s)},getFontSize:(window.getComputedStyle?function(t){var s=window.getComputedStyle(t);return parseFloat(s.fontSize)}:function(s){return s.style.pixelLeft}),getMaxWidth:(window.getComputedStyle?function(t){var s=window.getComputedStyle(t);if(s.maxWidth!=="none"){return parseFloat(s.maxWidth)}return 0}:function(t){var s=t.currentStyle.maxWidth;if(s!=="none"){if(s.match(/\d*px/)){return parseFloat(s)}var u=t.style.left;t.style.left=s;s=t.style.pixelLeft;t.style.left=u;return s}return 0}),loadFont:function(s){f.RestartAfter(o.Require(this.fontDir+"/"+s))},fontLoaded:function(s){if(!s.match(/-|fontdata/)){s+="-Regular"}if(!s.match(/\.js$/)){s+=".js"}MathJax.Callback.Queue(["Post",f.Startup.signal,"CommonHTML - font data loaded for "+s],["loadComplete",o,this.fontDir+"/"+s])},Element:function(s,u,t){if(s.substr(0,4)==="mjx-"){if(!u){u={}}if(u.isMathJax==null){u.isMathJax=true}if(u.className){u.className=s+" "+u.className}else{u.className=s}s="span"}return this.HTMLElement(s,u,t)},addElement:function(u,s,v,t){return u.appendChild(this.Element(s,v,t))},HTMLElement:m.Element,ucMatch:m.ucMatch,setScript:m.setScript,getNode:function(x,w){var u=RegExp("\\b"+w+"\\b");var t=[];while(x){for(var v=0,s=x.childNodes.length;v=x.CHTMLlast+x.CHTMLchunk){this.postTranslate(x);x.CHTMLchunk=Math.floor(x.CHTMLchunk*this.config.EqnChunkFactor);x.CHTMLdelay=true}},initCHTML:function(t,s){},savePreview:function(s){var t=s.MathJax.preview;if(t&&t.parentNode){s.MathJax.tmpPreview=document.createElement("span");t.parentNode.replaceChild(s.MathJax.tmpPreview,t)}},restorePreview:function(s){var t=s.MathJax.tmpPreview;if(t){t.parentNode.replaceChild(s.MathJax.preview,t);delete s.MathJax.tmpPreview}},getMetrics:function(s){var t=s.CHTML;this.jax=s;this.em=t.em;this.outerEm=t.outerEm;this.scale=t.scale;this.cwidth=t.cwidth;this.linebreakWidth=t.lineWidth},postTranslate:function(x){var t=x.jax[this.id];for(var v=x.CHTMLlast,s=x.CHTMLeqn;vC.h){t.marginTop=a.Em(C.t-C.h)}if(C.b>C.d){t.marginBottom=a.Em(C.b-C.d)}if(C.l<0){t.paddingLeft=a.Em(-C.l)}if(C.r>C.w){t.marginRight=a.Em(C.r-C.w)}t.position="absolute";var z=v.offsetWidth,x=v.offsetHeight,D=A.firstChild.offsetHeight,w=A.firstChild.offsetWidth;v.style.position="";return{Y:-e.getBBox(B).h,mW:w,mH:D,zW:z,zH:x}},Remove:function(s){var t=document.getElementById(s.inputID+"-Frame");if(t&&s.CHTML.display){t=t.parentNode}if(t){t.parentNode.removeChild(t)}delete s.CHTML},ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18,thin:0.04,medium:0.06,thick:0.1,infinity:i},SPACECLASS:{thinmathspace:"MJXc-space1",mediummathspace:"MJXc-space2",thickmathspace:"MJXc-space3"},pxPerInch:96,em:16,maxStretchyParts:1000,FONTDEF:{},TEXDEF:{x_height:0.442,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.45,big_op_spacing5:0.1,surd_height:0.075,scriptspace:0.05,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},isChar:function(s){if(s.length===1){return true}if(s.length!==2){return false}var t=s.charCodeAt(0);return(t>=55296&&t<56319)},unicodeChar:function(s){if(s<65535){return String.fromCharCode(s)}s-=65536;return String.fromCharCode((s>>10)+55296)+String.fromCharCode((s&1023)+56320)},getUnicode:function(s){var t=s.text.charCodeAt(s.i);s.i++;if(t>=55296&&t<56319){t=(((t-55296)<<10)+(s.text.charCodeAt(s.i)-56320))+65536;s.i++}return t},getCharList:function(w,v){var u,z,s=w.cache,B=v;if(s[v]){return s[v]}if(v>65535&&this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(v,w);v=y.n;w=y.variant}var t=this.FONTDATA.RANGES,A=this.FONTDATA.VARIANT;if(v>=t[0].low&&v<=t[t.length-1].high){for(u=0,z=t.length;u=t[u].low&&v<=t[u].high){if(t[u].remap&&t[u].remap[v]){v=x+t[u].remap[v]}else{v=v-t[u].low+x;if(t[u].add){v+=t[u].add}}if(w["variant"+t[u].offset]){w=A[w["variant"+t[u].offset]]}break}}}s[B]=this.remapChar(w,v,0);return s[B]},remapChar:function(t,y,w){var v=[],x=this.FONTDATA.VARIANT;if(t.remap&&t.remap[y]){y=t.remap[y];if(t.remap.variant){t=x[t.remap.variant]}}else{if(this.FONTDATA.REMAP[y]&&!t.noRemap){y=this.FONTDATA.REMAP[y]}}if(g(y)){if(y[2]){w=n}t=x[y[1]];y=y[0]}if(typeof(y)==="string"){var s={text:y,i:0,length:y.length};while(s.i(B.a||0)){B.a=u.a}u.className=w.className;var t=w[D.n];if(A){var v=w;if(g(A)){v=a.FONTDATA.FONTS[A[1]];A=A[0];if(typeof(v)==="string"){a.loadFont(v)}}if(v[D.n]){a.fixChar(v[D.n],D.n)}t=a.fixChar(v[A],A);u.className=v.className}u.text+=t.c;if(B.hB.w+t[3]){B.l=B.w+t[3]}if(B.rw.a){w.a=u.a}}s=this.flushText(s,u,t.style);if(v[2]<3){s.style.width=a.Em(v[2])}},flushText:function(t,u,s){t=a.addElement(t,"mjx-charbox",{className:u.className,style:s},[u.text]);if(u.a){t.style.paddingBottom=a.Em(u.a)}u.text="";u.className=null;u.a=0;u.flushed=true;return t}},handleText:function(u,x,t,w){if(u.childNodes.length===0){a.addElement(u,"mjx-char");w=a.BBOX.empty(w)}if(typeof(t)==="string"){t=this.FONTDATA.VARIANT[t]}if(!t){t=this.FONTDATA.VARIANT[d.VARIANT.NORMAL]}var s={text:x,i:0,length:x.length},v=[];if(t.style&&s.length){v.push(this.styledText(t,x))}else{while(s.i-w.b){u.firstChild.style.paddingBottom=this.EmRounded(w.d+w.b)}return w},createDelimiter:function(x,s,u,A,v){if(!s){var B=this.BBOX.zero();B.w=B.r=this.TEX.nulldelimiterspace;a.addElement(x,"mjx-box",{style:{width:B.w}});return B}if(!(u instanceof Array)){u=[u,u]}var z=u[1];u=u[0];var t={alias:s};while(t.alias){s=t.alias;t=this.FONTDATA.DELIMITERS[s];if(!t){t={HW:[0,this.FONTDATA.VARIANT[d.VARIANT.NORMAL]]}}}if(t.load){f.RestartAfter(o.Require(this.fontDir+"/TeX/fontdata-"+t.load+".js"))}for(var y=0,w=t.HW.length;y=u-0.01||(y==w-1&&!t.stretch)){if(t.HW[y][3]){s=t.HW[y][3]}B=this.createChar(x,[s,t.HW[y][1]],(t.HW[y][2]||1),v);B.offset=0.6*B.w;if(A){B.scale=A.scale;A.rscale=A.rscale}return B}}if(!t.stretch){return B}return this["extendDelimiter"+t.dir](x,z,t.stretch,A,v)},extendDelimiterV:function(E,x,P,w,C){E=a.addElement(E,"mjx-delim-v");var N=a.Element("span");var B,A,O,v,I,t,F,y,G=1,M;I=this.createChar(N,(P.top||P.ext),1,C);B=N.removeChild(N.firstChild);t=this.createChar(N,(P.bot||P.ext),1,C);A=N.removeChild(N.firstChild);F=y=a.BBOX.zero();var J=I.h+I.d+t.h+t.d-l;E.appendChild(B);if(P.mid){F=this.createChar(N,P.mid,1,C);O=N.removeChild(N.firstChild);J+=F.h+F.d;G=2}if(P.min&&xJ){y=this.createChar(N,P.ext,1,C);v=N.removeChild(N.firstChild);var L=y.h+y.d,u=L-l;var D=Math.min(Math.ceil((x-J)/(G*u)),this.maxStretchyParts);if(P.fullExtenders){x=D*G*u+J}else{u=(x-J)/(G*D)}M=y.d+y.a-L/2;v.style.margin=v.style.padding="";v.style.lineHeight=a.Em(u);v.style.marginBottom=a.Em(M-l/2/G);v.style.marginTop=a.Em(-M-l/2/G);var K=v.textContent,z="\n"+K;while(--D>0){K+=z}v.textContent=K;E.appendChild(v);if(P.mid){E.appendChild(O);E.appendChild(v.cloneNode(true))}}else{M=(x-J-l)/G;B.style.marginBottom=a.Em(M+parseFloat(B.style.marginBottom||"0"));if(P.mid){E.appendChild(O)}A.style.marginTop=a.Em(M+parseFloat(A.style.marginTop||"0"))}E.appendChild(A);var s=a.BBOX({w:Math.max(I.w,y.w,t.w,F.w),l:Math.min(I.l,y.l,t.l,F.l),r:Math.max(I.r,y.r,t.r,F.r),h:x-t.d,d:t.d,t:x-t.d,b:t.d});s.offset=0.5*s.w;if(w){s.scale=w.scale;s.rscale=w.rscale}return s},extendDelimiterH:function(F,s,P,v,D){F=a.addElement(F,"mjx-delim-h");var N=a.Element("span");var t,M,O,u,K,C,x,G,z,H=1;C=this.createChar(N,(P.left||P.rep),1,D);t=N.removeChild(N.firstChild);x=this.createChar(N,(P.right||P.rep),1,D);M=N.removeChild(N.firstChild);z=this.createChar(N,P.rep,1,D);u=N.removeChild(N.firstChild);t.style.marginLeft=a.Em(-C.l);M.style.marginRight=a.Em(x.r-x.w);F.appendChild(t);var Q=a.BBOX.zero();Q.h=Math.max(C.h,x.h,z.h);Q.d=Math.max(C.D||C.d,x.D||x.d,z.D||z.d);var y=(C.r-C.l)+(x.r-x.l)-l;if(P.mid){G=this.createChar(N,P.mid,1,D);O=N.removeChild(N.firstChild);O.style.marginleft=a.Em(-G.l);O.style.marginRight=a.Em(G.r-G.w);y+=G.r-G.l+l;H=2;if(G.h>Q.h){Q.h=G.h}if(G.d>Q.d){Q.d=G.d}}if(P.min&&sy){var B=z.r-z.l,J=B-l;var E=Math.min(Math.ceil((s-y)/(H*J)),this.maxStretchyParts);if(P.fullExtenders){s=E*H*J+y}else{J=(s-y)/(H*E)}var L=(B-J+l/H)/2;u.style.marginLeft=a.Em(-z.l-L);u.style.marginRight=a.Em(z.r-z.w+L);u.style.letterSpacing=a.Em(-(z.w-J));t.style.marginRight=a.Em(C.r-C.w);M.style.marginleft=a.Em(-x.l);var I=u.textContent,A=I;while(--E>0){I+=A}u.textContent=I;F.appendChild(u);if(P.mid){F.appendChild(O);K=F.appendChild(u.cloneNode(true))}}else{L=(s-y-l/H)/2;t.style.marginRight=a.Em(C.r-C.w+L);if(P.mid){F.appendChild(O)}M.style.marginLeft=a.Em(-x.l+L)}F.appendChild(M);this.adjustHeights([t,u,O,K,M],[C,z,G,z,x],Q);if(v){Q.scale=v.scale;Q.rscale=v.rscale}return Q},adjustHeights:function(t,w,x){var u=x.h,y=x.d;if(x.d<0){y=-x.d;x.D=x.d;x.d=0}for(var v=0,s=t.length;v0){delete this.D}},rescale:function(s){this.w*=s;this.h*=s;this.d*=s;this.l*=s;this.r*=s;this.t*=s;this.b*=s;if(this.L){this.L*=s}if(this.R){this.R*=s}if(this.D){this.D*=s}},combine:function(t,s,v){t.X=s;t.Y=v;var u=t.rscale;if(s+u*t.r>this.r){this.r=s+u*t.r}if(s+u*t.lthis.w){this.w=s+u*(t.w+(t.L||0)+(t.R||0))}if(v+u*t.h>this.h){this.h=v+u*t.h}if(t.D&&(this.D==null||u*t.D-v>this.D)&&u*t.D>this.d){this.D=u*t.D-v}else{if(t.D==null&&this.D){delete this.D}}if(u*t.d-v>this.d){this.d=u*t.d-v}if(v+u*t.t>this.t){this.t=v+u*t.t}if(u*t.b-v>this.b){this.b=u*t.b-v}},append:function(t){var u=t.rscale;var s=this.w;if(s+u*t.r>this.r){this.r=s+u*t.r}if(s+u*t.lthis.h){this.h=u*t.h}if(t.D&&(this.D==null||u*t.D>this.D)&&u*t.D>this.d){this.D=u*t.D}else{if(t.D==null&&this.D){delete this.D}}if(u*t.d>this.d){this.d=u*t.d}if(u*t.t>this.t){this.t=u*t.t}if(u*t.b>this.b){this.b=u*t.b}},updateFrom:function(s){this.h=s.h;this.d=s.d;this.w=s.w;this.r=s.r;this.l=s.l;this.t=s.t;this.b=s.b;if(s.pwidth){this.pwidth=s.pwidth}if(s.D){this.D=s.D}else{delete this.D}},adjust:function(t,s,v,u){this[s]+=a.length2em(t,1,this.scale);if(u==null){if(this[s]>this[v]){this[v]=this[s]}}else{if(this[v]z.r){z.r=z.w}if(t.h>z.h){z.h=t.h}if(t.d>z.d){z.d=t.d}if(t.t>z.t){z.t=t.t}if(t.b>z.b){z.b=t.b}}}},CHTMLstretchChildH:function(v,s,x){var y=this.data[v];if(y){var z=this.CHTML,u=y.CHTML;if(u.stretch||(u.stretch==null&&y.CHTMLcanStretch("Horizontal",s))){var t=u.w;u=y.CHTMLstretchH(this.CHTMLchildNode(x,v),s);z.w+=u.w-t;if(z.w>z.r){z.r=z.w}if(u.h>z.h){z.h=u.h}if(u.d>z.d){z.d=u.d}if(u.t>z.t){z.t=u.t}if(u.b>z.b){z.b=u.b}}}},CHTMLupdateFrom:function(s){this.CHTML.updateFrom(s);if(this.inferRow){this.data[0].CHTML.updateFrom(s)}},CHTMLcanStretch:function(w,u,v){var t=false;if(this.isEmbellished()){var s=this.Core();if(s&&s!==this){t=s.CHTMLcanStretch(w,u,v)}}this.CHTML.stretch=t;return t},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));return this.CHTML},CHTMLstretchCoreH:function(t,s){return this.Core().CHTMLstretchH(this.CHTMLcoreNode(t),s)},CHTMLcreateNode:function(s){if(!this.CHTML){this.CHTML={}}this.CHTML=a.BBOX.zero();if(this.href){s=a.addElement(s,"a",{href:this.href,isMathJax:true})}if(!this.CHTMLnodeID){this.CHTMLnodeID=a.GetID()}var t=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+a.idPostfix;return this.CHTMLhandleAttributes(a.addElement(s,"mjx-"+this.type,{id:t}))},CHTMLnodeElement:function(){if(!this.CHTMLnodeID){return null}return document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+a.idPostfix)},CHTMLlength2em:function(t,s){return a.length2em(t,s,this.CHTML.scale)},CHTMLhandleAttributes:function(v){if(this["class"]){if(v.className){v.className+=" "+this["class"]}else{v.className=this["class"]}}if(this.attrNames){var z=this.attrNames,u=d.nocopyAttributes,y=f.config.ignoreMMLattributes;var w=(this.type==="mstyle"?d.math.prototype.defaults:this.defaults);for(var t=0,s=z.length;t2){s.scriptlevel=2}x=Math.pow(this.Get("scriptsizemultiplier"),s.scriptlevel);s.scriptminsize=a.length2em(this.Get("scriptminsize"),0.8,1);if(x600?"bold":"normal")}var t=s.mathvariant;if(this.variantForm){t="-TeX-variant"}if(s.family&&!s.hasVariant){if(!s.weight&&s.mathvariant.match(/bold/)){s.weight="bold"}if(!s.style&&s.mathvariant.match(/italic/)){s.style="italic"}this.CHTMLvariant={fonts:[],noRemap:true,cache:{},style:{"font-family":s.family,"font-weight":s.weight||"normal","font-style":s.style||"normal"}};return}if(s.weight==="bold"){t={normal:d.VARIANT.BOLD,italic:d.VARIANT.BOLDITALIC,fraktur:d.VARIANT.BOLDFRAKTUR,script:d.VARIANT.BOLDSCRIPT,"sans-serif":d.VARIANT.BOLDSANSSERIF,"sans-serif-italic":d.VARIANT.SANSSERIFBOLDITALIC}[t]||t}else{if(s.weight==="normal"){t={bold:d.VARIANT.normal,"bold-italic":d.VARIANT.ITALIC,"bold-fraktur":d.VARIANT.FRAKTUR,"bold-script":d.VARIANT.SCRIPT,"bold-sans-serif":d.VARIANT.SANSSERIF,"sans-serif-bold-italic":d.VARIANT.SANSSERIFITALIC}[t]||t}}if(s.style==="italic"){t={normal:d.VARIANT.ITALIC,bold:d.VARIANT.BOLDITALIC,"sans-serif":d.VARIANT.SANSSERIFITALIC,"bold-sans-serif":d.VARIANT.SANSSERIFBOLDITALIC}[t]||t}else{if(s.style==="normal"){t={italic:d.VARIANT.NORMAL,"bold-italic":d.VARIANT.BOLD,"sans-serif-italic":d.VARIANT.SANSSERIF,"sans-serif-bold-italic":d.VARIANT.BOLDSANSSERIF}[t]||t}}this.CHTMLvariant=a.FONTDATA.VARIANT[t]||a.FONTDATA.VARIANT[d.VARIANT.NORMAL]},CHTMLbboxFor:function(s){if(this.data[s]&&this.data[s].CHTML){return this.data[s].CHTML}return a.BBOX.zero()},CHTMLdrawBBox:function(t,u){if(!u){u=this.CHTML}var s=a.Element("mjx-box",{style:{opacity:0.25,"margin-left":a.Em(-(u.w+(u.R||0)))}},[["mjx-box",{style:{height:a.Em(u.h),width:a.Em(u.w),"background-color":"red"}}],["mjx-box",{style:{height:a.Em(u.d),width:a.Em(u.w),"margin-left":a.Em(-u.w),"vertical-align":a.Em(-u.d),"background-color":"green"}}]]);if(t.nextSibling){t.parentNode.insertBefore(s,t.nextSibling)}else{t.parentNode.appendChild(s)}},CHTMLnotEmpty:function(s){while(s&&s.data.length<2&&(s.type==="mrow"||s.type==="texatom")){s=s.data[0]}return !!s}},{CHTMLautoload:function(){this.constructor.Augment({toCommonHTML:d.mbase.CHTMLautoloadFail});var s=a.autoloadDir+"/"+this.type+".js";f.RestartAfter(o.Require(s))},CHTMLautoloadFail:function(){throw Error("CommonHTML can't autoload '"+this.type+"'")},CHTMLautoloadList:{},CHTMLautoloadFile:function(s){if(d.mbase.CHTMLautoloadList.hasOwnProperty(s)){throw Error("CommonHTML can't autoload file '"+s+"'")}d.mbase.CHTMLautoloadList[s]=true;var t=a.autoloadDir+"/"+s+".js";f.RestartAfter(o.Require(t))},CHTMLstretchV:function(s,t){this.Core().CHTMLstretchV(s,t);this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.chars.Augment({toCommonHTML:function(t,s){this.CHTML=null;if(s==null){s={}}var u=this.toString();if(s.remap){u=s.remap(u,s.remapchars)}this.CHTMLhandleText(t,u,s.variant||this.parent.CHTMLvariant)}});d.entity.Augment({toCommonHTML:function(t,s){if(s==null){s={}}var u=this.toString();if(s.remapchars){u=s.remap(u,s.remapchars)}this.CHTMLhandleText(t,u,s.variant||this.parent.CHTMLvariant)}});d.math.Augment({toCommonHTML:function(x){x=this.CHTMLdefaultNode(x);if(this.CHTML.w<0){x.parentNode.style.width="0px";x.parentNode.style.marginRight=a.Em(this.CHTML.w)}var v=this.Get("alttext");if(v&&!x.getAttribute("aria-label")){x.setAttribute("aria-label",v)}if(this.CHTML.pwidth){x.parentNode.style.minWidth=this.CHTML.mwidth||a.Em(this.CHTML.w);x.parentNode.className="mjx-full-width "+x.parentNode.className;x.style.width=this.CHTML.pwidth}else{if(!this.isMultiline&&this.Get("display")==="block"){var u=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(u.indentalignfirst!==d.INDENTALIGN.INDENTALIGN){u.indentalign=u.indentalignfirst}if(u.indentalign===d.INDENTALIGN.AUTO){u.indentalign=r.displayAlign}if(u.indentshiftfirst!==d.INDENTSHIFT.INDENTSHIFT){u.indentshift=u.indentshiftfirst}if(u.indentshift==="auto"){u.indentshift="0"}var t=this.CHTMLlength2em(u.indentshift,a.cwidth);if(r.displayIndent!=="0"){var s=this.CHTMLlength2em(r.displayIndent,a.cwidth);t+=(u.indentalign===d.INDENTALIGN.RIGHT?-s:s)}var w=x.parentNode.parentNode.style;x.parentNode.style.textAlign=w.textAlign=u.indentalign;if(t){t*=a.em/a.outerEm;f.Insert(w,({left:{marginLeft:a.Em(t)},right:{marginRight:a.Em(-t)},center:{marginLeft:a.Em(t),marginRight:a.Em(-t)}})[u.indentalign])}}}return x}});d.mi.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&!a.isChar(t)){delete u.skew}if(u.r>u.w&&a.isChar(t)&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mn.Augment({CHTMLremapMinus:function(s){return s.replace(/^-/,"\u2212")},toCommonHTML:function(s){s=this.CHTMLdefaultNode(s,{childOptions:{remap:this.CHTMLremapMinus}});var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&!a.isChar(t)){delete u.skew}if(u.r>u.w&&a.isChar(t)&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mo.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLgetVariant();this.CHTMLhandleScale(v);a.BBOX.empty(this.CHTML);var t=this.getValues("displaystyle","largeop");t.variant=this.CHTMLvariant;t.text=this.data.join("");if(t.text==""){if(this.fence){v.style.width=a.Em(a.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(t);this.CHTMLadjustVariant(t);for(var u=0,s=this.data.length;u0){if(!this.hasValue("lspace")){t.lspace=0.15}if(!this.hasValue("rspace")){t.rspace=0.15}}var s=this,u=this.Parent();while(u&&u.isEmbellished()&&u.Core()===s){s=u;u=u.Parent();v=s.CHTMLnodeElement()}if(t.lspace){v.style.paddingLeft=a.Em(t.lspace)}if(t.rspace){v.style.paddingRight=a.Em(t.rspace)}this.CHTML.L=t.lspace;this.CHTML.R=t.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(u){var t=this.CoreParent();u.parent=t;if(a.isChar(u.text)&&t&&t.isa(d.munderover)){var v=t.data[t.over],s=t.data[t.under];if(v&&this===v.CoreMO()&&t.Get("accent")){u.remapchars=a.FONTDATA.REMAPACCENT}else{if(s&&this===s.CoreMO()&&t.Get("accentunder")){u.remapchars=a.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(t){var s=t.parent,u=(s&&s.isa(d.msubsup)&&this!==s.data[s.base]);if(t.largeop){t.mathvariant=(t.displaystyle?"-largeOp":"-smallOp")}if(u){t.remapchars=this.remapChars;if(t.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){t.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(s){s=s.firstChild;var t=a.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});s.insertBefore(t,s.firstChild)},CHTMLcenterOp:function(s){var u=this.CHTML;var t=(u.h-u.d)/2-a.TEX.axis_height;if(Math.abs(t)>0.001){s.style.verticalAlign=a.Em(-t)}u.h-=t;u.d+=t;if(u.r>u.w){u.ic=u.r-u.w;u.w=u.r;s.style.paddingRight=a.Em(u.ic)}},CHTMLcanStretch:function(w,u,v){if(!this.Get("stretchy")){return false}var x=this.data.join("");if(!a.isChar(x)){return false}var t={text:x};this.CHTMLadjustAccent(t);if(t.remapchars){x=t.remapchars[x]||x}x=a.FONTDATA.DELIMITERS[x.charCodeAt(0)];var s=(x&&x.dir===w.substr(0,1));if(s){s=(this.CHTML.h!==u||this.CHTML.d!==v||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(s){this.CHTML.stretch=true}}return s},CHTMLstretchV:function(v,y){var w=this.CHTMLnodeElement(),x=this.CHTML;var t=this.getValues("symmetric","maxsize","minsize");var u,s=a.TEX.axis_height;if(t.symmetric){u=2*Math.max(v-s,y+s)}else{u=v+y}t.maxsize=this.CHTMLlength2em(t.maxsize,x.h+x.d);t.minsize=this.CHTMLlength2em(t.minsize,x.h+x.d);u=Math.max(t.minsize,Math.min(t.maxsize,u));if(u!==x.sH){if(u!=t.minsize){u=[Math.max(u*a.TEX.delimiterfactor/1000,u-a.TEX.delimitershortfall),u]}while(w.firstChild){w.removeChild(w.firstChild)}this.CHTML=x=a.createDelimiter(w,this.data.join("").charCodeAt(0),u,x);x.sH=(u instanceof Array?u[1]:u);if(t.symmetric){u=(x.h+x.d)/2+s}else{u=(x.h+x.d)*v/(v+y)}u-=x.h;if(Math.abs(u)>0.05){w.style.verticalAlign=a.Em(u);x.h+=u;x.d-=u;x.t+=u;x.b-=u}}return this.CHTML},CHTMLstretchH:function(u,s){var v=this.CHTML;var t=this.getValues("maxsize","minsize","mathvariant","fontweight");if((t.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(t.fontweight)>=600)&&!this.Get("mathvariant",true)){t.mathvariant=d.VARIANT.BOLD}t.maxsize=this.CHTMLlength2em(t.maxsize,v.w);t.minsize=this.CHTMLlength2em(t.minsize,v.w);s=Math.max(t.minsize,Math.min(t.maxsize,s));if(s!==v.sW){while(u.firstChild){u.removeChild(u.firstChild)}this.CHTML=v=a.createDelimiter(u,this.data.join("").charCodeAt(0),s,v,t.mathvariant);v.sW=s}return this.CHTML}});d.mtext.Augment({CHTMLgetVariant:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){var u=(a.config.scale/100)/a.scale;var t={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:u,style:{"font-size":a.Percent(u)}};var s=this.Get("mathvariant");if(s.match(/bold/)){t.style["font-weight"]="bold"}if(s.match(/italic|-tex-mathit/)){t.style["font-style"]="italic"}if(s==="monospace"){t.className+=" MJXc-monospace-font"}if(s==="double-struck"){t.className+=" MJXc-double-struck-font"}if(s.match(/fraktur/)){t.className+=" MJXc-fraktur-font"}if(s.match(/sans-serif/)){t.className+=" MJXc-sans-serif-font"}if(s.match(/script/)){t.className+=" MJXc-script-font"}this.CHTMLvariant=t}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});d.merror.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var t=this.CHTML;t.rescale(0.9);t.h+=3/a.em;if(t.h>t.t){t.t=t.h}t.d+=3/a.em;if(t.d>t.b){t.b=t.d}t.w+=8/a.em;t.r=t.w;t.l=0;return s}});d.mspace.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);var t=this.getValues("height","depth","width");var s=this.CHTMLlength2em(t.width),u=this.CHTMLlength2em(t.height),y=this.CHTMLlength2em(t.depth);var x=this.CHTML;x.w=x.r=s;x.h=x.t=u;x.d=x.b=y;x.l=0;if(s<0){v.style.marginRight=a.Em(s);s=0}v.style.width=a.Em(s);v.style.height=a.Em(Math.max(0,u+y));if(y){v.style.verticalAlign=a.Em(-y)}this.CHTMLhandleBBox(v);this.CHTMLhandleColor(v);return v}});d.mpadded.Augment({toCommonHTML:function(t,F){var s;if(F&&F.stretch){t=t.firstChild;s=t.firstChild}else{t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:true});s=t.firstChild;t=a.addElement(t,"mjx-block");t.appendChild(s);a.addElement(t,"mjx-strut")}var z=this.CHTMLbboxFor(0);var D=this.getValues("width","height","depth","lspace","voffset");var B=0,A=0,C=z.w,u=z.h,v=z.d;s.style.width=0;s.style.margin=a.Em(-u)+" 0 "+a.Em(-v);if(D.width!==""){C=this.CHTMLdimen(D.width,"w",C,0)}if(D.height!==""){u=this.CHTMLdimen(D.height,"h",u,0)}if(D.depth!==""){v=this.CHTMLdimen(D.depth,"d",v,0)}if(D.voffset!==""){A=this.CHTMLdimen(D.voffset);if(A){s.style.position="relative";s.style.top=a.Em(-A)}}if(D.lspace!==""){B=this.CHTMLdimen(D.lspace);if(B){s.style.position="relative";s.style.left=a.Em(B)}}t.style.width=0;t.style.marginTop=a.Em(u-k);t.style.padding="0 "+a.Em(C)+" "+a.Em(v)+" 0";var E=a.BBOX({w:C,h:u,d:v,l:0,r:C,t:u,b:v,scale:this.CHTML.scale,rscale:this.CHTML.rscale});E.combine(z,B,A);E.w=C;E.h=u;E.d=v;this.CHTML=E;return t.parentNode},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLdimen:function(w,y,x,s){if(s==null){s=-i}w=String(w);var t=w.match(/width|height|depth/);var u=(t?this.CHTML[t[0].charAt(0)]:(y?this.CHTML[y]:0));var v=(this.CHTMLlength2em(w,u)||0);if(w.match(/^[-+]/)&&x!=null){v+=x}if(s!=null){v=Math.max(s,v)}return v}});d.munderover.Augment({toCommonHTML:function(w,G){var E=this.getValues("displaystyle","accent","accentunder","align");var u=this.data[this.base];if(!E.displaystyle&&u!=null&&(u.movablelimits||u.CoreMO().Get("movablelimits"))){return d.msubsup.prototype.toCommonHTML.call(this,w,t)}var B,z,s=[],t=false;if(G&&G.stretch){if(this.data[this.base]){u=a.getNode(w,"mjx-op")}if(this.data[this.under]){B=a.getNode(w,"mjx-under")}if(this.data[this.over]){z=a.getNode(w,"mjx-over")}s[0]=u;s[1]=B||z;s[2]=z;t=true}else{var y=["mjx-op","mjx-under","mjx-over"];if(this.over===1){y[1]=y[2]}w=this.CHTMLdefaultNode(w,{childNodes:y,noBBox:true,forceChild:true,minChildren:2});s[0]=u=w.removeChild(w.firstChild);s[1]=B=z=w.removeChild(w.firstChild);if(w.firstChild){s[2]=z=w.removeChild(w.firstChild)}}var x=[],v=this.CHTMLgetBBoxes(x,s,E);var F=x[this.base],C=this.CHTML;C.w=v;C.h=F.h;C.d=F.d;if(F.h<0.35){u.style.marginTop=a.Em(F.h-0.35)}if(E.accent&&F.hu){u=s}}if(u===-i){u=s}for(y=0;yD.w){D.skew+=(D.w-(A.x+u*A.w))/2}}}else{y=a.TEX.big_op_spacing1;x=a.TEX.big_op_spacing3;v=Math.max(y,x-Math.max(0,u*A.d))}A.x+=E/2;A.y=D.h+v+w+u*A.d;if(v){B.style.paddingBottom=a.Em(v/u)}if(w){B.style.paddingTop=a.Em(w/u)}return C},CHTMLaddUnderscript:function(B,z,E,D,t,A,s){var C=this.CHTML;var y,x,w=a.TEX.big_op_spacing5,v;var F=z[this.under],u=F.rscale;if(!s){a.addElement(t,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);t.firstChild.firstChild.firstChild.appendChild(A);t.firstChild.lastChild.appendChild(B)}if(F.D){F.d=F.D}if(F.d<0){B.firstChild.style.verticalAlign="top";t.firstChild.style.marginBottom=a.Em(F.d)}if(E.accentunder){v=2*a.TEX.rule_thickness;w=0}else{y=a.TEX.big_op_spacing2;x=a.TEX.big_op_spacing4;v=Math.max(y,x-u*F.h)}F.x=-D/2;F.y=-(C.d+v+w+u*F.h);if(v){B.style.paddingTop=a.Em(v/u)}if(w){B.style.paddingBottom=a.Em(w/u)}},CHTMLplaceBoxes:function(s,B,A,E,z){var t=this.CHTML.w,y,v=z.length,x;var D=a.BBOX.zero();D.scale=this.CHTML.scale;D.rscale=this.CHTML.rscale;z[this.base].x=z[this.base].y=0;var F=i;for(y=0;y0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=a.Em(N/B);z.style.paddingBottom=a.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=a.Em(Y/w);z.style.paddingRight=a.Em(N/w);E.style.verticalAlign=a.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.mfrac.Augment({toCommonHTML:function(N){N=this.CHTMLdefaultNode(N,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var x=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var O=x.displaystyle;var D=N.firstChild,w=N.lastChild;var y=a.addElement(N,"mjx-box");y.appendChild(D);y.appendChild(w);N.appendChild(y);if(x.numalign!=="center"){D.style.textAlign=x.numalign}if(x.denomalign!=="center"){w.style.textAlign=x.denomalign}var P=this.CHTMLbboxFor(0),B=this.CHTMLbboxFor(1),C=a.BBOX.empty(this.CHTML),F=P.rscale,z=B.rscale;x.linethickness=Math.max(0,a.thickness2em(x.linethickness||"0",C.scale));var M=a.TEX.min_rule_thickness/a.em,T=a.TEX.axis_height;var J=x.linethickness,L,K,I,G;if(x.bevelled){y.className+=" MJXc-bevelled";var S=(O?0.4:0.15);var E=Math.max(F*(P.h+P.d),z*(B.h+B.d))+2*S;var R=a.Element("mjx-bevel");y.insertBefore(R,w);var s=a.createDelimiter(R,47,E);I=F*(P.d-P.h)/2+T+S;G=z*(B.d-B.h)/2+T-S;if(I){D.style.verticalAlign=a.Em(I/F)}if(G){w.style.verticalAlign=a.Em(G/z)}R.style.marginLeft=R.style.marginRight=a.Em(-S/2);C.combine(P,0,I);C.combine(s,F*P.w-S/2,0);C.combine(B,F*P.w+s.w-S,G);C.clean()}else{y.className+=" MJXc-stacked";if(O){I=a.TEX.num1;G=a.TEX.denom1}else{I=(J===0?a.TEX.num3:a.TEX.num2);G=a.TEX.denom2}if(J===0){L=Math.max((O?7:3)*a.TEX.rule_thickness,2*M);K=(I-P.d*F)-(B.h*z-G);if(KD){s=((A.h+A.d)-(D-G))/2}D=F.h+s+G;var B=this.CHTMLaddRoot(w,A,A.h+A.d-D);v.style.paddingTop=a.Em(s);v.style.borderTop=a.Px(y*F.scale,1)+" solid";E.style.paddingTop=a.Em(2*G-y);F.h+=s+2*G;C.combine(A,B,D-A.h);C.combine(F,B+A.w,0);C.clean();return w},CHTMLaddRoot:function(){return 0},CHTMLhandleBBox:function(s){var t=this.CHTMLbboxFor(0);delete t.pwidth;this.SUPER(arguments).CHTMLhandleBBox.apply(this,arguments)}});d.mroot.Augment({toCommonHTML:d.msqrt.prototype.toCommonHTML,CHTMLhandleBBox:d.msqrt.prototype.CHTMLhandleBBox,CHTMLaddRoot:function(A,u,v){if(!this.data[1]){return}var z=this.CHTML,B=this.data[1].CHTML,x=A.firstChild;var s=B.rscale;var t=this.CHTMLrootHeight(B,u,s)-v;var y=Math.min(B.w,B.r);var C=Math.max(y,u.offset/s);if(t){x.style.verticalAlign=a.Em(t/s)}if(C>y){x.firstChild.style.paddingLeft=a.Em(C-y)}C-=u.offset/s;x.style.width=a.Em(C);z.combine(B,0,t);return C*s},CHTMLrootHeight:function(u,s,t){return 0.45*(s.h+s.d-0.9)+s.offset+Math.max(0,u.d-0.075)}});d.mfenced.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);this.CHTMLaddChild(v,"open",{});for(var u=0,s=this.data.length;ua.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(s,t){this.CHTMLstretchChildV(this.CoreIndex(),s,t);return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLstretchChildH(this.CoreIndex(),s,t);return this.CHTML}});d.TeXAtom.Augment({toCommonHTML:function(x,w){if(!w||!w.stretch){x=this.CHTMLdefaultNode(x)}if(this.texClass===d.TEXCLASS.VCENTER){var s=a.TEX.axis_height,u=this.CHTML;var t=s-(u.h+u.d)/2+u.d;if(Math.abs(t)>0.001){x.style.verticalAlign=a.Em(t);u.h+=t;u.t+=t;u.d-=t;u.b-=t}}return x},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.semantics.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);if(this.data[0]){this.data[0].toCommonHTML(s);this.CHTMLupdateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(s)}return s}});d.annotation.Augment({toCommonHTML:function(s){return this.CHTMLcreateNode(s)}});d["annotation-xml"].Augment({toCommonHTML:d.mbase.CHTMLautoload});d.ms.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mglyph.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.menclose.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.maction.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mmultiscripts.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mtable.Augment({toCommonHTML:d.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(f.config.menuSettings.zoom!=="None"){o.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML); +MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var g="2.7.6";var b=MathJax.ElementJax.mml,a=MathJax.Hub.config,e=MathJax.OutputJax.CommonHTML,d=MathJax.Hub.SplitList;var c=-1,f=1000000;b.mtable.Augment({toCommonHTML:function(l){var m={rows:[],labels:[],labeled:false};l=this.CHTMLdefaultNode(l,{noBBox:true,childOptions:m});var k=e.Element("mjx-table");while(l.firstChild){k.appendChild(l.firstChild)}l.appendChild(k);var h=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width","side","minlabelspacing","useHeight");var j=e.TEX.min_rule_thickness/e.em;m.t=e.Px(j*this.CHTML.scale,1);this.CHTMLgetBoxSizes(h,m);this.CHTMLgetAttributes(h,m);this.CHTMLadjustCells(h,m);if(h.frame){k.style.border=m.t+" "+h.frame}this.CHTMLalignV(h,m,l);this.CHTMLcolumnWidths(h,m,l);this.CHTMLstretchCells(h,m);if(m.labeled){this.CHTMLaddLabels(h,m,l,k)}var i=this.CHTML;i.w=i.r=m.R;i.h=i.t=m.T-m.B;i.d=i.b=m.B;if(!h.frame&&!i.pwidth){l.style.padding="0 "+e.Em(1/6);i.L=i.R=1/6}this.CHTMLhandleSpace(l);this.CHTMLhandleBBox(l);this.CHTMLhandleColor(l);return l},CHTMLgetBoxSizes:function(z,k){var r=e.FONTDATA.lineH*z.useHeight,t=e.FONTDATA.lineD*z.useHeight;var y=[],h=[],l=[],w=-1,q,n;for(q=0,n=this.data.length;qw){w=p}}var u=B.data[p-A].CHTML;if(u.h>y[q]){y[q]=u.h}if(u.d>h[q]){h[q]=u.d}if(u.w>l[p]){l[p]=u.w}}}if(z.equalrows){k.HD=true;var x=Math.max.apply(Math,y);var o=Math.max.apply(Math,h);for(q=0,n=y.length;qt||m<=0){m=null}}else{w.align=this.defaults.align}var p=0,l=0,u=e.TEX.axis_height;if(w.fspace){p+=k.FSPACE[1]}if(w.frame){p+=2/e.em;l+=1/e.em}for(var q=0;q=m){l+=r+s+x[q]}}}if(!m){l=({top:p,bottom:0,center:p/2,baseline:p/2,axis:p/2-u})[w.align]}if(l){o.style.verticalAlign=e.Em(-l)}k.T=p;k.B=l},CHTMLcolumnWidths:function(l,r,A){var I=r.CWIDTH,K=r.CSPACE,u=r.J,F;var G=0,n=false,y=l.width.match(/%$/);var H,B,v;if(l.width!=="auto"&&!y){G=Math.max(0,this.CHTMLlength2em(l.width,r.R));n=true}if(l.equalcolumns){if(y){var z=e.Percent(1/(u+1));for(F=0;F<=u;F++){I[F]=z}}else{v=Math.max.apply(Math,r.W);if(l.width!=="auto"){var q=(l.fspace?r.FSPACE[0]+(l.frame?2/e.em:0):0);for(F=0;F<=u;F++){q+=K[F]}v=Math.max((G-q)/(u+1),v)}v=e.Em(v);for(F=0;F<=u;F++){I[F]=v}}n=true}var E=0;if(l.fspace){E=r.FSPACE[0]}var s=[],D=[],h=[],o=[];var t=r.rows[0];for(F=0;F<=u;F++){o[F]=r.W[F];if(I[F]==="auto"){s.push(F)}else{if(I[F]==="fit"){D.push(F)}else{if(I[F].match(/%$/)){h.push(F)}else{o[F]=this.CHTMLlength2em(I[F],o[F])}}}E+=o[F]+K[F];if(t[F]){t[F].style.width=e.Em(o[F])}}if(l.frame){E+=2/e.em}var C=(D.length>0);if(n){if(y){for(F=0;F<=u;F++){cell=t[F].style;if(I[F]==="auto"&&!C){cell.width=""}else{if(I[F]==="fit"){cell.width=""}else{if(I[F].match(/%$/)){cell.width=I[F]}else{cell.minWidth=cell.maxWidth=cell.width}}}}}else{if(G>E){var k=0;for(H=0,B=h.length;HE&&D.length){var x=(G-E)/D.length;for(H=0,B=D.length;Ht*z){z=t*p}z+=y;z*=t;D+=z}else{D+=p-t*z+n;z-=t*n;z*=-t}}var o=e.addElement(w,"mjx-box",{style:{width:"100%","text-align":q.indentalign}});o.appendChild(B);var C=e.Element("mjx-itable");B.style.display="inline-table";if(!B.style.width){B.style.width="auto"}C.style.verticalAlign="top";B.style.verticalAlign=e.Em(k.T-k.B-k.H[0]);w.style.verticalAlign="";if(z){if(q.indentalign===b.INDENTALIGN.CENTER){B.style.marginLeft=e.Em(z);B.style.marginRight=e.Em(-z)}else{var u="margin"+(q.indentalign===b.INDENTALIGN.RIGHT?"Right":"Left");B.style[u]=e.Em(z)}}if(k.CALIGN[c]==="left"){w.insertBefore(C,o);C.style.marginRight=e.Em(-k.W[c]-y);if(y){C.style.marginLeft=e.Em(y)}}else{w.appendChild(C);C.style.marginLeft=e.Em(-k.W[c]+y)}var l=k.labels,j=0;if(h.fspace){j=k.FSPACE[0]+(h.frame?1/e.em:0)}for(var x=0,v=l.length;x1){h.h*=k;h.d*=k}}}else{h.w=Math.max(h.w,this.CHTMLlength2em(j,h.w))}}}}return l}});MathJax.Hub.Startup.signal.Post("CommonHTML mtable Ready");MathJax.Ajax.loadComplete(e.autoloadDir+"/mtable.js")}); +(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_CHTML-full.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-AMS_CHTML.js b/revisions_report_files/mathjax-27/config/TeX-AMS_CHTML.js new file mode 100644 index 0000000..1abb34a --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-AMS_CHTML.js @@ -0,0 +1,57 @@ +/* + * /MathJax/config/TeX-AMS_CHTML.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_CHTML.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-AMS_SVG-full.js b/revisions_report_files/mathjax-27/config/TeX-AMS_SVG-full.js new file mode 100644 index 0000000..c136618 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-AMS_SVG-full.js @@ -0,0 +1,61 @@ +/* + * /MathJax/config/TeX-AMS_SVG-full.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/output/SVG/jax.js", + "[MathJax]/jax/output/SVG/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k div":{display:"inline-block"},".mjx-svg-href":{fill:"blue",stroke:"blue"},".MathJax_SVG_Processing":{visibility:"hidden",position:"absolute",top:0,left:0,width:0,height:0,overflow:"hidden",display:"block!important"},".MathJax_SVG_Processed":{display:"none!important"},".MathJax_SVG_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_SVG_test.mjx-test-display":{display:"table!important"},".MathJax_SVG_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_SVG_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_SVG_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .MathJax_SVG_left_box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .MathJax_SVG_right_box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .MathJax_SVG_right_box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_SVG_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}}},hideProcessedMath:true,fontNames:["TeX","STIX","STIX-Web","Asana-Math","Gyre-Termes","Gyre-Pagella","Latin-Modern","Neo-Euler"],Config:function(){this.SUPER(arguments).Config.apply(this,arguments);var p=e.config.menuSettings,o=this.config,n=p.font;if(p.scale){o.scale=p.scale}if(n&&n!=="Auto"){n=n.replace(/(Local|Web|Image)$/i,"");n=n.replace(/([a-z])([A-Z])/,"$1-$2");this.fontInUse=n}else{this.fontInUse=o.font||"TeX"}if(this.fontNames.indexOf(this.fontInUse)<0){this.fontInUse="TeX"}this.fontDir+="/"+this.fontInUse;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){k=MathJax.Extension.MathEvents.Event;c=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=k.ContextMenu;this.Mousedown=k.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=g.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=g.addElement(this.hiddenDiv,"div",{id:"MathJax_SVG_Hidden"});var n=g.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;this.hiddenDiv.removeChild(n);this.textSVG=this.Element("svg");l.GLYPH.defs=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});this.TestSpan=g.Element("span",{className:"MathJax_SVG_test"},[["span",{className:"MathJax_SVG_left_box"}],["span",{className:"MathJax_SVG_ex_box"}],["span",{className:"MathJax_SVG_right_box"}]]);return j.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){var n=document.body.appendChild(this.TestSpan.cloneNode(true));n.className+=" mjx-test-inline mjx-test-default";this.defaultEx=n.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,n.lastChild.offsetLeft-n.firstChild.offsetLeft-2);document.body.removeChild(n)},preTranslate:function(s){var r=s.jax[this.id],D,z=r.length,y,G,w,C,u,E,p,F,o,v,t=false,A,q=this.config.linebreaks.automatic,x=this.config.linebreaks.width;if(q){t=(x.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(t){x=x.replace(/\s*container\s*/,"")}else{v=this.defaultWidth}if(x===""){x="100%"}}else{v=100000}for(D=0;D=s.SVGlast+s.SVGchunk){this.postTranslate(s,true);s.SVGchunk=Math.floor(s.SVGchunk*this.config.EqnChunkFactor);s.SVGdelay=true}}},postTranslate:function(t,q){var o=t.jax[this.id];if(!this.hideProcessedMath){return}for(var r=t.SVGlast,n=t.SVGeqn;r=55296&&q<56319){v++;q=(((q-55296)<<10)+(D.charCodeAt(v)-56320))+65536;if(this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(q,u);q=y.n;u=y.variant}}else{o=this.FONTDATA.RANGES;for(p=0,A=o.length;p=o[p].low&&q<=o[p].high){if(o[p].remap&&o[p].remap[q]){q=z+o[p].remap[q]}else{if(o[p].remapOnly){break}q=q-o[p].low+z;if(o[p].add){q+=o[p].add}}if(u["variant"+o[p].offset]){u=this.FONTDATA.VARIANT[u["variant"+o[p].offset]]}break}}}if(u.remap&&u.remap[q]){q=u.remap[q];if(u.remap.variant){u=this.FONTDATA.VARIANT[u.remap.variant]}}else{if(this.FONTDATA.REMAP[q]&&!u.noRemap){q=this.FONTDATA.REMAP[q]}}if(h(q)){u=this.FONTDATA.VARIANT[q[1]];q=q[0]}if(typeof(q)==="string"){D=q+D.substr(v+1);s=D.length;v=-1;continue}r=this.lookupChar(u,q);B=r[q];if(B){if((B[5]&&B[5].space)||(B[5]===""&&B[0]+B[1]===0)){x.w+=B[2]}else{B=[t,r.id+"-"+q.toString(16).toUpperCase()].concat(B);x.Add(l.GLYPH.apply(l,B),x.w,0)}}else{if(this.FONTDATA.DELIMITERS[q]){B=this.createDelimiter(q,0,1,r);x.Add(B,x.w,(this.FONTDATA.DELIMITERS[q].dir==="V"?B.d:0))}else{if(q<=65535){B=String.fromCharCode(q)}else{z=q-65536;B=String.fromCharCode((z>>10)+55296)+String.fromCharCode((z&1023)+56320)}var w=l.TEXT(t*100/a.config.scale,B,{"font-family":u.defaultFamily||a.config.undefinedFamily,"font-style":(u.italic?"italic":""),"font-weight":(u.bold?"bold":"")});if(u.h!=null){w.h=u.h}if(u.d!=null){w.d=u.d}B=l.G();B.Add(w);x.Add(B,x.w,0);e.signal.Post(["SVG Jax - unknown char",q,u])}}}if(a.isChar(D)&&r.skew&&r.skew[q]){x.skew=r.skew[q]*1000}if(x.element.childNodes.length===1&&!x.element.firstChild.getAttribute("x")){x.element=x.element.firstChild;x.removeable=false;x.scale=t}return x},lookupChar:function(r,u){var q,o;if(!r.FONTS){var t=this.FONTDATA.FONTS;var s=(r.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(s instanceof Array)){s=[s]}if(r.fonts!=s){r.fonts=s}r.FONTS=[];for(q=0,o=s.length;q=55296&&p<56319)},findBlock:function(o,s){if(o.Ranges){for(var r=0,n=o.Ranges.length;r=0;p--){if(o.Ranges[p][2]==q){o.Ranges.splice(p,1)}}this.loadFont(o.directory+"/"+q+".js")}}}},loadFont:function(n){e.RestartAfter(j.Require(this.fontDir+"/"+n))},createDelimiter:function(n,p,s,q){if(!s){s=1}var u=l.G();if(!n){u.Clean();delete u.element;u.w=u.r=this.TeX.nulldelimiterspace*s;return u}if(!(p instanceof Array)){p=[p,p]}var v=p[1];p=p[0];var o={alias:n};while(o.alias){n=o.alias;o=this.FONTDATA.DELIMITERS[n];if(!o){o={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(o.load){e.RestartAfter(j.Require(this.fontDir+"/fontdata-"+o.load+".js"))}for(var t=0,r=o.HW.length;t=p-10-a.config.blacker||(t==r-1&&!o.stretch)){if(o.HW[t][2]){s*=o.HW[t][2]}if(o.HW[t][3]){n=o.HW[t][3]}return this.createChar(s,[n,o.HW[t][1]],q).With({stretched:true})}}if(o.stretch){this["extendDelimiter"+o.dir](u,v,o.stretch,s,q)}return u},createChar:function(u,s,p){var t="",r={fonts:[s[1]],noRemap:true};if(p&&p===i.VARIANT.BOLD){r.fonts=[s[1]+"-bold",s[1]]}if(typeof(s[1])!=="string"){r=s[1]}if(s[0] instanceof Array){for(var q=0,n=s[0].length;qt){var n=this.createChar(q,o.ext,p);var r=(o.mid?2:1),x=(C-t)/r,D=(x+100)/(n.h+n.d);while(r-->0){var v=a.Element("g",{transform:"translate("+n.y+","+(z-D*n.h+50+n.y)+") scale(1,"+D+")"});v.appendChild(n.element.cloneNode(false));u.element.appendChild(v);z-=x;if(o.mid&&r){u.Add(B,0,z-B.h);z-=(B.h+B.d)}}}else{if(o.mid){z+=(t-C)/2;u.Add(B,0,z-B.h);z+=-(B.h+B.d)+(t-C)/2}else{z+=(t-C)}}u.Add(w,0,z-w.h);u.Clean();u.scale=q;u.isMultiChar=true},extendDelimiterH:function(v,q,o,t,p){var r=this.createChar(t,(o.left||o.rep),p);var E=this.createChar(t,(o.right||o.rep),p);v.Add(r,-r.l,0);var D=(r.r-r.l)+(E.r-E.l),B=r.r-r.l;if(o.mid){var C=this.createChar(t,o.mid,p);D+=C.w}if(o.min&&qD){var A=this.createChar(t,o.rep,p),n=o.fuzz||0;var u=(o.mid?2:1),z=(q-D)/u,F=(z+n)/(A.r-A.l);while(u-->0){var y=a.Element("g",{transform:"translate("+(B-n/2-F*A.l+A.x)+","+A.y+") scale("+F+",1)"});y.appendChild(A.element.cloneNode(false));v.element.appendChild(y);B+=z;if(o.mid&&u){v.Add(C,B,0);B+=C.w}}}else{if(o.mid){B-=(D-q)/2;v.Add(C,B,0);B+=C.w-(D-q)/2}else{B-=(D-q)}}v.Add(E,B-E.l,0);v.Clean();v.scale=t;v.isMultiChar=true},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:300,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,NBSP:"\u00A0"});var l=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(n){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,n)}},With:function(n){return e.Insert(this,n)},Add:function(q,w,v,n,u){if(w){q.x+=w}if(v){q.y+=v}if(q.element){if(q.removeable&&q.element.childNodes.length===1&&q.n===1){var o=q.element.firstChild,s=o.nodeName.toLowerCase();if(s==="use"||s==="rect"){q.element=o;q.scale=q.childScale;var t=q.childX,r=q.childY;q.x+=t;q.y+=r;q.h-=r;q.d+=r;q.H-=r;q.D+=r;q.w-=t;q.r-=t;q.l+=t;q.removeable=false;o.setAttribute("x",Math.floor(q.x/q.scale));o.setAttribute("y",Math.floor(q.y/q.scale))}}if(Math.abs(q.x)<1&&Math.abs(q.y)<1){q.remove=q.removeable}else{s=q.element.nodeName.toLowerCase();if(s==="g"){if(!q.element.firstChild){q.remove=q.removeable}else{q.element.setAttribute("transform","translate("+Math.floor(q.x)+","+Math.floor(q.y)+")")}}else{if(s==="line"||s==="polygon"||s==="path"||s==="a"){var p=q.element.getAttribute("transform")||"";if(p){p=" "+p}p="translate("+Math.floor(q.x)+","+Math.floor(q.y)+")"+p;q.element.setAttribute("transform",p)}else{q.element.setAttribute("x",Math.floor(q.x/q.scale));q.element.setAttribute("y",Math.floor(q.y/q.scale))}}}if(q.remove){this.n+=q.n;while(q.element.firstChild){if(u&&this.element.firstChild){this.element.insertBefore(q.element.firstChild,this.element.firstChild)}else{this.element.appendChild(q.element.firstChild)}}}else{if(u){this.element.insertBefore(q.element,this.element.firstChild)}else{this.element.appendChild(q.element)}}delete q.element}if(q.hasIndent){this.hasIndent=q.hasIndent}if(q.tw!=null){this.tw=q.tw}if(q.d-q.y>this.d){this.d=q.d-q.y;if(this.d>this.D){this.D=this.d}}if(q.y+q.h>this.h){this.h=q.y+q.h;if(this.h>this.H){this.H=this.h}}if(q.D-q.y>this.D){this.D=q.D-q.y}if(q.y+q.H>this.H){this.H=q.y+q.H}if(q.x+q.lthis.r){this.r=q.x+q.r}if(n||q.x+q.w+(q.X||0)>this.w){this.w=q.x+q.w+(q.X||0)}this.childScale=q.scale;this.childX=q.x;this.childY=q.y;this.n++;return q},Align:function(r,s,q,p,o){q=({left:q,center:(this.w-r.w)/2,right:this.w-r.w-q})[s]||0;var n=this.w;this.Add(r,q+(o||0),p);this.w=n},Clean:function(){if(this.h===-a.BIGDIMEN){this.h=this.d=this.l=0}return this}});l.ROW=l.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(o){var n=o.toSVG();this.svg.push(n);if(o.SVGcanStretch("Vertical")){n.mml=o}if(n.h+n.y>this.sh){this.sh=n.h+n.y}if(n.d-n.y>this.sd){this.sd=n.d-n.y}},Stretch:function(){for(var q=0,n=this.svg.length;qo.w&&a.isChar(r)&&!q.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGchildSVG:function(n){return(this.data[n]?this.data[n].toSVG():l())},SVGdataStretched:function(o,n,p){this.SVGdata={HW:n,D:p};if(!this.data[o]){return l()}if(p!=null){return this.data[o].SVGstretchV(n,p)}if(n!=null){return this.data[o].SVGstretchH(n)}return this.data[o].toSVG()},SVGsaveData:function(n){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=n.w,this.SVGdata.x=n.x;this.SVGdata.h=n.h,this.SVGdata.d=n.d;if(n.y){this.SVGdata.h+=n.y;this.SVGdata.d-=n.y}if(n.X!=null){this.SVGdata.X=n.X}if(n.tw!=null){this.SVGdata.tw=n.tw}if(n.skew){this.SVGdata.skew=n.skew}if(n.ic){this.SVGdata.ic=n.ic}if(this["class"]){n.removeable=false;a.Element(n.element,{"class":this["class"]})}if(this.id){n.removeable=false;a.Element(n.element,{id:this.id})}if(this.href){this.SVGaddHref(n)}if(a.config.addMMLclasses){this.SVGaddClass(n.element,"mjx-svg-"+this.type);n.removeable=false}var o=this.style;if(o&&n.element){n.element.style.cssText=o;if(n.element.style.fontSize){n.element.style.fontSize=""}n.element.style.border=n.element.style.padding="";if(n.removeable){n.removeable=(n.element.style.cssText==="")}}this.SVGaddAttributes(n)},SVGaddClass:function(p,n){var o=p.getAttribute("class");p.setAttribute("class",(o?o+" ":"")+n)},SVGaddAttributes:function(o){if(this.attrNames){var u=this.attrNames,q=i.nocopyAttributes,t=e.config.ignoreMMLattributes;var r=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var p=0,n=u.length;p600?"bold":"normal")}return o},SVGhandleSpace:function(q){if(this.hasMMLspacing()){if(this.type!=="mo"){return}var p=this.getValues("scriptlevel","lspace","rspace");if(p.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var o=this.SVGgetMu(q);p.lspace=Math.max(0,a.length2em(p.lspace,o));p.rspace=Math.max(0,a.length2em(p.rspace,o));var n=this,r=this.Parent();while(r&&r.isEmbellished()&&r.Core()===n){n=r;r=r.Parent()}if(p.lspace){q.x+=p.lspace}if(p.rspace){q.X=p.rspace}}}else{var s=this.texSpacing();this.SVGgetScale();if(s!==""){q.x+=a.length2em(s,this.scale)*this.mscale}}},SVGhandleColor:function(r){var A=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!A.color){A.color=this.styles.color}if(A.color&&!this.mathcolor){A.mathcolor=A.color}if(A.mathcolor){a.Element(r.element,{fill:A.mathcolor,stroke:A.mathcolor});r.removeable=false}var v=(this.styles||{}).border,y=(this.styles||{}).padding,w=((v||{}).left||0),t=((y||{}).left||0),n;A.background=(this.mathbackground||this.background||(this.styles||{}).background||i.COLOR.TRANSPARENT);if(w+t){var o=l();for(n in r){if(r.hasOwnProperty(n)){o[n]=r[n]}}o.x=0;o.y=0;r.element=a.Element("g");r.removeable=true;r.Add(o,w+t,0)}if(y){r.w+=y.right||0;r.h+=y.top||0;r.d+=y.bottom||0}if(v){r.w+=v.right||0;r.h+=v.top||0;r.d+=v.bottom||0}if(A.background!==i.COLOR.TRANSPARENT){var x=r.element.nodeName.toLowerCase();if(x!=="g"&&x!=="svg"){var s=a.Element("g");s.appendChild(r.element);r.element=s;r.removeable=true}r.Add(l.RECT(r.h,r.d,r.w,{fill:A.background,stroke:"none"}),0,0,false,true)}if(v){var z=5;var p={left:["V",r.h+r.d,-z,-r.d],right:["V",r.h+r.d,r.w-v.right+z,-r.d],top:["H",r.w,0,r.h-v.top+z],bottom:["H",r.w,0,-r.d-z]};for(n in p){if(p.hasOwnProperty(n)){if(v[n]){var u=p[n],q=l[u[0]+"LINE"];r.Add(q(u[1],v[n],v[n+"Style"],v[n+"Color"]),u[2],u[3])}}}}},SVGhandleVariant:function(n,p,o){return a.HandleVariant(n,p,o)},SVGgetVariant:function(){var n=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var o=n.mathvariant;if(this.variantForm){o="-"+a.fontInUse+"-variant"}n.hasVariant=this.Get("mathvariant",true);if(!n.hasVariant){n.family=n.fontfamily;n.weight=n.fontweight;n.style=n.fontstyle}if(this.styles){if(!n.style&&this.styles.fontStyle){n.style=this.styles.fontStyle}if(!n.weight&&this.styles.fontWeight){n.weight=this.styles.fontWeight}if(!n.family&&this.styles.fontFamily){n.family=this.styles.fontFamily}}if(n.family&&!n.hasVariant){if(!n.weight&&n.mathvariant.match(/bold/)){n.weight="bold"}if(!n.style&&n.mathvariant.match(/italic/)){n.style="italic"}o={forceFamily:true,font:{"font-family":n.family}};if(n.style){o.font["font-style"]=n.style}if(n.weight){o.font["font-weight"]=n.weight}return o}if(n.weight==="bold"){o={normal:i.VARIANT.BOLD,italic:i.VARIANT.BOLDITALIC,fraktur:i.VARIANT.BOLDFRAKTUR,script:i.VARIANT.BOLDSCRIPT,"sans-serif":i.VARIANT.BOLDSANSSERIF,"sans-serif-italic":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.weight==="normal"){o={bold:i.VARIANT.normal,"bold-italic":i.VARIANT.ITALIC,"bold-fraktur":i.VARIANT.FRAKTUR,"bold-script":i.VARIANT.SCRIPT,"bold-sans-serif":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.SANSSERIFITALIC}[o]||o}}if(n.style==="italic"){o={normal:i.VARIANT.ITALIC,bold:i.VARIANT.BOLDITALIC,"sans-serif":i.VARIANT.SANSSERIFITALIC,"bold-sans-serif":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.style==="normal"){o={italic:i.VARIANT.NORMAL,"bold-italic":i.VARIANT.BOLD,"sans-serif-italic":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.BOLDSANSSERIF}[o]||o}}if(!(o in a.FONTDATA.VARIANT)){o="normal"}return a.FONTDATA.VARIANT[o]},SVGgetScale:function(o){var p=1;if(this.mscale){p=this.scale}else{var n=this.getValues("scriptlevel","fontsize");n.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if((this.styles||{}).fontSize&&!n.fontsize){n.fontsize=this.styles.fontSize}if(n.fontsize&&!this.mathsize){n.mathsize=n.fontsize}if(n.scriptlevel!==0){if(n.scriptlevel>2){n.scriptlevel=2}p=Math.pow(this.Get("scriptsizemultiplier"),n.scriptlevel);n.scriptminsize=a.length2em(this.Get("scriptminsize"))/1000;if(p2){o.scriptlevel=2}n=Math.sqrt(Math.pow(o.scriptsizemultiplier,o.scriptlevel))}return n},SVGnotEmpty:function(n){while(n){if((n.type!=="mrow"&&n.type!=="texatom")||n.data.length>1){return true}n=n.data[0]}return false},SVGcanStretch:function(p){var o=false;if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){o=n.SVGcanStretch(p);if(o&&n.forceStretch){this.forceStretch=true}}}return o},SVGstretchV:function(n,o){return this.toSVG(n,o)},SVGstretchH:function(n){return this.toSVG(n)},SVGlineBreaks:function(){return false}},{SVGemptySVG:function(){var n=this.SVG();n.Clean();this.SVGsaveData(n);return n},SVGautoload:function(){this.constructor.Augment({toSVG:i.mbase.SVGautoloadFail});var n=a.autoloadDir+"/"+this.type+".js";e.RestartAfter(j.Require(n))},SVGautoloadFail:function(){throw Error("SVG can't autoload '"+this.type+"'")},SVGautoloadList:{},SVGautoloadFile:function(n){if(i.mbase.SVGautoloadList.hasOwnProperty(n)){throw Error("SVG can't autoload file '"+n+"'")}i.mbase.SVGautoloadList[n]=true;var o=a.autoloadDir+"/"+n+".js";e.RestartAfter(j.Require(o))}});i.chars.Augment({toSVG:function(o,r,n,p){var q=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.entity.Augment({toSVG:function(o,r,n,p){var q=this.toString().replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.mo.Augment({toSVG:function(o,n){this.SVGgetStyles();var v=this.svg=this.SVG();var r=this.SVGgetScale(v);this.SVGhandleSpace(v);if(this.data.length==0){v.Clean();this.SVGsaveData(v);return v}if(n!=null){return this.SVGstretchV(o,n)}else{if(o!=null){return this.SVG.strechH(o)}}var t=this.SVGgetVariant();var B=this.getValues("largeop","displaystyle");if(B.largeop){t=a.FONTDATA.VARIANT[B.displaystyle?"-largeOp":"-smallOp"]}var A=this.CoreParent(),s=(A&&A.isa(i.msubsup)&&this!==A.data[0]),p=(s?this.remapChars:null);if(a.isChar(this.data.join(""))&&A&&A.isa(i.munderover)&&a.isChar(this.CoreText(A.data[A.base]))){var w=A.data[A.over],z=A.data[A.under];if(w&&this===w.CoreMO()&&A.Get("accent")){p=a.FONTDATA.REMAPACCENT}else{if(z&&this===z.CoreMO()&&A.Get("accentunder")){p=a.FONTDATA.REMAPACCENTUNDER}}}if(s&&this.data.join("").match(/['`"\u00B4\u2032-\u2037\u2057]/)){t=a.FONTDATA.VARIANT["-"+a.fontInUse+"-variant"]}for(var u=0,q=this.data.length;u10*C.w){y+=-C.l}v.Add(C,y,0,true);if(C.skew){v.skew=C.skew}}}v.Clean();if(!a.isChar(this.data.join(""))){delete v.skew}if(B.largeop){v.y=a.TeX.axis_height-(v.h-v.d)/2/r;if(v.r>v.w){v.ic=v.r-v.w;v.w=v.r}}this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGcanStretch:function(r){if(!this.Get("stretchy")){return false}var s=this.data.join("");if(s.length>1){return false}var o=this.CoreParent();if(o&&o.isa(i.munderover)&&a.isChar(this.CoreText(o.data[o.base]))){var q=o.data[o.over],n=o.data[o.under];if(q&&this===q.CoreMO()&&o.Get("accent")){s=a.FONTDATA.REMAPACCENT[s]||s}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){s=a.FONTDATA.REMAPACCENTUNDER[s]||s}}}s=a.FONTDATA.DELIMITERS[s.charCodeAt(0)];var p=(s&&s.dir==r.substr(0,1));if(!p){delete this.svg}this.forceStretch=p&&(this.Get("minsize",true)||this.Get("maxsize",true));return p},SVGstretchV:function(s,t){var p=this.svg||this.toSVG();var o=this.getValues("symmetric","maxsize","minsize");var r=a.TeX.axis_height*p.scale,n=this.SVGgetMu(p),q;if(o.symmetric){q=2*Math.max(s-r,t+r)}else{q=s+t}o.maxsize=a.length2em(o.maxsize,n,p.h+p.d);o.minsize=a.length2em(o.minsize,n,p.h+p.d);q=Math.max(o.minsize,Math.min(o.maxsize,q));if(q!=o.minsize){q=[Math.max(q*a.TeX.delimiterfactor/1000,q-a.TeX.delimitershortfall),q]}p=a.createDelimiter(this.data.join("").charCodeAt(0),q,p.scale);if(o.symmetric){q=(p.h+p.d)/2+r}else{q=(p.h+p.d)*s/(s+t)}p.y=q-p.h;this.SVGhandleSpace(p);this.SVGhandleColor(p);delete this.svg.element;this.SVGsaveData(p);p.stretched=true;return p},SVGstretchH:function(o){var q=this.svg||this.toSVG(),n=this.SVGgetMu(q);var p=this.getValues("maxsize","minsize","mathvariant","fontweight");if((p.fontweight==="bold"||parseInt(p.fontweight)>=600)&&!this.Get("mathvariant",true)){p.mathvariant=i.VARIANT.BOLD}p.maxsize=a.length2em(p.maxsize,n,q.w);p.minsize=a.length2em(p.minsize,n,q.w);o=Math.max(p.minsize,Math.min(p.maxsize,o));q=a.createDelimiter(this.data.join("").charCodeAt(0),o,q.scale,p.mathvariant);this.SVGhandleSpace(q);this.SVGhandleColor(q);delete this.svg.element;this.SVGsaveData(q);q.stretched=true;return q}});i.mn.Augment({SVGremapMinus:function(n){return n.replace(/^-/,"\u2212")},toSVG:function(){this.SVGgetStyles();var r=this.SVGgetVariant();var o=this.SVG();this.SVGgetScale(o);this.SVGhandleSpace(o);var q=this.SVGremapMinus;for(var p=0,n=this.data.length;po.w&&a.isChar(s)&&!r.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},}),i.mtext.Augment({toSVG:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){this.SVGgetStyles();var n=this.SVG(),q=this.SVGgetScale(n);this.SVGhandleSpace(n);var o=this.SVGgetVariant(),p={direction:this.Get("dir")};if(o.bold){p["font-weight"]="bold"}if(o.italic){p["font-style"]="italic"}o=this.Get("mathvariant");if(o==="monospace"){p["class"]="MJX-monospace"}else{if(o.match(/sans-serif/)){p["class"]="MJX-sans-serif"}}n.Add(l.TEXT(q*100/a.config.scale,this.data.join(""),p));n.Clean();this.SVGhandleColor(n);this.SVGsaveData(n);return n}else{return this.SUPER(arguments).toSVG.call(this)}}});i.merror.Augment({toSVG:function(p,n){this.SVGgetStyles();var t=this.SVG(),r=a.length2em(this.styles.fontSize||1)/1000;this.SVGhandleSpace(t);var o=(r!==1?{transform:"scale("+a.Fixed(r)+")"}:{});var v=l(o);v.Add(this.SVGchildSVG(0));v.Clean();if(r!==1){v.removeable=false;var u=["w","h","d","l","r","D","H"];for(var s=0,q=u.length;st.H){t.H=t.h}if(t.d>t.D){t.D=t.d}}this.SVGhandleColor(t);this.SVGsaveData(t);return t},SVGlength2em:function(q,t,o,u,n){if(n==null){n=-a.BIGDIMEN}var r=String(t).match(/width|height|depth/);var s=(r?q[r[0].charAt(0)]:(u?q[u]:0));var p=a.length2em(t,o,s/this.mscale)*this.mscale;if(u&&String(t).match(/^\s*[-+]/)){return Math.max(n,q[u]+p)}else{return p}}});i.mrow.Augment({SVG:l.ROW,toSVG:function(q,s){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(s!=null){o.sh=q;o.sd=s}for(var p=0,n=this.data.length;pa.linebreakWidth)||this.hasNewline()},SVGmultiline:function(n){i.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(o){var p=this.SVG();this.SVGhandleSpace(p);for(var q=0,n=this.data.length;qz){n=((u.h+u.d)-(z-A))/2}w=l.RECT(A,0,r.w);z=r.h+n+A;y=this.SVGaddRoot(v,u,y,u.h+u.d-z,s);v.Add(u,y,z-u.h);v.Add(w,y+u.w,z-w.h);v.Add(r,y+u.w,0);v.Clean();v.h+=A;v.H+=A;this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGaddRoot:function(o,p,n,r,q){return n}});i.mroot.Augment({toSVG:i.msqrt.prototype.toSVG,SVGaddRoot:function(q,o,t,r,n){var v=(o.isMultiChar?0.55:0.65)*o.w;if(this.data[1]){var s=this.data[1].toSVG();s.x=0;var p=this.SVGrootHeight(o.h+o.d,n,s)-r;var u=Math.min(s.w,s.r);t=Math.max(u,v);q.Add(s,t-u,p)}else{v=t}return t-v},SVGrootHeight:function(p,o,n){return 0.45*(p-900*o)+600*o+Math.max(0,n.d-75)}});i.mfenced.Augment({SVG:l.ROW,toSVG:function(){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data.open){o.Check(this.data.open)}if(this.data[0]!=null){o.Check(this.data[0])}for(var p=1,n=this.data.length;pJ){J=N}if(!L[K]&&J>o){o=J}}}if(E==null&&G!=null){o=G}else{if(o==-a.BIGDIMEN){o=J}}for(K=J=0,H=this.data.length;KJ){J=N}}}var C=a.TeX.rule_thickness*this.mscale;var u,r,z,w,s,B,I,M=0;p=q[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,y:0,scale:O};if(p.ic){M=1.3*p.ic+0.05}for(K=0,H=this.data.length;KJ){F.skew+=(J-N-u)/2}}}else{z=a.TeX.big_op_spacing1*O;w=a.TeX.big_op_spacing3*O;I=Math.max(z,w-Math.max(0,v.d))}I=Math.max(I,1500/a.em);u+=M/2;r=p.y+p.h+v.d+I;v.h+=s;if(v.h>v.H){v.H=v.h}}else{if(K==this.under){if(A){I=3*C*O;s=0}else{z=a.TeX.big_op_spacing2*O;w=a.TeX.big_op_spacing4*O;I=Math.max(z,w-v.h)}I=Math.max(I,1500/a.em);u-=M/2;r=p.y-(p.d+v.h+I);v.d+=s;if(v.d>v.D){v.D=v.d}}}F.Add(v,u,r)}}F.Clean();this.SVGhandleColor(F);this.SVGsaveData(F);return F}});i.msubsup.Augment({toSVG:function(M,G){this.SVGgetStyles();var I=this.SVG(),Q=this.SVGgetScale(I);this.SVGhandleSpace(I);var K=this.SVGgetMu(I);var y=I.Add(this.SVGdataStretched(this.base,M,G));var w=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var O=a.TeX.x_height*Q,F=a.TeX.scriptspace*Q;var n,z;if(this.SVGnotEmpty(this.data[this.sup])){n=this.data[this.sup].toSVG();n.w+=F;n.r=Math.max(n.w,n.r)}if(this.SVGnotEmpty(this.data[this.sub])){z=this.data[this.sub].toSVG();z.w+=F;z.r=Math.max(z.w,z.r)}var J=a.TeX.sup_drop*w,H=a.TeX.sub_drop*w;var C=y.h+(y.y||0)-J,B=y.d-(y.y||0)+H,P=0,L;if(y.ic){y.w-=y.ic;P=1.3*y.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(a.isChar(this.data[this.base].data.join(""))&&y.scale===1&&!y.stretched&&!this.data[this.base].Get("largeop")){C=B=0}}var N=this.getValues("subscriptshift","superscriptshift");N.subscriptshift=(N.subscriptshift===""?0:a.length2em(N.subscriptshift,K));N.superscriptshift=(N.superscriptshift===""?0:a.length2em(N.superscriptshift,K));var A=y.w+y.x;if(!n){if(z){B=Math.max(B,a.TeX.sub1*Q,z.h-(4/5)*O,N.subscriptshift);I.Add(z,A,-B);this.data[this.sub].SVGdata.dy=-B}}else{if(!z){var o=this.getValues("displaystyle","texprimestyle");L=a.TeX[(o.displaystyle?"sup1":(o.texprimestyle?"sup3":"sup2"))];C=Math.max(C,L*Q,n.d+(1/4)*O,N.superscriptshift);I.Add(n,A+P,C);this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=C}else{B=Math.max(B,a.TeX.sub2*Q);var E=a.TeX.rule_thickness*Q;if((C-n.d)-(z.h-B)<3*E){B=3*E-C+n.d+z.h;J=(4/5)*O-(C-n.d);if(J>0){C+=J;B-=J}}I.Add(n,A+P,Math.max(C,N.superscriptshift));I.Add(z,A,-Math.max(B,N.subscriptshift));this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=Math.max(C,N.superscriptshift);this.data[this.sub].SVGdata.dy=-Math.max(B,N.subscriptshift)}}I.Clean();this.SVGhandleColor(I);this.SVGsaveData(I);return I}});i.mmultiscripts.Augment({toSVG:i.mbase.SVGautoload});i.mtable.Augment({toSVG:i.mbase.SVGautoload});i["annotation-xml"].Augment({toSVG:i.mbase.SVGautoload});i.math.Augment({SVG:l.Subclass({type:"svg",removeable:false}),toSVG:function(B,p){var F=a.config;if(this.data[0]){this.SVGgetStyles();i.mbase.prototype.displayAlign=e.config.displayAlign;i.mbase.prototype.displayIndent=e.config.displayIndent;if(String(e.config.displayIndent).match(/^0($|[a-z%])/i)){i.mbase.prototype.displayIndent="0"}var v=l.G();v.Add(this.data[0].toSVG(),0,0,true);v.Clean();this.SVGhandleColor(v);a.Element(v.element,{stroke:"currentColor",fill:"currentColor","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"});v.removeable=false;var x=this.SVG();x.element.setAttribute("xmlns:xlink",m);if(F.useFontCache&&!F.useGlobalCache){x.element.appendChild(l.GLYPH.defs)}x.Add(v);x.Clean();this.SVGsaveData(x);if(!B){x.element=x.element.firstChild;x.element.removeAttribute("transform");x.removable=true;return x}var u=Math.max(-x.l,0),o=Math.max(x.r-x.w,0);var q=x.element.style,A=a.TeX.x_height/a.ex;var E=(Math.ceil(x.H/A)+1)*A+a.HFUZZ,n=(Math.ceil(x.D/A)+1)*A+a.DFUZZ;var z=u+x.w+o;x.element.setAttribute("width",a.Ex(z));x.element.setAttribute("height",a.Ex(E+n));q.verticalAlign=a.Ex(-n);if(u){q.marginLeft=a.Ex(-u)}if(o){q.marginRight=a.Ex(-o)}x.element.setAttribute("viewBox",a.Fixed(-u,1)+" "+a.Fixed(-E,1)+" "+a.Fixed(z,1)+" "+a.Fixed(E+n,1));if(x.H>x.h){q.marginTop=a.Ex(x.h-E)}if(x.D>x.d){q.marginBottom=a.Ex(x.d-n);q.verticalAlign=a.Ex(-x.d)}if(Math.abs(z-a.cwidth)<10){q.maxWidth=a.Fixed(a.cwidth*a.em/1000*a.config.scale)+"px"}var y=this.Get("alttext");if(y&&!x.element.getAttribute("aria-label")){x.element.setAttribute("aria-label",y)}if(!x.element.getAttribute("role")){x.element.setAttribute("role","img")}x.element.setAttribute("focusable","false");B.appendChild(x.element);x.element=null;if(!this.isMultiline&&this.Get("display")==="block"&&!x.hasIndent){var C=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(C.indentalignfirst!==i.INDENTALIGN.INDENTALIGN){C.indentalign=C.indentalignfirst}if(C.indentalign===i.INDENTALIGN.AUTO){C.indentalign=this.displayAlign}if(C.indentshiftfirst!==i.INDENTSHIFT.INDENTSHIFT){C.indentshift=C.indentshiftfirst}if(C.indentshift==="auto"){C.indentshift="0"}var s=a.length2em(C.indentshift,1,a.cwidth);if(this.displayIndent!=="0"){var t=a.length2em(this.displayIndent,1,a.cwidth);s+=(C.indentalign===i.INDENTALIGN.RIGHT?-t:t)}p.style.textAlign=C.indentalign;if(s){e.Insert(q,({left:{marginLeft:a.Ex(s)},right:{marginRight:a.Ex(-s),marginLeft:a.Ex(Math.max(0,s-z))},center:{marginLeft:a.Ex(s),marginRight:a.Ex(-s)}})[C.indentalign])}}}return B}});i.TeXAtom.Augment({toSVG:function(n,q){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data[0]!=null){var p=this.SVGdataStretched(0,n,q),r=0;if(this.texClass===i.TEXCLASS.VCENTER){r=a.TeX.axis_height-(p.h+p.d)/2+p.d}o.Add(p,0,r);o.ic=p.ic;o.skew=p.skew}this.SVGhandleColor(o);this.SVGsaveData(o);return o}});i.maligngroup.Augment({toSVG:i.mbase.SVGemptySVG});i.malignmark.Augment({toSVG:i.mbase.SVGemptySVG});i.mprescripts.Augment({toSVG:i.mbase.SVGemptySVG});i.none.Augment({toSVG:i.mbase.SVGemptySVG});e.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});e.Browser.Select({Opera:function(n){a.Augment({operaZoomRefresh:true})}});e.Register.StartupHook("End Cookie",function(){if(e.config.menuSettings.zoom!=="None"){j.Require("[MathJax]/extensions/MathZoom.js")}});if(!document.createElementNS){if(!document.namespaces.svg){document.namespaces.add("svg",b)}a.Augment({Element:function(n,o){var p=(typeof(n)==="string"?document.createElement("svg:"+n):n);p.isMathJax=true;if(o){for(var q in o){if(o.hasOwnProperty(q)){p.setAttribute(q,o[q].toString())}}}return p}})}})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG); +MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,d=MathJax.OutputJax.SVG,b=d.BBOX;a.mtable.Augment({toSVG:function(aa){this.SVGgetStyles();var o=this.SVG(),ap=this.SVGgetScale(o);if(this.data.length===0){this.SVGsaveData(o);return o}var aN=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");if(aN.width.match(/%$/)){o.width=aN.width=d.Em((d.cwidth/1000)*(parseFloat(aN.width)/100))}var v=this.SVGgetMu(o);var aK=-1;var z=[],I=[],k=[],O=[],K=[],aI,aG,w=-1,aE,u,az,S,an,E,aA;var ac=d.FONTDATA.lineH*ap*aN.useHeight,ag=d.FONTDATA.lineD*ap*aN.useHeight;for(aI=0,aE=this.data.length;aIw){w=aG}K[aG]=b.G();k[aG]=-d.BIGDIMEN}an=S.data[aG-az];O[aI][aG]=an.toSVG();if(an.isEmbellished()){E=an.CoreMO();var aM=E.Get("minsize",true);if(aM){if(E.SVGcanStretch("Vertical")){aA=E.SVGdata.h+E.SVGdata.d;if(aA){aM=d.length2em(aM,v,aA);if(aM*E.SVGdata.h/aA>z[aI]){z[aI]=aM*E.SVGdata.h/aA}if(aM*E.SVGdata.d/aA>I[aI]){I[aI]=aM*E.SVGdata.d/aA}}}else{if(E.SVGcanStretch("Horizontal")){aM=d.length2em(aM,v,E.SVGdata.w);if(aM>k[aG]){k[aG]=aM}}}}}if(O[aI][aG].h>z[aI]){z[aI]=O[aI][aG].h}if(O[aI][aG].d>I[aI]){I[aI]=O[aI][aG].d}if(O[aI][aG].w>k[aG]){k[aG]=O[aI][aG].w}}}var ao=MathJax.Hub.SplitList;var am=ao(aN.columnspacing),T=ao(aN.rowspacing),ai=ao(aN.columnalign),L=ao(aN.rowalign),N=ao(aN.columnlines),h=ao(aN.rowlines),ar=ao(aN.columnwidth),aw=[];for(aI=0,aE=am.length;aIO.length){aD=O.length}}g=0;ay=-(aA+ab)+z[0];for(aI=0,aE=aD-1;aI0.98){aj=X/(V+X);at=V+X}else{at=V/(1-ax)}}else{at=Math.max(V+X,d.length2em(aN.width,v));for(aI=0,aE=Math.min(w,am.length);aI0.01){if(aJ&&at>V){at=(at-V)/aJ;for(aI=0,aE=B.length;aIq+az*ak){R.indentalign=ai[aK];ak=az*(al+az*aO);aH+=al+Math.max(0,ak)}}else{if(ai[aK]===R.indentalign){if(e<0){aO=az*e;e=0}ak+=az*e;if(al>az*ak){ak=az*al}ak+=aO;aH+=az*ak}else{ak-=az*e;if(aH-az*ak+al>d.cwidth){ak=az*(aH+al-d.cwidth);if(az*ak>0){aH=d.cwidth+az*ak;ak=0}}}}var G=o;o=this.SVG();o.hasIndent=true;o.w=o.r=Math.max(aH,d.cwidth);o.Align(K[aK],ai[aK],0,0,aO);o.Align(G,R.indentalign,0,0,ak);o.tw=aH}this.SVGsaveData(o);return o},SVGhandleSpace:function(e){if(!this.hasFrame&&!e.width){e.x=e.X=167}this.SUPER(arguments).SVGhandleSpace.call(this,e)}});a.mtd.Augment({toSVG:function(e,g){var f=this.svg=this.SVG();if(this.data[0]){f.Add(this.SVGdataStretched(0,e,g));f.Clean()}this.SVGhandleColor(f);this.SVGsaveData(f);return f}});MathJax.Hub.Startup.signal.Post("SVG mtable Ready");MathJax.Ajax.loadComplete(d.autoloadDir+"/mtable.js")}); +(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_SVG-full.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-AMS_SVG.js b/revisions_report_files/mathjax-27/config/TeX-AMS_SVG.js new file mode 100644 index 0000000..5e50d7f --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-AMS_SVG.js @@ -0,0 +1,57 @@ +/* + * /MathJax/config/TeX-AMS_SVG.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-AMS_SVG.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-MML-AM_CHTML-full.js b/revisions_report_files/mathjax-27/config/TeX-MML-AM_CHTML-full.js new file mode 100644 index 0000000..f95db14 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-MML-AM_CHTML-full.js @@ -0,0 +1,73 @@ +/* + * /MathJax/config/TeX-MML-AM_CHTML-full.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/CommonHTML/jax.js", + "[MathJax]/jax/output/CommonHTML/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); +MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +MathJax.Extension.asciimath2jax={version:"2.7.6",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g=ab-1){this.lastChild=ae}this.childNodes[ad]=ae;ae.nextSibling=ac.nextSibling;ac.nextSibling=ac.parent=null;return ac},hasChildNodes:function(ab){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var ab=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ac=ab.apply(this,arguments)||this;ac.childNodes=ac.data;ac.nodeName=ac.type;return ac},appendChild:function(af){if(af.parent){af.parent.removeChild(af)}var ad=arguments;if(af.isa(X)){ad=af.childNodes;af.data=af.childNodes=[];af.firstChild=af.lastChild=null}for(var ae=0,ac=ad.length;ae=ac-1){this.lastChild=af}this.SetData(ae,af);af.nextSibling=ad.nextSibling;ad.nextSibling=ad.parent=null;return ad},hasChildNodes:function(ac){return(this.childNodes.length>0)},setAttribute:function(ac,ad){this[ac]=ad}})};var Q={};var e={getElementById:true,createElementNS:function(ac,ab){var ad=g[ab]();if(ab==="mo"&&aa.config.useMathMLspacing){ad.useMMLspacing=128}return ad},createTextNode:function(ab){return g.chars(ab).With({nodeValue:ab})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var C="blue";var o=true;var v=true;var d=".";var f=true;var l=(J.appName.slice(0,9)=="Microsoft");function E(ab){if(l){return e.createElement(ab)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",ab)}}var W="http://www.w3.org/1998/Math/MathML";function P(ab){if(l){return e.createElement("m:"+ab)}else{return e.createElementNS(W,ab)}}function O(ab,ad){var ac;if(l){ac=e.createElement("m:"+ab)}else{ac=e.createElementNS(W,ab)}if(ad){ac.appendChild(ad)}return ac}function u(ab,ac){z.push({input:ab,tag:"mo",output:ac,tex:null,ttype:V});B()}function r(ab){z.push(ab);B()}var D=["\uD835\uDC9C","\u212C","\uD835\uDC9E","\uD835\uDC9F","\u2130","\u2131","\uD835\uDCA2","\u210B","\u2110","\uD835\uDCA5","\uD835\uDCA6","\u2112","\u2133","\uD835\uDCA9","\uD835\uDCAA","\uD835\uDCAB","\uD835\uDCAC","\u211B","\uD835\uDCAE","\uD835\uDCAF","\uD835\uDCB0","\uD835\uDCB1","\uD835\uDCB2","\uD835\uDCB3","\uD835\uDCB4","\uD835\uDCB5","\uD835\uDCB6","\uD835\uDCB7","\uD835\uDCB8","\uD835\uDCB9","\u212F","\uD835\uDCBB","\u210A","\uD835\uDCBD","\uD835\uDCBE","\uD835\uDCBF","\uD835\uDCC0","\uD835\uDCC1","\uD835\uDCC2","\uD835\uDCC3","\u2134","\uD835\uDCC5","\uD835\uDCC6","\uD835\uDCC7","\uD835\uDCC8","\uD835\uDCC9","\uD835\uDCCA","\uD835\uDCCB","\uD835\uDCCC","\uD835\uDCCD","\uD835\uDCCE","\uD835\uDCCF"];var H=["\uD835\uDD04","\uD835\uDD05","\u212D","\uD835\uDD07","\uD835\uDD08","\uD835\uDD09","\uD835\uDD0A","\u210C","\u2111","\uD835\uDD0D","\uD835\uDD0E","\uD835\uDD0F","\uD835\uDD10","\uD835\uDD11","\uD835\uDD12","\uD835\uDD13","\uD835\uDD14","\u211C","\uD835\uDD16","\uD835\uDD17","\uD835\uDD18","\uD835\uDD19","\uD835\uDD1A","\uD835\uDD1B","\uD835\uDD1C","\u2128","\uD835\uDD1E","\uD835\uDD1F","\uD835\uDD20","\uD835\uDD21","\uD835\uDD22","\uD835\uDD23","\uD835\uDD24","\uD835\uDD25","\uD835\uDD26","\uD835\uDD27","\uD835\uDD28","\uD835\uDD29","\uD835\uDD2A","\uD835\uDD2B","\uD835\uDD2C","\uD835\uDD2D","\uD835\uDD2E","\uD835\uDD2F","\uD835\uDD30","\uD835\uDD31","\uD835\uDD32","\uD835\uDD33","\uD835\uDD34","\uD835\uDD35","\uD835\uDD36","\uD835\uDD37"];var w=["\uD835\uDD38","\uD835\uDD39","\u2102","\uD835\uDD3B","\uD835\uDD3C","\uD835\uDD3D","\uD835\uDD3E","\u210D","\uD835\uDD40","\uD835\uDD41","\uD835\uDD42","\uD835\uDD43","\uD835\uDD44","\u2115","\uD835\uDD46","\u2119","\u211A","\u211D","\uD835\uDD4A","\uD835\uDD4B","\uD835\uDD4C","\uD835\uDD4D","\uD835\uDD4E","\uD835\uDD4F","\uD835\uDD50","\u2124","\uD835\uDD52","\uD835\uDD53","\uD835\uDD54","\uD835\uDD55","\uD835\uDD56","\uD835\uDD57","\uD835\uDD58","\uD835\uDD59","\uD835\uDD5A","\uD835\uDD5B","\uD835\uDD5C","\uD835\uDD5D","\uD835\uDD5E","\uD835\uDD5F","\uD835\uDD60","\uD835\uDD61","\uD835\uDD62","\uD835\uDD63","\uD835\uDD64","\uD835\uDD65","\uD835\uDD66","\uD835\uDD67","\uD835\uDD68","\uD835\uDD69","\uD835\uDD6A","\uD835\uDD6B"];var c=0,A=1,U=2,i=3,b=4,h=5,a=6,L=7,V=8,m=9,Y=10,K=15;var k={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:Y};var z=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:c},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:c},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:c},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:c},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:c},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:c},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:c},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:c},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:c},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:c},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:c},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:c},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"lamda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lamda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:c},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:c},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:c},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:c},{input:"phi",tag:"mi",output:f?"\u03D5":"\u03C6",tex:null,ttype:c},{input:"varphi",tag:"mi",output:f?"\u03C6":"\u03D5",tex:null,ttype:c},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:c},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:c},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:c},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:c},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:c},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:c},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:c},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:c},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:c},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:c},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:c},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:c},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:c},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:c},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:c},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:c},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:c},{input:"**",tag:"mo",output:"\u2217",tex:"ast",ttype:c},{input:"***",tag:"mo",output:"\u22C6",tex:"star",ttype:c},{input:"//",tag:"mo",output:"/",tex:null,ttype:c},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:c},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:c},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:c},{input:"|><",tag:"mo",output:"\u22C9",tex:"ltimes",ttype:c},{input:"><|",tag:"mo",output:"\u22CA",tex:"rtimes",ttype:c},{input:"|><|",tag:"mo",output:"\u22C8",tex:"bowtie",ttype:c},{input:"-:",tag:"mo",output:"\u00F7",tex:"div",ttype:c},{input:"divide",tag:"mo",output:"-:",tex:null,ttype:V},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:c},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:c},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:c},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:c},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:L},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:L},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:c},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:L},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:c},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:L},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:c},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:L},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:c},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:L},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:c},{input:":=",tag:"mo",output:":=",tex:null,ttype:c},{input:"lt",tag:"mo",output:"<",tex:null,ttype:c},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:c},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:c},{input:"gt",tag:"mo",output:">",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:"left(",ttype:b},{input:")",tag:"mo",output:")",tex:"right)",ttype:h},{input:"[",tag:"mo",output:"[",tex:"left[",ttype:b},{input:"]",tag:"mo",output:"]",tex:"right]",ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:m},{input:":|:",tag:"mo",output:"|",tex:null,ttype:c},{input:"|:",tag:"mo",output:"|",tex:null,ttype:b},{input:":|",tag:"mo",output:"|",tex:null,ttype:h},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:":'",tag:"mo",output:"\u2235",tex:"because",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"frown",tag:"mo",output:"\u2322",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"Sin",tag:"mo",output:"Sin",tex:null,ttype:A,func:true},{input:"Cos",tag:"mo",output:"Cos",tex:null,ttype:A,func:true},{input:"Tan",tag:"mo",output:"Tan",tex:null,ttype:A,func:true},{input:"Arcsin",tag:"mo",output:"Arcsin",tex:null,ttype:A,func:true},{input:"Arccos",tag:"mo",output:"Arccos",tex:null,ttype:A,func:true},{input:"Arctan",tag:"mo",output:"Arctan",tex:null,ttype:A,func:true},{input:"Sinh",tag:"mo",output:"Sinh",tex:null,ttype:A,func:true},{input:"Cosh",tag:"mo",output:"Cosh",tex:null,ttype:A,func:true},{input:"Tanh",tag:"mo",output:"Tanh",tex:null,ttype:A,func:true},{input:"Cot",tag:"mo",output:"Cot",tex:null,ttype:A,func:true},{input:"Sec",tag:"mo",output:"Sec",tex:null,ttype:A,func:true},{input:"Csc",tag:"mo",output:"Csc",tex:null,ttype:A,func:true},{input:"Log",tag:"mo",output:"Log",tex:null,ttype:A,func:true},{input:"Ln",tag:"mo",output:"Ln",tex:null,ttype:A,func:true},{input:"Abs",tag:"mo",output:"abs",tex:null,ttype:A,notexcopy:true,rewriteleftright:["|","|"]},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:i},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"overset",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"underset",tag:"munder",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:i},{input:"^",tag:"msup",output:"^",tex:null,ttype:i},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"overarc",tag:"mover",output:"\u23DC",tex:"overparen",ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"id",tag:"mrow",ttype:U},{input:"class",tag:"mrow",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},k,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ac,ab){if(ac.input>ab.input){return 1}else{return -1}}var S=[];function n(){var ac;var ab=z.length;for(ac=0;ac>1;if(ac[ab]=S[ab]}s=y;if(af!=""){y=z[ae].ttype;return z[ae]}y=c;ab=1;ak=ah.slice(0,1);var ai=true;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}if(ak==d){ak=ah.slice(ab,ab+1);if("0"<=ak&&ak<="9"){ai=false;ab++;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}}}if((ai&&ab>1)||ab>2){ak=ah.slice(0,ab-1);aj="mn"}else{ab=2;ak=ah.slice(0,1);aj=(("A">ak||ak>"Z")&&("a">ak||ak>"z")?"mo":"mi")}if(ak=="-"&&s==i){y=i;return{input:ak,tag:aj,output:ak,ttype:A,func:true}}return{input:ak,tag:aj,output:ak,ttype:c}}function R(ac){var ab;if(!ac.hasChildNodes()){return}if(ac.firstChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.firstChild.firstChild.nodeValue;if(ab=="("||ab=="["||ab=="{"){ac.removeChild(ac.firstChild)}}if(ac.lastChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.lastChild.firstChild.nodeValue;if(ab==")"||ab=="]"||ab=="}"){ac.removeChild(ac.lastChild)}}}var F,s,y;function G(ai){var ad,ac,al,af,ak,ag=e.createDocumentFragment();ai=p(ai,0);ad=j(ai);if(ad==null||ad.ttype==h&&F>0){return[null,ai]}if(ad.ttype==V){ai=ad.output+p(ai,ad.input.length);ad=j(ai)}switch(ad.ttype){case L:case c:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai];case b:F++;ai=p(ai,ad.input.length);al=q(ai,true);F--;if(typeof ad.invisible=="boolean"&&ad.invisible){ac=O("mrow",al[0])}else{ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0])}return[ac,al[1]];case Y:if(ad!=k){ai=p(ai,ad.input.length)}if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}else{if(ad==k){af=ai.slice(1).indexOf('"')+1}else{af=0}}}}if(af==-1){af=ai.length}ak=ai.slice(1,af);if(ak.charAt(0)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ag.appendChild(O(ad.tag,e.createTextNode(ak)));if(ak.charAt(ak.length-1)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ai=p(ai,af+1);return[O("mrow",ag),ai];case K:case A:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O(ad.tag,e.createTextNode(ad.output)),ai]}if(typeof ad.func=="boolean"&&ad.func){ak=ai.charAt(0);if(ak=="^"||ak=="_"||ak=="/"||ak=="|"||ak==","||(ad.input.length==1&&ad.input.match(/\w/)&&ak!="(")){return[O(ad.tag,e.createTextNode(ad.output)),ai]}else{ac=O("mrow",O(ad.tag,e.createTextNode(ad.output)));ac.appendChild(al[0]);return[ac,al[1]]}}R(al[0]);if(ad.input=="sqrt"){return[O(ad.tag,al[0]),al[1]]}else{if(typeof ad.rewriteleftright!="undefined"){ac=O("mrow",O("mo",e.createTextNode(ad.rewriteleftright[0])));ac.appendChild(al[0]);ac.appendChild(O("mo",e.createTextNode(ad.rewriteleftright[1])));return[ac,al[1]]}else{if(ad.input=="cancel"){ac=O(ad.tag,al[0]);ac.setAttribute("notation","updiagonalstrike");return[ac,al[1]]}else{if(typeof ad.acc=="boolean"&&ad.acc){ac=O(ad.tag,al[0]);var ah=O("mo",e.createTextNode(ad.output));if(ad.input=="vec"&&((al[0].nodeName=="mrow"&&al[0].childNodes.length==1&&al[0].firstChild.firstChild.nodeValue!==null&&al[0].firstChild.firstChild.nodeValue.length==1)||(al[0].firstChild.nodeValue!==null&&al[0].firstChild.nodeValue.length==1))){ah.setAttribute("stretchy",false)}ac.appendChild(ah);return[ac,al[1]]}else{if(!l&&typeof ad.codes!="undefined"){for(af=0;af64&&ak.charCodeAt(ae)<91){aj=aj+ad.codes[ak.charCodeAt(ae)-65]}else{if(ak.charCodeAt(ae)>96&&ak.charCodeAt(ae)<123){aj=aj+ad.codes[ak.charCodeAt(ae)-71]}else{aj=aj+ak.charAt(ae)}}}if(al[0].nodeName=="mi"){al[0]=O("mo").appendChild(e.createTextNode(aj))}else{al[0].replaceChild(O("mo").appendChild(e.createTextNode(aj)),al[0].childNodes[af])}}}}ac=O(ad.tag,al[0]);ac.setAttribute(ad.atname,ad.atval);return[ac,al[1]]}}}}case U:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(al[0]);var ab=G(al[1]);if(ab[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(ab[0]);if(["color","class","id"].indexOf(ad.input)>=0){if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}}}ak=ai.slice(1,af);ac=O(ad.tag,ab[0]);if(ad.input==="color"){ac.setAttribute("mathcolor",ak)}else{if(ad.input==="class"){ac.setAttribute("class",ak)}else{if(ad.input==="id"){ac.setAttribute("id",ak)}}}return[ac,ab[1]]}if(ad.input=="root"||ad.output=="stackrel"){ag.appendChild(ab[0])}ag.appendChild(al[0]);if(ad.input=="frac"){ag.appendChild(ab[0])}return[O(ad.tag,ag),ab[1]];case i:ai=p(ai,ad.input.length);return[O("mo",e.createTextNode(ad.output)),ai];case a:ai=p(ai,ad.input.length);ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);ag.appendChild(O(ad.tag,e.createTextNode(ad.output)));ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);return[O("mrow",ag),ai];case m:F++;ai=p(ai,ad.input.length);al=q(ai,false);F--;ak="";if(al[0].lastChild!=null){ak=al[0].lastChild.firstChild.nodeValue}if(ak=="|"&&ai.charAt(0)!==","){ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0]);return[ac,al[1]]}else{ac=O("mo",e.createTextNode("\u2223"));ac=O("mrow",ac);return[ac,ai]}default:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai]}}function t(ah){var af,ai,ag,ae,ab,ad;ah=p(ah,0);ai=j(ah);ab=G(ah);ae=ab[0];ah=ab[1];af=j(ah);if(af.ttype==i&&af.input!="/"){ah=p(ah,af.input.length);ab=G(ah);if(ab[0]==null){ab[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ab[0])}ah=ab[1];ad=(ai.ttype==L||ai.ttype==K);if(af.input=="_"){ag=j(ah);if(ag.input=="^"){ah=p(ah,ag.input.length);var ac=G(ah);R(ac[0]);ah=ac[1];ae=O((ad?"munderover":"msubsup"),ae);ae.appendChild(ab[0]);ae.appendChild(ac[0]);ae=O("mrow",ae)}else{ae=O((ad?"munder":"msub"),ae);ae.appendChild(ab[0])}}else{if(af.input=="^"&&ad){ae=O("mover",ae);ae.appendChild(ab[0])}else{ae=O(af.tag,ae);ae.appendChild(ab[0])}}if(typeof ai.func!="undefined"&&ai.func){ag=j(ah);if(ag.ttype!=i&&ag.ttype!=h){ab=t(ah);ae=O("mrow",ae);ae.appendChild(ab[0]);ah=ab[1]}}}return[ae,ah]}function q(ak,aj){var ao,al,ag,ar,ah=e.createDocumentFragment();do{ak=p(ak,0);ag=t(ak);al=ag[0];ak=ag[1];ao=j(ak);if(ao.ttype==i&&ao.input=="/"){ak=p(ak,ao.input.length);ag=t(ak);if(ag[0]==null){ag[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ag[0])}ak=ag[1];R(al);al=O(ao.tag,al);al.appendChild(ag[0]);ah.appendChild(al);ao=j(ak)}else{if(al!=undefined){ah.appendChild(al)}}}while((ao.ttype!=h&&(ao.ttype!=m||aj)||F==0)&&ao!=null&&ao.output!="");if(ao.ttype==h||ao.ttype==m){var at=ah.childNodes.length;if(at>0&&ah.childNodes[at-1].nodeName=="mrow"&&ah.childNodes[at-1].lastChild&&ah.childNodes[at-1].lastChild.firstChild){var av=ah.childNodes[at-1].lastChild.firstChild.nodeValue;if(av==")"||av=="]"){var ac=ah.childNodes[at-1].firstChild.firstChild.nodeValue;if(ac=="("&&av==")"&&ao.output!="}"||ac=="["&&av=="]"){var ad=[];var ap=true;var am=ah.childNodes.length;for(ar=0;ap&&ar1){ap=ad[ar].length==ad[ar-2].length}}ap=ap&&(ad.length>1||ad[0].length>0);var af=[];if(ap){var ae,ab,ai,an,au=e.createDocumentFragment();for(ar=0;ar2){ah.removeChild(ah.firstChild);ah.removeChild(ah.firstChild)}au.appendChild(O("mtr",ae))}al=O("mtable",au);al.setAttribute("columnlines",af.join(" "));if(typeof ao.invisible=="boolean"&&ao.invisible){al.setAttribute("columnalign","left")}ah.replaceChild(al,ah.firstChild)}}}}ak=p(ak,ao.input.length);if(typeof ao.invisible!="boolean"||!ao.invisible){al=O("mo",e.createTextNode(ao.output));ah.appendChild(al)}}return[ah,ak]}function M(ad,ac){var ae,ab;F=0;ad=ad.replace(/ /g,"");ad=ad.replace(/>/g,">");ad=ad.replace(/</g,"<");ae=q(ad.replace(/^\s+/g,""),false)[0];ab=O("mstyle",ae);if(C!=""){ab.setAttribute("mathcolor",C)}if(mathfontsize!=""){ab.setAttribute("fontsize",mathfontsize);ab.setAttribute("mathsize",mathfontsize)}if(mathfontfamily!=""){ab.setAttribute("fontfamily",mathfontfamily);ab.setAttribute("mathvariant",mathfontfamily)}if(o){ab.setAttribute("displaystyle","true")}ab=O("math",ab);if(v){ab.setAttribute("title",ad.replace(/\s+/g," "))}return ab}v=false;mathfontfamily="";C="";mathfontsize="";(function(){for(var ac=0,ab=z.length;ac *":{position:"absolute"},".MJXc-bevelled > *":{display:"inline-block"},".mjx-stack":{display:"inline-block"},".mjx-op":{display:"block"},".mjx-under":{display:"table-cell"},".mjx-over":{display:"block"},".mjx-over > *":{"padding-left":"0px!important","padding-right":"0px!important"},".mjx-under > *":{"padding-left":"0px!important","padding-right":"0px!important"},".mjx-stack > .mjx-sup":{display:"block"},".mjx-stack > .mjx-sub":{display:"block"},".mjx-prestack > .mjx-presup":{display:"block"},".mjx-prestack > .mjx-presub":{display:"block"},".mjx-delim-h > .mjx-char":{display:"inline-block"},".mjx-surd":{"vertical-align":"top"},".mjx-mphantom *":{visibility:"hidden"},".mjx-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"2px 3px","font-style":"normal","font-size":"90%"},".mjx-annotation-xml":{"line-height":"normal"},".mjx-menclose > svg":{fill:"none",stroke:"currentColor"},".mjx-mtr":{display:"table-row"},".mjx-mlabeledtr":{display:"table-row"},".mjx-mtd":{display:"table-cell","text-align":"center"},".mjx-label":{display:"table-row"},".mjx-box":{display:"inline-block"},".mjx-block":{display:"block"},".mjx-span":{display:"inline"},".mjx-char":{display:"block","white-space":"pre"},".mjx-itable":{display:"inline-table",width:"auto"},".mjx-row":{display:"table-row"},".mjx-cell":{display:"table-cell"},".mjx-table":{display:"table",width:"100%"},".mjx-line":{display:"block",height:0},".mjx-strut":{width:0,"padding-top":k+"em"},".mjx-vsize":{width:0},".MJXc-space1":{"margin-left":".167em"},".MJXc-space2":{"margin-left":".222em"},".MJXc-space3":{"margin-left":".278em"},".mjx-chartest":{display:"block",visibility:"hidden",position:"absolute",top:0,"line-height":"normal","font-size":"500%"},".mjx-chartest .mjx-char":{display:"inline"},".mjx-chartest .mjx-box":{"padding-top":"1000px"},".MJXc-processing":{visibility:"hidden",position:"fixed",width:0,height:0,overflow:"hidden"},".MJXc-processed":{display:"none"},".mjx-test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".mjx-test.mjx-test-display":{display:"table!important"},".mjx-test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".mjx-test.mjx-test-default":{display:"block!important",clear:"both"},".mjx-ex-box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .mjx-left-box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .mjx-right-box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .mjx-right-box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_CHTML_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401,position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}};var i=1000000;var n=5;var c={},r=MathJax.Hub.config;a.Augment({settings:f.config.menuSettings,config:{styles:p},Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var s=this.settings;if(s.scale){this.config.scale=s.scale}this.require.push(this.fontDir+"/TeX/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js");c=this.config.linebreaks},Startup:function(){e=MathJax.Extension.MathEvents.Event;q=MathJax.Extension.MathEvents.Touch;h=MathJax.Extension.MathEvents.Hover;this.ContextMenu=e.ContextMenu;this.Mousedown=e.AltContextMenu;this.Mouseover=h.Mouseover;this.Mouseout=h.Mouseout;this.Mousemove=h.Mousemove;var s=a.addElement(document.body,"mjx-block",{style:{display:"block",width:"5in"}});this.pxPerInch=s.offsetWidth/5;s.parentNode.removeChild(s);this.TestSpan=a.Element("mjx-test",{style:{left:"1em"}},[["mjx-left-box"],["mjx-ex-box"],["mjx-right-box"]]);return o.Styles(this.config.styles,["InitializeCHTML",this])},InitializeCHTML:function(){this.getDefaultExEm();if(this.defaultEm){return}var s=MathJax.Callback();o.timer.start(o,function(t){if(t.time(s)){f.signal.Post(["CommonHTML Jax - no default em size"]);return}a.getDefaultExEm();if(a.defaultEm){s()}else{setTimeout(t,t.delay)}},this.defaultEmDelay,this.defaultEmTimeout);return s},defaultEmDelay:100,defaultEmTimeout:1000,getDefaultExEm:function(){var s=document.body.appendChild(this.TestSpan.cloneNode(true));s.className+=" mjx-test-inline mjx-test-default";this.defaultEm=this.getFontSize(s);this.defaultEx=s.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,s.lastChild.offsetLeft-s.firstChild.offsetLeft-2);document.body.removeChild(s)},getFontSize:(window.getComputedStyle?function(t){var s=window.getComputedStyle(t);return parseFloat(s.fontSize)}:function(s){return s.style.pixelLeft}),getMaxWidth:(window.getComputedStyle?function(t){var s=window.getComputedStyle(t);if(s.maxWidth!=="none"){return parseFloat(s.maxWidth)}return 0}:function(t){var s=t.currentStyle.maxWidth;if(s!=="none"){if(s.match(/\d*px/)){return parseFloat(s)}var u=t.style.left;t.style.left=s;s=t.style.pixelLeft;t.style.left=u;return s}return 0}),loadFont:function(s){f.RestartAfter(o.Require(this.fontDir+"/"+s))},fontLoaded:function(s){if(!s.match(/-|fontdata/)){s+="-Regular"}if(!s.match(/\.js$/)){s+=".js"}MathJax.Callback.Queue(["Post",f.Startup.signal,"CommonHTML - font data loaded for "+s],["loadComplete",o,this.fontDir+"/"+s])},Element:function(s,u,t){if(s.substr(0,4)==="mjx-"){if(!u){u={}}if(u.isMathJax==null){u.isMathJax=true}if(u.className){u.className=s+" "+u.className}else{u.className=s}s="span"}return this.HTMLElement(s,u,t)},addElement:function(u,s,v,t){return u.appendChild(this.Element(s,v,t))},HTMLElement:m.Element,ucMatch:m.ucMatch,setScript:m.setScript,getNode:function(x,w){var u=RegExp("\\b"+w+"\\b");var t=[];while(x){for(var v=0,s=x.childNodes.length;v=x.CHTMLlast+x.CHTMLchunk){this.postTranslate(x);x.CHTMLchunk=Math.floor(x.CHTMLchunk*this.config.EqnChunkFactor);x.CHTMLdelay=true}},initCHTML:function(t,s){},savePreview:function(s){var t=s.MathJax.preview;if(t&&t.parentNode){s.MathJax.tmpPreview=document.createElement("span");t.parentNode.replaceChild(s.MathJax.tmpPreview,t)}},restorePreview:function(s){var t=s.MathJax.tmpPreview;if(t){t.parentNode.replaceChild(s.MathJax.preview,t);delete s.MathJax.tmpPreview}},getMetrics:function(s){var t=s.CHTML;this.jax=s;this.em=t.em;this.outerEm=t.outerEm;this.scale=t.scale;this.cwidth=t.cwidth;this.linebreakWidth=t.lineWidth},postTranslate:function(x){var t=x.jax[this.id];for(var v=x.CHTMLlast,s=x.CHTMLeqn;vC.h){t.marginTop=a.Em(C.t-C.h)}if(C.b>C.d){t.marginBottom=a.Em(C.b-C.d)}if(C.l<0){t.paddingLeft=a.Em(-C.l)}if(C.r>C.w){t.marginRight=a.Em(C.r-C.w)}t.position="absolute";var z=v.offsetWidth,x=v.offsetHeight,D=A.firstChild.offsetHeight,w=A.firstChild.offsetWidth;v.style.position="";return{Y:-e.getBBox(B).h,mW:w,mH:D,zW:z,zH:x}},Remove:function(s){var t=document.getElementById(s.inputID+"-Frame");if(t&&s.CHTML.display){t=t.parentNode}if(t){t.parentNode.removeChild(t)}delete s.CHTML},ID:0,idPostfix:"",GetID:function(){this.ID++;return this.ID},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18,thin:0.04,medium:0.06,thick:0.1,infinity:i},SPACECLASS:{thinmathspace:"MJXc-space1",mediummathspace:"MJXc-space2",thickmathspace:"MJXc-space3"},pxPerInch:96,em:16,maxStretchyParts:1000,FONTDEF:{},TEXDEF:{x_height:0.442,quad:1,num1:0.676508,num2:0.393732,num3:0.44373,denom1:0.685951,denom2:0.344841,sup1:0.412892,sup2:0.362892,sup3:0.288888,sub1:0.15,sub2:0.247217,sup_drop:0.386108,sub_drop:0.05,delim1:2.39,delim2:1,axis_height:0.25,rule_thickness:0.06,big_op_spacing1:0.111111,big_op_spacing2:0.166666,big_op_spacing3:0.2,big_op_spacing4:0.45,big_op_spacing5:0.1,surd_height:0.075,scriptspace:0.05,nulldelimiterspace:0.12,delimiterfactor:901,delimitershortfall:0.3,min_rule_thickness:1.25},isChar:function(s){if(s.length===1){return true}if(s.length!==2){return false}var t=s.charCodeAt(0);return(t>=55296&&t<56319)},unicodeChar:function(s){if(s<65535){return String.fromCharCode(s)}s-=65536;return String.fromCharCode((s>>10)+55296)+String.fromCharCode((s&1023)+56320)},getUnicode:function(s){var t=s.text.charCodeAt(s.i);s.i++;if(t>=55296&&t<56319){t=(((t-55296)<<10)+(s.text.charCodeAt(s.i)-56320))+65536;s.i++}return t},getCharList:function(w,v){var u,z,s=w.cache,B=v;if(s[v]){return s[v]}if(v>65535&&this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(v,w);v=y.n;w=y.variant}var t=this.FONTDATA.RANGES,A=this.FONTDATA.VARIANT;if(v>=t[0].low&&v<=t[t.length-1].high){for(u=0,z=t.length;u=t[u].low&&v<=t[u].high){if(t[u].remap&&t[u].remap[v]){v=x+t[u].remap[v]}else{v=v-t[u].low+x;if(t[u].add){v+=t[u].add}}if(w["variant"+t[u].offset]){w=A[w["variant"+t[u].offset]]}break}}}s[B]=this.remapChar(w,v,0);return s[B]},remapChar:function(t,y,w){var v=[],x=this.FONTDATA.VARIANT;if(t.remap&&t.remap[y]){y=t.remap[y];if(t.remap.variant){t=x[t.remap.variant]}}else{if(this.FONTDATA.REMAP[y]&&!t.noRemap){y=this.FONTDATA.REMAP[y]}}if(g(y)){if(y[2]){w=n}t=x[y[1]];y=y[0]}if(typeof(y)==="string"){var s={text:y,i:0,length:y.length};while(s.i(B.a||0)){B.a=u.a}u.className=w.className;var t=w[D.n];if(A){var v=w;if(g(A)){v=a.FONTDATA.FONTS[A[1]];A=A[0];if(typeof(v)==="string"){a.loadFont(v)}}if(v[D.n]){a.fixChar(v[D.n],D.n)}t=a.fixChar(v[A],A);u.className=v.className}u.text+=t.c;if(B.hB.w+t[3]){B.l=B.w+t[3]}if(B.rw.a){w.a=u.a}}s=this.flushText(s,u,t.style);if(v[2]<3){s.style.width=a.Em(v[2])}},flushText:function(t,u,s){t=a.addElement(t,"mjx-charbox",{className:u.className,style:s},[u.text]);if(u.a){t.style.paddingBottom=a.Em(u.a)}u.text="";u.className=null;u.a=0;u.flushed=true;return t}},handleText:function(u,x,t,w){if(u.childNodes.length===0){a.addElement(u,"mjx-char");w=a.BBOX.empty(w)}if(typeof(t)==="string"){t=this.FONTDATA.VARIANT[t]}if(!t){t=this.FONTDATA.VARIANT[d.VARIANT.NORMAL]}var s={text:x,i:0,length:x.length},v=[];if(t.style&&s.length){v.push(this.styledText(t,x))}else{while(s.i-w.b){u.firstChild.style.paddingBottom=this.EmRounded(w.d+w.b)}return w},createDelimiter:function(x,s,u,A,v){if(!s){var B=this.BBOX.zero();B.w=B.r=this.TEX.nulldelimiterspace;a.addElement(x,"mjx-box",{style:{width:B.w}});return B}if(!(u instanceof Array)){u=[u,u]}var z=u[1];u=u[0];var t={alias:s};while(t.alias){s=t.alias;t=this.FONTDATA.DELIMITERS[s];if(!t){t={HW:[0,this.FONTDATA.VARIANT[d.VARIANT.NORMAL]]}}}if(t.load){f.RestartAfter(o.Require(this.fontDir+"/TeX/fontdata-"+t.load+".js"))}for(var y=0,w=t.HW.length;y=u-0.01||(y==w-1&&!t.stretch)){if(t.HW[y][3]){s=t.HW[y][3]}B=this.createChar(x,[s,t.HW[y][1]],(t.HW[y][2]||1),v);B.offset=0.6*B.w;if(A){B.scale=A.scale;A.rscale=A.rscale}return B}}if(!t.stretch){return B}return this["extendDelimiter"+t.dir](x,z,t.stretch,A,v)},extendDelimiterV:function(E,x,P,w,C){E=a.addElement(E,"mjx-delim-v");var N=a.Element("span");var B,A,O,v,I,t,F,y,G=1,M;I=this.createChar(N,(P.top||P.ext),1,C);B=N.removeChild(N.firstChild);t=this.createChar(N,(P.bot||P.ext),1,C);A=N.removeChild(N.firstChild);F=y=a.BBOX.zero();var J=I.h+I.d+t.h+t.d-l;E.appendChild(B);if(P.mid){F=this.createChar(N,P.mid,1,C);O=N.removeChild(N.firstChild);J+=F.h+F.d;G=2}if(P.min&&xJ){y=this.createChar(N,P.ext,1,C);v=N.removeChild(N.firstChild);var L=y.h+y.d,u=L-l;var D=Math.min(Math.ceil((x-J)/(G*u)),this.maxStretchyParts);if(P.fullExtenders){x=D*G*u+J}else{u=(x-J)/(G*D)}M=y.d+y.a-L/2;v.style.margin=v.style.padding="";v.style.lineHeight=a.Em(u);v.style.marginBottom=a.Em(M-l/2/G);v.style.marginTop=a.Em(-M-l/2/G);var K=v.textContent,z="\n"+K;while(--D>0){K+=z}v.textContent=K;E.appendChild(v);if(P.mid){E.appendChild(O);E.appendChild(v.cloneNode(true))}}else{M=(x-J-l)/G;B.style.marginBottom=a.Em(M+parseFloat(B.style.marginBottom||"0"));if(P.mid){E.appendChild(O)}A.style.marginTop=a.Em(M+parseFloat(A.style.marginTop||"0"))}E.appendChild(A);var s=a.BBOX({w:Math.max(I.w,y.w,t.w,F.w),l:Math.min(I.l,y.l,t.l,F.l),r:Math.max(I.r,y.r,t.r,F.r),h:x-t.d,d:t.d,t:x-t.d,b:t.d});s.offset=0.5*s.w;if(w){s.scale=w.scale;s.rscale=w.rscale}return s},extendDelimiterH:function(F,s,P,v,D){F=a.addElement(F,"mjx-delim-h");var N=a.Element("span");var t,M,O,u,K,C,x,G,z,H=1;C=this.createChar(N,(P.left||P.rep),1,D);t=N.removeChild(N.firstChild);x=this.createChar(N,(P.right||P.rep),1,D);M=N.removeChild(N.firstChild);z=this.createChar(N,P.rep,1,D);u=N.removeChild(N.firstChild);t.style.marginLeft=a.Em(-C.l);M.style.marginRight=a.Em(x.r-x.w);F.appendChild(t);var Q=a.BBOX.zero();Q.h=Math.max(C.h,x.h,z.h);Q.d=Math.max(C.D||C.d,x.D||x.d,z.D||z.d);var y=(C.r-C.l)+(x.r-x.l)-l;if(P.mid){G=this.createChar(N,P.mid,1,D);O=N.removeChild(N.firstChild);O.style.marginleft=a.Em(-G.l);O.style.marginRight=a.Em(G.r-G.w);y+=G.r-G.l+l;H=2;if(G.h>Q.h){Q.h=G.h}if(G.d>Q.d){Q.d=G.d}}if(P.min&&sy){var B=z.r-z.l,J=B-l;var E=Math.min(Math.ceil((s-y)/(H*J)),this.maxStretchyParts);if(P.fullExtenders){s=E*H*J+y}else{J=(s-y)/(H*E)}var L=(B-J+l/H)/2;u.style.marginLeft=a.Em(-z.l-L);u.style.marginRight=a.Em(z.r-z.w+L);u.style.letterSpacing=a.Em(-(z.w-J));t.style.marginRight=a.Em(C.r-C.w);M.style.marginleft=a.Em(-x.l);var I=u.textContent,A=I;while(--E>0){I+=A}u.textContent=I;F.appendChild(u);if(P.mid){F.appendChild(O);K=F.appendChild(u.cloneNode(true))}}else{L=(s-y-l/H)/2;t.style.marginRight=a.Em(C.r-C.w+L);if(P.mid){F.appendChild(O)}M.style.marginLeft=a.Em(-x.l+L)}F.appendChild(M);this.adjustHeights([t,u,O,K,M],[C,z,G,z,x],Q);if(v){Q.scale=v.scale;Q.rscale=v.rscale}return Q},adjustHeights:function(t,w,x){var u=x.h,y=x.d;if(x.d<0){y=-x.d;x.D=x.d;x.d=0}for(var v=0,s=t.length;v0){delete this.D}},rescale:function(s){this.w*=s;this.h*=s;this.d*=s;this.l*=s;this.r*=s;this.t*=s;this.b*=s;if(this.L){this.L*=s}if(this.R){this.R*=s}if(this.D){this.D*=s}},combine:function(t,s,v){t.X=s;t.Y=v;var u=t.rscale;if(s+u*t.r>this.r){this.r=s+u*t.r}if(s+u*t.lthis.w){this.w=s+u*(t.w+(t.L||0)+(t.R||0))}if(v+u*t.h>this.h){this.h=v+u*t.h}if(t.D&&(this.D==null||u*t.D-v>this.D)&&u*t.D>this.d){this.D=u*t.D-v}else{if(t.D==null&&this.D){delete this.D}}if(u*t.d-v>this.d){this.d=u*t.d-v}if(v+u*t.t>this.t){this.t=v+u*t.t}if(u*t.b-v>this.b){this.b=u*t.b-v}},append:function(t){var u=t.rscale;var s=this.w;if(s+u*t.r>this.r){this.r=s+u*t.r}if(s+u*t.lthis.h){this.h=u*t.h}if(t.D&&(this.D==null||u*t.D>this.D)&&u*t.D>this.d){this.D=u*t.D}else{if(t.D==null&&this.D){delete this.D}}if(u*t.d>this.d){this.d=u*t.d}if(u*t.t>this.t){this.t=u*t.t}if(u*t.b>this.b){this.b=u*t.b}},updateFrom:function(s){this.h=s.h;this.d=s.d;this.w=s.w;this.r=s.r;this.l=s.l;this.t=s.t;this.b=s.b;if(s.pwidth){this.pwidth=s.pwidth}if(s.D){this.D=s.D}else{delete this.D}},adjust:function(t,s,v,u){this[s]+=a.length2em(t,1,this.scale);if(u==null){if(this[s]>this[v]){this[v]=this[s]}}else{if(this[v]z.r){z.r=z.w}if(t.h>z.h){z.h=t.h}if(t.d>z.d){z.d=t.d}if(t.t>z.t){z.t=t.t}if(t.b>z.b){z.b=t.b}}}},CHTMLstretchChildH:function(v,s,x){var y=this.data[v];if(y){var z=this.CHTML,u=y.CHTML;if(u.stretch||(u.stretch==null&&y.CHTMLcanStretch("Horizontal",s))){var t=u.w;u=y.CHTMLstretchH(this.CHTMLchildNode(x,v),s);z.w+=u.w-t;if(z.w>z.r){z.r=z.w}if(u.h>z.h){z.h=u.h}if(u.d>z.d){z.d=u.d}if(u.t>z.t){z.t=u.t}if(u.b>z.b){z.b=u.b}}}},CHTMLupdateFrom:function(s){this.CHTML.updateFrom(s);if(this.inferRow){this.data[0].CHTML.updateFrom(s)}},CHTMLcanStretch:function(w,u,v){var t=false;if(this.isEmbellished()){var s=this.Core();if(s&&s!==this){t=s.CHTMLcanStretch(w,u,v)}}this.CHTML.stretch=t;return t},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));return this.CHTML},CHTMLstretchCoreH:function(t,s){return this.Core().CHTMLstretchH(this.CHTMLcoreNode(t),s)},CHTMLcreateNode:function(s){if(!this.CHTML){this.CHTML={}}this.CHTML=a.BBOX.zero();if(this.href){s=a.addElement(s,"a",{href:this.href,isMathJax:true})}if(!this.CHTMLnodeID){this.CHTMLnodeID=a.GetID()}var t=(this.id||"MJXc-Node-"+this.CHTMLnodeID)+a.idPostfix;return this.CHTMLhandleAttributes(a.addElement(s,"mjx-"+this.type,{id:t}))},CHTMLnodeElement:function(){if(!this.CHTMLnodeID){return null}return document.getElementById((this.id||"MJXc-Node-"+this.CHTMLnodeID)+a.idPostfix)},CHTMLlength2em:function(t,s){return a.length2em(t,s,this.CHTML.scale)},CHTMLhandleAttributes:function(v){if(this["class"]){if(v.className){v.className+=" "+this["class"]}else{v.className=this["class"]}}if(this.attrNames){var z=this.attrNames,u=d.nocopyAttributes,y=f.config.ignoreMMLattributes;var w=(this.type==="mstyle"?d.math.prototype.defaults:this.defaults);for(var t=0,s=z.length;t2){s.scriptlevel=2}x=Math.pow(this.Get("scriptsizemultiplier"),s.scriptlevel);s.scriptminsize=a.length2em(this.Get("scriptminsize"),0.8,1);if(x600?"bold":"normal")}var t=s.mathvariant;if(this.variantForm){t="-TeX-variant"}if(s.family&&!s.hasVariant){if(!s.weight&&s.mathvariant.match(/bold/)){s.weight="bold"}if(!s.style&&s.mathvariant.match(/italic/)){s.style="italic"}this.CHTMLvariant={fonts:[],noRemap:true,cache:{},style:{"font-family":s.family,"font-weight":s.weight||"normal","font-style":s.style||"normal"}};return}if(s.weight==="bold"){t={normal:d.VARIANT.BOLD,italic:d.VARIANT.BOLDITALIC,fraktur:d.VARIANT.BOLDFRAKTUR,script:d.VARIANT.BOLDSCRIPT,"sans-serif":d.VARIANT.BOLDSANSSERIF,"sans-serif-italic":d.VARIANT.SANSSERIFBOLDITALIC}[t]||t}else{if(s.weight==="normal"){t={bold:d.VARIANT.normal,"bold-italic":d.VARIANT.ITALIC,"bold-fraktur":d.VARIANT.FRAKTUR,"bold-script":d.VARIANT.SCRIPT,"bold-sans-serif":d.VARIANT.SANSSERIF,"sans-serif-bold-italic":d.VARIANT.SANSSERIFITALIC}[t]||t}}if(s.style==="italic"){t={normal:d.VARIANT.ITALIC,bold:d.VARIANT.BOLDITALIC,"sans-serif":d.VARIANT.SANSSERIFITALIC,"bold-sans-serif":d.VARIANT.SANSSERIFBOLDITALIC}[t]||t}else{if(s.style==="normal"){t={italic:d.VARIANT.NORMAL,"bold-italic":d.VARIANT.BOLD,"sans-serif-italic":d.VARIANT.SANSSERIF,"sans-serif-bold-italic":d.VARIANT.BOLDSANSSERIF}[t]||t}}this.CHTMLvariant=a.FONTDATA.VARIANT[t]||a.FONTDATA.VARIANT[d.VARIANT.NORMAL]},CHTMLbboxFor:function(s){if(this.data[s]&&this.data[s].CHTML){return this.data[s].CHTML}return a.BBOX.zero()},CHTMLdrawBBox:function(t,u){if(!u){u=this.CHTML}var s=a.Element("mjx-box",{style:{opacity:0.25,"margin-left":a.Em(-(u.w+(u.R||0)))}},[["mjx-box",{style:{height:a.Em(u.h),width:a.Em(u.w),"background-color":"red"}}],["mjx-box",{style:{height:a.Em(u.d),width:a.Em(u.w),"margin-left":a.Em(-u.w),"vertical-align":a.Em(-u.d),"background-color":"green"}}]]);if(t.nextSibling){t.parentNode.insertBefore(s,t.nextSibling)}else{t.parentNode.appendChild(s)}},CHTMLnotEmpty:function(s){while(s&&s.data.length<2&&(s.type==="mrow"||s.type==="texatom")){s=s.data[0]}return !!s}},{CHTMLautoload:function(){this.constructor.Augment({toCommonHTML:d.mbase.CHTMLautoloadFail});var s=a.autoloadDir+"/"+this.type+".js";f.RestartAfter(o.Require(s))},CHTMLautoloadFail:function(){throw Error("CommonHTML can't autoload '"+this.type+"'")},CHTMLautoloadList:{},CHTMLautoloadFile:function(s){if(d.mbase.CHTMLautoloadList.hasOwnProperty(s)){throw Error("CommonHTML can't autoload file '"+s+"'")}d.mbase.CHTMLautoloadList[s]=true;var t=a.autoloadDir+"/"+s+".js";f.RestartAfter(o.Require(t))},CHTMLstretchV:function(s,t){this.Core().CHTMLstretchV(s,t);this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.chars.Augment({toCommonHTML:function(t,s){this.CHTML=null;if(s==null){s={}}var u=this.toString();if(s.remap){u=s.remap(u,s.remapchars)}this.CHTMLhandleText(t,u,s.variant||this.parent.CHTMLvariant)}});d.entity.Augment({toCommonHTML:function(t,s){if(s==null){s={}}var u=this.toString();if(s.remapchars){u=s.remap(u,s.remapchars)}this.CHTMLhandleText(t,u,s.variant||this.parent.CHTMLvariant)}});d.math.Augment({toCommonHTML:function(x){x=this.CHTMLdefaultNode(x);if(this.CHTML.w<0){x.parentNode.style.width="0px";x.parentNode.style.marginRight=a.Em(this.CHTML.w)}var v=this.Get("alttext");if(v&&!x.getAttribute("aria-label")){x.setAttribute("aria-label",v)}if(this.CHTML.pwidth){x.parentNode.style.minWidth=this.CHTML.mwidth||a.Em(this.CHTML.w);x.parentNode.className="mjx-full-width "+x.parentNode.className;x.style.width=this.CHTML.pwidth}else{if(!this.isMultiline&&this.Get("display")==="block"){var u=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(u.indentalignfirst!==d.INDENTALIGN.INDENTALIGN){u.indentalign=u.indentalignfirst}if(u.indentalign===d.INDENTALIGN.AUTO){u.indentalign=r.displayAlign}if(u.indentshiftfirst!==d.INDENTSHIFT.INDENTSHIFT){u.indentshift=u.indentshiftfirst}if(u.indentshift==="auto"){u.indentshift="0"}var t=this.CHTMLlength2em(u.indentshift,a.cwidth);if(r.displayIndent!=="0"){var s=this.CHTMLlength2em(r.displayIndent,a.cwidth);t+=(u.indentalign===d.INDENTALIGN.RIGHT?-s:s)}var w=x.parentNode.parentNode.style;x.parentNode.style.textAlign=w.textAlign=u.indentalign;if(t){t*=a.em/a.outerEm;f.Insert(w,({left:{marginLeft:a.Em(t)},right:{marginRight:a.Em(-t)},center:{marginLeft:a.Em(t),marginRight:a.Em(-t)}})[u.indentalign])}}}return x}});d.mi.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&!a.isChar(t)){delete u.skew}if(u.r>u.w&&a.isChar(t)&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mn.Augment({CHTMLremapMinus:function(s){return s.replace(/^-/,"\u2212")},toCommonHTML:function(s){s=this.CHTMLdefaultNode(s,{childOptions:{remap:this.CHTMLremapMinus}});var u=this.CHTML,t=this.data.join("");if(u.skew!=null&&!a.isChar(t)){delete u.skew}if(u.r>u.w&&a.isChar(t)&&!this.CHTMLvariant.noIC){u.ic=u.r-u.w;u.w=u.r;s.lastChild.style.paddingRight=a.Em(u.ic)}return s}});d.mo.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLgetVariant();this.CHTMLhandleScale(v);a.BBOX.empty(this.CHTML);var t=this.getValues("displaystyle","largeop");t.variant=this.CHTMLvariant;t.text=this.data.join("");if(t.text==""){if(this.fence){v.style.width=a.Em(a.TEX.nulldelimiterspace)}}else{this.CHTMLadjustAccent(t);this.CHTMLadjustVariant(t);for(var u=0,s=this.data.length;u0){if(!this.hasValue("lspace")){t.lspace=0.15}if(!this.hasValue("rspace")){t.rspace=0.15}}var s=this,u=this.Parent();while(u&&u.isEmbellished()&&u.Core()===s){s=u;u=u.Parent();v=s.CHTMLnodeElement()}if(t.lspace){v.style.paddingLeft=a.Em(t.lspace)}if(t.rspace){v.style.paddingRight=a.Em(t.rspace)}this.CHTML.L=t.lspace;this.CHTML.R=t.rspace}else{this.SUPER(arguments).CHTMLhandleSpace.apply(this,arguments)}},CHTMLadjustAccent:function(u){var t=this.CoreParent();u.parent=t;if(a.isChar(u.text)&&t&&t.isa(d.munderover)){var v=t.data[t.over],s=t.data[t.under];if(v&&this===v.CoreMO()&&t.Get("accent")){u.remapchars=a.FONTDATA.REMAPACCENT}else{if(s&&this===s.CoreMO()&&t.Get("accentunder")){u.remapchars=a.FONTDATA.REMAPACCENTUNDER}}}},CHTMLadjustVariant:function(t){var s=t.parent,u=(s&&s.isa(d.msubsup)&&this!==s.data[s.base]);if(t.largeop){t.mathvariant=(t.displaystyle?"-largeOp":"-smallOp")}if(u){t.remapchars=this.remapChars;if(t.text.match(/['`"\u00B4\u2032-\u2037\u2057]/)){t.mathvariant="-TeX-variant"}}},CHTMLfixCombiningChar:function(s){s=s.firstChild;var t=a.Element("mjx-box",{style:{width:".25em","margin-left":"-.25em"}});s.insertBefore(t,s.firstChild)},CHTMLcenterOp:function(s){var u=this.CHTML;var t=(u.h-u.d)/2-a.TEX.axis_height;if(Math.abs(t)>0.001){s.style.verticalAlign=a.Em(-t)}u.h-=t;u.d+=t;if(u.r>u.w){u.ic=u.r-u.w;u.w=u.r;s.style.paddingRight=a.Em(u.ic)}},CHTMLcanStretch:function(w,u,v){if(!this.Get("stretchy")){return false}var x=this.data.join("");if(!a.isChar(x)){return false}var t={text:x};this.CHTMLadjustAccent(t);if(t.remapchars){x=t.remapchars[x]||x}x=a.FONTDATA.DELIMITERS[x.charCodeAt(0)];var s=(x&&x.dir===w.substr(0,1));if(s){s=(this.CHTML.h!==u||this.CHTML.d!==v||!!this.Get("minsize",true)||!!this.Get("maxsize",true));if(s){this.CHTML.stretch=true}}return s},CHTMLstretchV:function(v,y){var w=this.CHTMLnodeElement(),x=this.CHTML;var t=this.getValues("symmetric","maxsize","minsize");var u,s=a.TEX.axis_height;if(t.symmetric){u=2*Math.max(v-s,y+s)}else{u=v+y}t.maxsize=this.CHTMLlength2em(t.maxsize,x.h+x.d);t.minsize=this.CHTMLlength2em(t.minsize,x.h+x.d);u=Math.max(t.minsize,Math.min(t.maxsize,u));if(u!==x.sH){if(u!=t.minsize){u=[Math.max(u*a.TEX.delimiterfactor/1000,u-a.TEX.delimitershortfall),u]}while(w.firstChild){w.removeChild(w.firstChild)}this.CHTML=x=a.createDelimiter(w,this.data.join("").charCodeAt(0),u,x);x.sH=(u instanceof Array?u[1]:u);if(t.symmetric){u=(x.h+x.d)/2+s}else{u=(x.h+x.d)*v/(v+y)}u-=x.h;if(Math.abs(u)>0.05){w.style.verticalAlign=a.Em(u);x.h+=u;x.d-=u;x.t+=u;x.b-=u}}return this.CHTML},CHTMLstretchH:function(u,s){var v=this.CHTML;var t=this.getValues("maxsize","minsize","mathvariant","fontweight");if((t.fontweight==="bold"||(this.removedStyles||{}).fontWeight==="bold"||parseInt(t.fontweight)>=600)&&!this.Get("mathvariant",true)){t.mathvariant=d.VARIANT.BOLD}t.maxsize=this.CHTMLlength2em(t.maxsize,v.w);t.minsize=this.CHTMLlength2em(t.minsize,v.w);s=Math.max(t.minsize,Math.min(t.maxsize,s));if(s!==v.sW){while(u.firstChild){u.removeChild(u.firstChild)}this.CHTML=v=a.createDelimiter(u,this.data.join("").charCodeAt(0),s,v,t.mathvariant);v.sW=s}return this.CHTML}});d.mtext.Augment({CHTMLgetVariant:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){var u=(a.config.scale/100)/a.scale;var t={cache:{},fonts:[],className:"MJXc-font-inherit",rscale:u,style:{"font-size":a.Percent(u)}};var s=this.Get("mathvariant");if(s.match(/bold/)){t.style["font-weight"]="bold"}if(s.match(/italic|-tex-mathit/)){t.style["font-style"]="italic"}if(s==="monospace"){t.className+=" MJXc-monospace-font"}if(s==="double-struck"){t.className+=" MJXc-double-struck-font"}if(s.match(/fraktur/)){t.className+=" MJXc-fraktur-font"}if(s.match(/sans-serif/)){t.className+=" MJXc-sans-serif-font"}if(s.match(/script/)){t.className+=" MJXc-script-font"}this.CHTMLvariant=t}else{this.SUPER(arguments).CHTMLgetVariant.call(this)}}});d.merror.Augment({toCommonHTML:function(s){s=this.CHTMLdefaultNode(s);var t=this.CHTML;t.rescale(0.9);t.h+=3/a.em;if(t.h>t.t){t.t=t.h}t.d+=3/a.em;if(t.d>t.b){t.b=t.d}t.w+=8/a.em;t.r=t.w;t.l=0;return s}});d.mspace.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);var t=this.getValues("height","depth","width");var s=this.CHTMLlength2em(t.width),u=this.CHTMLlength2em(t.height),y=this.CHTMLlength2em(t.depth);var x=this.CHTML;x.w=x.r=s;x.h=x.t=u;x.d=x.b=y;x.l=0;if(s<0){v.style.marginRight=a.Em(s);s=0}v.style.width=a.Em(s);v.style.height=a.Em(Math.max(0,u+y));if(y){v.style.verticalAlign=a.Em(-y)}this.CHTMLhandleBBox(v);this.CHTMLhandleColor(v);return v}});d.mpadded.Augment({toCommonHTML:function(t,F){var s;if(F&&F.stretch){t=t.firstChild;s=t.firstChild}else{t=this.CHTMLdefaultNode(t,{childNodes:"mjx-box",forceChild:true});s=t.firstChild;t=a.addElement(t,"mjx-block");t.appendChild(s);a.addElement(t,"mjx-strut")}var z=this.CHTMLbboxFor(0);var D=this.getValues("width","height","depth","lspace","voffset");var B=0,A=0,C=z.w,u=z.h,v=z.d;s.style.width=0;s.style.margin=a.Em(-u)+" 0 "+a.Em(-v);if(D.width!==""){C=this.CHTMLdimen(D.width,"w",C,0)}if(D.height!==""){u=this.CHTMLdimen(D.height,"h",u,0)}if(D.depth!==""){v=this.CHTMLdimen(D.depth,"d",v,0)}if(D.voffset!==""){A=this.CHTMLdimen(D.voffset);if(A){s.style.position="relative";s.style.top=a.Em(-A)}}if(D.lspace!==""){B=this.CHTMLdimen(D.lspace);if(B){s.style.position="relative";s.style.left=a.Em(B)}}t.style.width=0;t.style.marginTop=a.Em(u-k);t.style.padding="0 "+a.Em(C)+" "+a.Em(v)+" 0";var E=a.BBOX({w:C,h:u,d:v,l:0,r:C,t:u,b:v,scale:this.CHTML.scale,rscale:this.CHTML.rscale});E.combine(z,B,A);E.w=C;E.h=u;E.d=v;this.CHTML=E;return t.parentNode},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLdimen:function(w,y,x,s){if(s==null){s=-i}w=String(w);var t=w.match(/width|height|depth/);var u=(t?this.CHTML[t[0].charAt(0)]:(y?this.CHTML[y]:0));var v=(this.CHTMLlength2em(w,u)||0);if(w.match(/^[-+]/)&&x!=null){v+=x}if(s!=null){v=Math.max(s,v)}return v}});d.munderover.Augment({toCommonHTML:function(w,G){var E=this.getValues("displaystyle","accent","accentunder","align");var u=this.data[this.base];if(!E.displaystyle&&u!=null&&(u.movablelimits||u.CoreMO().Get("movablelimits"))){return d.msubsup.prototype.toCommonHTML.call(this,w,t)}var B,z,s=[],t=false;if(G&&G.stretch){if(this.data[this.base]){u=a.getNode(w,"mjx-op")}if(this.data[this.under]){B=a.getNode(w,"mjx-under")}if(this.data[this.over]){z=a.getNode(w,"mjx-over")}s[0]=u;s[1]=B||z;s[2]=z;t=true}else{var y=["mjx-op","mjx-under","mjx-over"];if(this.over===1){y[1]=y[2]}w=this.CHTMLdefaultNode(w,{childNodes:y,noBBox:true,forceChild:true,minChildren:2});s[0]=u=w.removeChild(w.firstChild);s[1]=B=z=w.removeChild(w.firstChild);if(w.firstChild){s[2]=z=w.removeChild(w.firstChild)}}var x=[],v=this.CHTMLgetBBoxes(x,s,E);var F=x[this.base],C=this.CHTML;C.w=v;C.h=F.h;C.d=F.d;if(F.h<0.35){u.style.marginTop=a.Em(F.h-0.35)}if(E.accent&&F.hu){u=s}}if(u===-i){u=s}for(y=0;yD.w){D.skew+=(D.w-(A.x+u*A.w))/2}}}else{y=a.TEX.big_op_spacing1;x=a.TEX.big_op_spacing3;v=Math.max(y,x-Math.max(0,u*A.d))}A.x+=E/2;A.y=D.h+v+w+u*A.d;if(v){B.style.paddingBottom=a.Em(v/u)}if(w){B.style.paddingTop=a.Em(w/u)}return C},CHTMLaddUnderscript:function(B,z,E,D,t,A,s){var C=this.CHTML;var y,x,w=a.TEX.big_op_spacing5,v;var F=z[this.under],u=F.rscale;if(!s){a.addElement(t,"mjx-itable",{},[["mjx-row",{},[["mjx-cell"]]],["mjx-row"]]);t.firstChild.firstChild.firstChild.appendChild(A);t.firstChild.lastChild.appendChild(B)}if(F.D){F.d=F.D}if(F.d<0){B.firstChild.style.verticalAlign="top";t.firstChild.style.marginBottom=a.Em(F.d)}if(E.accentunder){v=2*a.TEX.rule_thickness;w=0}else{y=a.TEX.big_op_spacing2;x=a.TEX.big_op_spacing4;v=Math.max(y,x-u*F.h)}F.x=-D/2;F.y=-(C.d+v+w+u*F.h);if(v){B.style.paddingTop=a.Em(v/u)}if(w){B.style.paddingBottom=a.Em(w/u)}},CHTMLplaceBoxes:function(s,B,A,E,z){var t=this.CHTML.w,y,v=z.length,x;var D=a.BBOX.zero();D.scale=this.CHTML.scale;D.rscale=this.CHTML.rscale;z[this.base].x=z[this.base].y=0;var F=i;for(y=0;y0){L+=Q;J-=Q}}L=Math.max(L,A.superscriptshift);J=Math.max(J,A.subscriptshift);H.style.paddingRight=a.Em(N/B);z.style.paddingBottom=a.Em(L/w+J/B-W.d-P.h/B*w);z.style.paddingLeft=a.Em(Y/w);z.style.paddingRight=a.Em(N/w);E.style.verticalAlign=a.Em(-J);G.combine(W,I+Y,L);G.combine(P,I,-J)}}G.clean();return S},CHTMLstretchV:d.mbase.CHTMLstretchV,CHTMLstretchH:d.mbase.CHTMLstretchH,CHTMLchildNode:function(u,t){var s=["mjx-base","mjx-sub","mjx-sup"];if(this.over===1){s[1]=s[2]}return a.getNode(u,s[t])}});d.mfrac.Augment({toCommonHTML:function(N){N=this.CHTMLdefaultNode(N,{childNodes:["mjx-numerator","mjx-denominator"],childOptions:{autowidth:true},forceChild:true,noBBox:true,minChildren:2});var x=this.getValues("linethickness","displaystyle","numalign","denomalign","bevelled");var O=x.displaystyle;var D=N.firstChild,w=N.lastChild;var y=a.addElement(N,"mjx-box");y.appendChild(D);y.appendChild(w);N.appendChild(y);if(x.numalign!=="center"){D.style.textAlign=x.numalign}if(x.denomalign!=="center"){w.style.textAlign=x.denomalign}var P=this.CHTMLbboxFor(0),B=this.CHTMLbboxFor(1),C=a.BBOX.empty(this.CHTML),F=P.rscale,z=B.rscale;x.linethickness=Math.max(0,a.thickness2em(x.linethickness||"0",C.scale));var M=a.TEX.min_rule_thickness/a.em,T=a.TEX.axis_height;var J=x.linethickness,L,K,I,G;if(x.bevelled){y.className+=" MJXc-bevelled";var S=(O?0.4:0.15);var E=Math.max(F*(P.h+P.d),z*(B.h+B.d))+2*S;var R=a.Element("mjx-bevel");y.insertBefore(R,w);var s=a.createDelimiter(R,47,E);I=F*(P.d-P.h)/2+T+S;G=z*(B.d-B.h)/2+T-S;if(I){D.style.verticalAlign=a.Em(I/F)}if(G){w.style.verticalAlign=a.Em(G/z)}R.style.marginLeft=R.style.marginRight=a.Em(-S/2);C.combine(P,0,I);C.combine(s,F*P.w-S/2,0);C.combine(B,F*P.w+s.w-S,G);C.clean()}else{y.className+=" MJXc-stacked";if(O){I=a.TEX.num1;G=a.TEX.denom1}else{I=(J===0?a.TEX.num3:a.TEX.num2);G=a.TEX.denom2}if(J===0){L=Math.max((O?7:3)*a.TEX.rule_thickness,2*M);K=(I-P.d*F)-(B.h*z-G);if(KD){s=((A.h+A.d)-(D-G))/2}D=F.h+s+G;var B=this.CHTMLaddRoot(w,A,A.h+A.d-D);v.style.paddingTop=a.Em(s);v.style.borderTop=a.Px(y*F.scale,1)+" solid";E.style.paddingTop=a.Em(2*G-y);F.h+=s+2*G;C.combine(A,B,D-A.h);C.combine(F,B+A.w,0);C.clean();return w},CHTMLaddRoot:function(){return 0},CHTMLhandleBBox:function(s){var t=this.CHTMLbboxFor(0);delete t.pwidth;this.SUPER(arguments).CHTMLhandleBBox.apply(this,arguments)}});d.mroot.Augment({toCommonHTML:d.msqrt.prototype.toCommonHTML,CHTMLhandleBBox:d.msqrt.prototype.CHTMLhandleBBox,CHTMLaddRoot:function(A,u,v){if(!this.data[1]){return}var z=this.CHTML,B=this.data[1].CHTML,x=A.firstChild;var s=B.rscale;var t=this.CHTMLrootHeight(B,u,s)-v;var y=Math.min(B.w,B.r);var C=Math.max(y,u.offset/s);if(t){x.style.verticalAlign=a.Em(t/s)}if(C>y){x.firstChild.style.paddingLeft=a.Em(C-y)}C-=u.offset/s;x.style.width=a.Em(C);z.combine(B,0,t);return C*s},CHTMLrootHeight:function(u,s,t){return 0.45*(s.h+s.d-0.9)+s.offset+Math.max(0,u.d-0.075)}});d.mfenced.Augment({toCommonHTML:function(v){v=this.CHTMLcreateNode(v);this.CHTMLhandleStyle(v);this.CHTMLhandleScale(v);this.CHTMLaddChild(v,"open",{});for(var u=0,s=this.data.length;ua.linebreakWidth)||this.hasNewline()},CHTMLstretchV:function(s,t){this.CHTMLstretchChildV(this.CoreIndex(),s,t);return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLstretchChildH(this.CoreIndex(),s,t);return this.CHTML}});d.TeXAtom.Augment({toCommonHTML:function(x,w){if(!w||!w.stretch){x=this.CHTMLdefaultNode(x)}if(this.texClass===d.TEXCLASS.VCENTER){var s=a.TEX.axis_height,u=this.CHTML;var t=s-(u.h+u.d)/2+u.d;if(Math.abs(t)>0.001){x.style.verticalAlign=a.Em(t);u.h+=t;u.t+=t;u.d-=t;u.b-=t}}return x},CHTMLstretchV:function(s,t){this.CHTMLupdateFrom(this.Core().CHTMLstretchV(s,t));this.toCommonHTML(this.CHTMLnodeElement(),{stretch:true});return this.CHTML},CHTMLstretchH:function(t,s){this.CHTMLupdateFrom(this.CHTMLstretchCoreH(t,s));this.toCommonHTML(t,{stretch:true});return this.CHTML}});d.semantics.Augment({toCommonHTML:function(s){s=this.CHTMLcreateNode(s);if(this.data[0]){this.data[0].toCommonHTML(s);this.CHTMLupdateFrom(this.data[0].CHTML);this.CHTMLhandleBBox(s)}return s}});d.annotation.Augment({toCommonHTML:function(s){return this.CHTMLcreateNode(s)}});d["annotation-xml"].Augment({toCommonHTML:d.mbase.CHTMLautoload});d.ms.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mglyph.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.menclose.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.maction.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mmultiscripts.Augment({toCommonHTML:d.mbase.CHTMLautoload});d.mtable.Augment({toCommonHTML:d.mbase.CHTMLautoload});MathJax.Hub.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});MathJax.Hub.Register.StartupHook("End Cookie",function(){if(f.config.menuSettings.zoom!=="None"){o.Require("[MathJax]/extensions/MathZoom.js")}})})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.CommonHTML); +MathJax.Hub.Register.StartupHook("CommonHTML Jax Ready",function(){var g="2.7.6";var b=MathJax.ElementJax.mml,a=MathJax.Hub.config,e=MathJax.OutputJax.CommonHTML,d=MathJax.Hub.SplitList;var c=-1,f=1000000;b.mtable.Augment({toCommonHTML:function(l){var m={rows:[],labels:[],labeled:false};l=this.CHTMLdefaultNode(l,{noBBox:true,childOptions:m});var k=e.Element("mjx-table");while(l.firstChild){k.appendChild(l.firstChild)}l.appendChild(k);var h=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","width","side","minlabelspacing","useHeight");var j=e.TEX.min_rule_thickness/e.em;m.t=e.Px(j*this.CHTML.scale,1);this.CHTMLgetBoxSizes(h,m);this.CHTMLgetAttributes(h,m);this.CHTMLadjustCells(h,m);if(h.frame){k.style.border=m.t+" "+h.frame}this.CHTMLalignV(h,m,l);this.CHTMLcolumnWidths(h,m,l);this.CHTMLstretchCells(h,m);if(m.labeled){this.CHTMLaddLabels(h,m,l,k)}var i=this.CHTML;i.w=i.r=m.R;i.h=i.t=m.T-m.B;i.d=i.b=m.B;if(!h.frame&&!i.pwidth){l.style.padding="0 "+e.Em(1/6);i.L=i.R=1/6}this.CHTMLhandleSpace(l);this.CHTMLhandleBBox(l);this.CHTMLhandleColor(l);return l},CHTMLgetBoxSizes:function(z,k){var r=e.FONTDATA.lineH*z.useHeight,t=e.FONTDATA.lineD*z.useHeight;var y=[],h=[],l=[],w=-1,q,n;for(q=0,n=this.data.length;qw){w=p}}var u=B.data[p-A].CHTML;if(u.h>y[q]){y[q]=u.h}if(u.d>h[q]){h[q]=u.d}if(u.w>l[p]){l[p]=u.w}}}if(z.equalrows){k.HD=true;var x=Math.max.apply(Math,y);var o=Math.max.apply(Math,h);for(q=0,n=y.length;qt||m<=0){m=null}}else{w.align=this.defaults.align}var p=0,l=0,u=e.TEX.axis_height;if(w.fspace){p+=k.FSPACE[1]}if(w.frame){p+=2/e.em;l+=1/e.em}for(var q=0;q=m){l+=r+s+x[q]}}}if(!m){l=({top:p,bottom:0,center:p/2,baseline:p/2,axis:p/2-u})[w.align]}if(l){o.style.verticalAlign=e.Em(-l)}k.T=p;k.B=l},CHTMLcolumnWidths:function(l,r,A){var I=r.CWIDTH,K=r.CSPACE,u=r.J,F;var G=0,n=false,y=l.width.match(/%$/);var H,B,v;if(l.width!=="auto"&&!y){G=Math.max(0,this.CHTMLlength2em(l.width,r.R));n=true}if(l.equalcolumns){if(y){var z=e.Percent(1/(u+1));for(F=0;F<=u;F++){I[F]=z}}else{v=Math.max.apply(Math,r.W);if(l.width!=="auto"){var q=(l.fspace?r.FSPACE[0]+(l.frame?2/e.em:0):0);for(F=0;F<=u;F++){q+=K[F]}v=Math.max((G-q)/(u+1),v)}v=e.Em(v);for(F=0;F<=u;F++){I[F]=v}}n=true}var E=0;if(l.fspace){E=r.FSPACE[0]}var s=[],D=[],h=[],o=[];var t=r.rows[0];for(F=0;F<=u;F++){o[F]=r.W[F];if(I[F]==="auto"){s.push(F)}else{if(I[F]==="fit"){D.push(F)}else{if(I[F].match(/%$/)){h.push(F)}else{o[F]=this.CHTMLlength2em(I[F],o[F])}}}E+=o[F]+K[F];if(t[F]){t[F].style.width=e.Em(o[F])}}if(l.frame){E+=2/e.em}var C=(D.length>0);if(n){if(y){for(F=0;F<=u;F++){cell=t[F].style;if(I[F]==="auto"&&!C){cell.width=""}else{if(I[F]==="fit"){cell.width=""}else{if(I[F].match(/%$/)){cell.width=I[F]}else{cell.minWidth=cell.maxWidth=cell.width}}}}}else{if(G>E){var k=0;for(H=0,B=h.length;HE&&D.length){var x=(G-E)/D.length;for(H=0,B=D.length;Ht*z){z=t*p}z+=y;z*=t;D+=z}else{D+=p-t*z+n;z-=t*n;z*=-t}}var o=e.addElement(w,"mjx-box",{style:{width:"100%","text-align":q.indentalign}});o.appendChild(B);var C=e.Element("mjx-itable");B.style.display="inline-table";if(!B.style.width){B.style.width="auto"}C.style.verticalAlign="top";B.style.verticalAlign=e.Em(k.T-k.B-k.H[0]);w.style.verticalAlign="";if(z){if(q.indentalign===b.INDENTALIGN.CENTER){B.style.marginLeft=e.Em(z);B.style.marginRight=e.Em(-z)}else{var u="margin"+(q.indentalign===b.INDENTALIGN.RIGHT?"Right":"Left");B.style[u]=e.Em(z)}}if(k.CALIGN[c]==="left"){w.insertBefore(C,o);C.style.marginRight=e.Em(-k.W[c]-y);if(y){C.style.marginLeft=e.Em(y)}}else{w.appendChild(C);C.style.marginLeft=e.Em(-k.W[c]+y)}var l=k.labels,j=0;if(h.fspace){j=k.FSPACE[0]+(h.frame?1/e.em:0)}for(var x=0,v=l.length;x1){h.h*=k;h.d*=k}}}else{h.w=Math.max(h.w,this.CHTMLlength2em(j,h.w))}}}}return l}});MathJax.Hub.Startup.signal.Post("CommonHTML mtable Ready");MathJax.Ajax.loadComplete(e.autoloadDir+"/mtable.js")}); +(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-MML-AM_CHTML-full.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-MML-AM_CHTML.js b/revisions_report_files/mathjax-27/config/TeX-MML-AM_CHTML.js new file mode 100644 index 0000000..e775e55 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-MML-AM_CHTML.js @@ -0,0 +1,69 @@ +/* + * /MathJax/config/TeX-MML-AM_CHTML.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/CommonHTML/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); +MathJax.OutputJax.CommonHTML=MathJax.OutputJax({id:"CommonHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/CommonHTML",extensionDir:MathJax.OutputJax.extensionDir+"/CommonHTML",autoloadDir:MathJax.OutputJax.directory+"/CommonHTML/autoload",fontDir:MathJax.OutputJax.directory+"/CommonHTML/fonts",webfontDir:MathJax.OutputJax.fontDir+"/HTML-CSS",config:{matchFontHeight:true,scale:100,minScaleAdjust:50,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Cambria Math','Arial Unicode MS',serif",EqnChunk:(MathJax.Hub.Browser.isMobile?20:100),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.CommonHTML.Register("jax/mml")}MathJax.OutputJax.CommonHTML.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +MathJax.Extension.asciimath2jax={version:"2.7.6",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g=ab-1){this.lastChild=ae}this.childNodes[ad]=ae;ae.nextSibling=ac.nextSibling;ac.nextSibling=ac.parent=null;return ac},hasChildNodes:function(ab){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var ab=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ac=ab.apply(this,arguments)||this;ac.childNodes=ac.data;ac.nodeName=ac.type;return ac},appendChild:function(af){if(af.parent){af.parent.removeChild(af)}var ad=arguments;if(af.isa(X)){ad=af.childNodes;af.data=af.childNodes=[];af.firstChild=af.lastChild=null}for(var ae=0,ac=ad.length;ae=ac-1){this.lastChild=af}this.SetData(ae,af);af.nextSibling=ad.nextSibling;ad.nextSibling=ad.parent=null;return ad},hasChildNodes:function(ac){return(this.childNodes.length>0)},setAttribute:function(ac,ad){this[ac]=ad}})};var Q={};var e={getElementById:true,createElementNS:function(ac,ab){var ad=g[ab]();if(ab==="mo"&&aa.config.useMathMLspacing){ad.useMMLspacing=128}return ad},createTextNode:function(ab){return g.chars(ab).With({nodeValue:ab})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var C="blue";var o=true;var v=true;var d=".";var f=true;var l=(J.appName.slice(0,9)=="Microsoft");function E(ab){if(l){return e.createElement(ab)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",ab)}}var W="http://www.w3.org/1998/Math/MathML";function P(ab){if(l){return e.createElement("m:"+ab)}else{return e.createElementNS(W,ab)}}function O(ab,ad){var ac;if(l){ac=e.createElement("m:"+ab)}else{ac=e.createElementNS(W,ab)}if(ad){ac.appendChild(ad)}return ac}function u(ab,ac){z.push({input:ab,tag:"mo",output:ac,tex:null,ttype:V});B()}function r(ab){z.push(ab);B()}var D=["\uD835\uDC9C","\u212C","\uD835\uDC9E","\uD835\uDC9F","\u2130","\u2131","\uD835\uDCA2","\u210B","\u2110","\uD835\uDCA5","\uD835\uDCA6","\u2112","\u2133","\uD835\uDCA9","\uD835\uDCAA","\uD835\uDCAB","\uD835\uDCAC","\u211B","\uD835\uDCAE","\uD835\uDCAF","\uD835\uDCB0","\uD835\uDCB1","\uD835\uDCB2","\uD835\uDCB3","\uD835\uDCB4","\uD835\uDCB5","\uD835\uDCB6","\uD835\uDCB7","\uD835\uDCB8","\uD835\uDCB9","\u212F","\uD835\uDCBB","\u210A","\uD835\uDCBD","\uD835\uDCBE","\uD835\uDCBF","\uD835\uDCC0","\uD835\uDCC1","\uD835\uDCC2","\uD835\uDCC3","\u2134","\uD835\uDCC5","\uD835\uDCC6","\uD835\uDCC7","\uD835\uDCC8","\uD835\uDCC9","\uD835\uDCCA","\uD835\uDCCB","\uD835\uDCCC","\uD835\uDCCD","\uD835\uDCCE","\uD835\uDCCF"];var H=["\uD835\uDD04","\uD835\uDD05","\u212D","\uD835\uDD07","\uD835\uDD08","\uD835\uDD09","\uD835\uDD0A","\u210C","\u2111","\uD835\uDD0D","\uD835\uDD0E","\uD835\uDD0F","\uD835\uDD10","\uD835\uDD11","\uD835\uDD12","\uD835\uDD13","\uD835\uDD14","\u211C","\uD835\uDD16","\uD835\uDD17","\uD835\uDD18","\uD835\uDD19","\uD835\uDD1A","\uD835\uDD1B","\uD835\uDD1C","\u2128","\uD835\uDD1E","\uD835\uDD1F","\uD835\uDD20","\uD835\uDD21","\uD835\uDD22","\uD835\uDD23","\uD835\uDD24","\uD835\uDD25","\uD835\uDD26","\uD835\uDD27","\uD835\uDD28","\uD835\uDD29","\uD835\uDD2A","\uD835\uDD2B","\uD835\uDD2C","\uD835\uDD2D","\uD835\uDD2E","\uD835\uDD2F","\uD835\uDD30","\uD835\uDD31","\uD835\uDD32","\uD835\uDD33","\uD835\uDD34","\uD835\uDD35","\uD835\uDD36","\uD835\uDD37"];var w=["\uD835\uDD38","\uD835\uDD39","\u2102","\uD835\uDD3B","\uD835\uDD3C","\uD835\uDD3D","\uD835\uDD3E","\u210D","\uD835\uDD40","\uD835\uDD41","\uD835\uDD42","\uD835\uDD43","\uD835\uDD44","\u2115","\uD835\uDD46","\u2119","\u211A","\u211D","\uD835\uDD4A","\uD835\uDD4B","\uD835\uDD4C","\uD835\uDD4D","\uD835\uDD4E","\uD835\uDD4F","\uD835\uDD50","\u2124","\uD835\uDD52","\uD835\uDD53","\uD835\uDD54","\uD835\uDD55","\uD835\uDD56","\uD835\uDD57","\uD835\uDD58","\uD835\uDD59","\uD835\uDD5A","\uD835\uDD5B","\uD835\uDD5C","\uD835\uDD5D","\uD835\uDD5E","\uD835\uDD5F","\uD835\uDD60","\uD835\uDD61","\uD835\uDD62","\uD835\uDD63","\uD835\uDD64","\uD835\uDD65","\uD835\uDD66","\uD835\uDD67","\uD835\uDD68","\uD835\uDD69","\uD835\uDD6A","\uD835\uDD6B"];var c=0,A=1,U=2,i=3,b=4,h=5,a=6,L=7,V=8,m=9,Y=10,K=15;var k={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:Y};var z=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:c},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:c},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:c},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:c},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:c},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:c},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:c},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:c},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:c},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:c},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:c},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:c},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"lamda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lamda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:c},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:c},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:c},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:c},{input:"phi",tag:"mi",output:f?"\u03D5":"\u03C6",tex:null,ttype:c},{input:"varphi",tag:"mi",output:f?"\u03C6":"\u03D5",tex:null,ttype:c},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:c},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:c},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:c},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:c},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:c},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:c},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:c},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:c},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:c},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:c},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:c},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:c},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:c},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:c},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:c},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:c},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:c},{input:"**",tag:"mo",output:"\u2217",tex:"ast",ttype:c},{input:"***",tag:"mo",output:"\u22C6",tex:"star",ttype:c},{input:"//",tag:"mo",output:"/",tex:null,ttype:c},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:c},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:c},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:c},{input:"|><",tag:"mo",output:"\u22C9",tex:"ltimes",ttype:c},{input:"><|",tag:"mo",output:"\u22CA",tex:"rtimes",ttype:c},{input:"|><|",tag:"mo",output:"\u22C8",tex:"bowtie",ttype:c},{input:"-:",tag:"mo",output:"\u00F7",tex:"div",ttype:c},{input:"divide",tag:"mo",output:"-:",tex:null,ttype:V},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:c},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:c},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:c},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:c},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:L},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:L},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:c},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:L},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:c},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:L},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:c},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:L},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:c},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:L},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:c},{input:":=",tag:"mo",output:":=",tex:null,ttype:c},{input:"lt",tag:"mo",output:"<",tex:null,ttype:c},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:c},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:c},{input:"gt",tag:"mo",output:">",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:"left(",ttype:b},{input:")",tag:"mo",output:")",tex:"right)",ttype:h},{input:"[",tag:"mo",output:"[",tex:"left[",ttype:b},{input:"]",tag:"mo",output:"]",tex:"right]",ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:m},{input:":|:",tag:"mo",output:"|",tex:null,ttype:c},{input:"|:",tag:"mo",output:"|",tex:null,ttype:b},{input:":|",tag:"mo",output:"|",tex:null,ttype:h},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:":'",tag:"mo",output:"\u2235",tex:"because",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"frown",tag:"mo",output:"\u2322",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"Sin",tag:"mo",output:"Sin",tex:null,ttype:A,func:true},{input:"Cos",tag:"mo",output:"Cos",tex:null,ttype:A,func:true},{input:"Tan",tag:"mo",output:"Tan",tex:null,ttype:A,func:true},{input:"Arcsin",tag:"mo",output:"Arcsin",tex:null,ttype:A,func:true},{input:"Arccos",tag:"mo",output:"Arccos",tex:null,ttype:A,func:true},{input:"Arctan",tag:"mo",output:"Arctan",tex:null,ttype:A,func:true},{input:"Sinh",tag:"mo",output:"Sinh",tex:null,ttype:A,func:true},{input:"Cosh",tag:"mo",output:"Cosh",tex:null,ttype:A,func:true},{input:"Tanh",tag:"mo",output:"Tanh",tex:null,ttype:A,func:true},{input:"Cot",tag:"mo",output:"Cot",tex:null,ttype:A,func:true},{input:"Sec",tag:"mo",output:"Sec",tex:null,ttype:A,func:true},{input:"Csc",tag:"mo",output:"Csc",tex:null,ttype:A,func:true},{input:"Log",tag:"mo",output:"Log",tex:null,ttype:A,func:true},{input:"Ln",tag:"mo",output:"Ln",tex:null,ttype:A,func:true},{input:"Abs",tag:"mo",output:"abs",tex:null,ttype:A,notexcopy:true,rewriteleftright:["|","|"]},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:i},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"overset",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"underset",tag:"munder",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:i},{input:"^",tag:"msup",output:"^",tex:null,ttype:i},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"overarc",tag:"mover",output:"\u23DC",tex:"overparen",ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"id",tag:"mrow",ttype:U},{input:"class",tag:"mrow",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},k,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ac,ab){if(ac.input>ab.input){return 1}else{return -1}}var S=[];function n(){var ac;var ab=z.length;for(ac=0;ac>1;if(ac[ab]=S[ab]}s=y;if(af!=""){y=z[ae].ttype;return z[ae]}y=c;ab=1;ak=ah.slice(0,1);var ai=true;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}if(ak==d){ak=ah.slice(ab,ab+1);if("0"<=ak&&ak<="9"){ai=false;ab++;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}}}if((ai&&ab>1)||ab>2){ak=ah.slice(0,ab-1);aj="mn"}else{ab=2;ak=ah.slice(0,1);aj=(("A">ak||ak>"Z")&&("a">ak||ak>"z")?"mo":"mi")}if(ak=="-"&&s==i){y=i;return{input:ak,tag:aj,output:ak,ttype:A,func:true}}return{input:ak,tag:aj,output:ak,ttype:c}}function R(ac){var ab;if(!ac.hasChildNodes()){return}if(ac.firstChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.firstChild.firstChild.nodeValue;if(ab=="("||ab=="["||ab=="{"){ac.removeChild(ac.firstChild)}}if(ac.lastChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.lastChild.firstChild.nodeValue;if(ab==")"||ab=="]"||ab=="}"){ac.removeChild(ac.lastChild)}}}var F,s,y;function G(ai){var ad,ac,al,af,ak,ag=e.createDocumentFragment();ai=p(ai,0);ad=j(ai);if(ad==null||ad.ttype==h&&F>0){return[null,ai]}if(ad.ttype==V){ai=ad.output+p(ai,ad.input.length);ad=j(ai)}switch(ad.ttype){case L:case c:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai];case b:F++;ai=p(ai,ad.input.length);al=q(ai,true);F--;if(typeof ad.invisible=="boolean"&&ad.invisible){ac=O("mrow",al[0])}else{ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0])}return[ac,al[1]];case Y:if(ad!=k){ai=p(ai,ad.input.length)}if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}else{if(ad==k){af=ai.slice(1).indexOf('"')+1}else{af=0}}}}if(af==-1){af=ai.length}ak=ai.slice(1,af);if(ak.charAt(0)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ag.appendChild(O(ad.tag,e.createTextNode(ak)));if(ak.charAt(ak.length-1)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ai=p(ai,af+1);return[O("mrow",ag),ai];case K:case A:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O(ad.tag,e.createTextNode(ad.output)),ai]}if(typeof ad.func=="boolean"&&ad.func){ak=ai.charAt(0);if(ak=="^"||ak=="_"||ak=="/"||ak=="|"||ak==","||(ad.input.length==1&&ad.input.match(/\w/)&&ak!="(")){return[O(ad.tag,e.createTextNode(ad.output)),ai]}else{ac=O("mrow",O(ad.tag,e.createTextNode(ad.output)));ac.appendChild(al[0]);return[ac,al[1]]}}R(al[0]);if(ad.input=="sqrt"){return[O(ad.tag,al[0]),al[1]]}else{if(typeof ad.rewriteleftright!="undefined"){ac=O("mrow",O("mo",e.createTextNode(ad.rewriteleftright[0])));ac.appendChild(al[0]);ac.appendChild(O("mo",e.createTextNode(ad.rewriteleftright[1])));return[ac,al[1]]}else{if(ad.input=="cancel"){ac=O(ad.tag,al[0]);ac.setAttribute("notation","updiagonalstrike");return[ac,al[1]]}else{if(typeof ad.acc=="boolean"&&ad.acc){ac=O(ad.tag,al[0]);var ah=O("mo",e.createTextNode(ad.output));if(ad.input=="vec"&&((al[0].nodeName=="mrow"&&al[0].childNodes.length==1&&al[0].firstChild.firstChild.nodeValue!==null&&al[0].firstChild.firstChild.nodeValue.length==1)||(al[0].firstChild.nodeValue!==null&&al[0].firstChild.nodeValue.length==1))){ah.setAttribute("stretchy",false)}ac.appendChild(ah);return[ac,al[1]]}else{if(!l&&typeof ad.codes!="undefined"){for(af=0;af64&&ak.charCodeAt(ae)<91){aj=aj+ad.codes[ak.charCodeAt(ae)-65]}else{if(ak.charCodeAt(ae)>96&&ak.charCodeAt(ae)<123){aj=aj+ad.codes[ak.charCodeAt(ae)-71]}else{aj=aj+ak.charAt(ae)}}}if(al[0].nodeName=="mi"){al[0]=O("mo").appendChild(e.createTextNode(aj))}else{al[0].replaceChild(O("mo").appendChild(e.createTextNode(aj)),al[0].childNodes[af])}}}}ac=O(ad.tag,al[0]);ac.setAttribute(ad.atname,ad.atval);return[ac,al[1]]}}}}case U:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(al[0]);var ab=G(al[1]);if(ab[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(ab[0]);if(["color","class","id"].indexOf(ad.input)>=0){if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}}}ak=ai.slice(1,af);ac=O(ad.tag,ab[0]);if(ad.input==="color"){ac.setAttribute("mathcolor",ak)}else{if(ad.input==="class"){ac.setAttribute("class",ak)}else{if(ad.input==="id"){ac.setAttribute("id",ak)}}}return[ac,ab[1]]}if(ad.input=="root"||ad.output=="stackrel"){ag.appendChild(ab[0])}ag.appendChild(al[0]);if(ad.input=="frac"){ag.appendChild(ab[0])}return[O(ad.tag,ag),ab[1]];case i:ai=p(ai,ad.input.length);return[O("mo",e.createTextNode(ad.output)),ai];case a:ai=p(ai,ad.input.length);ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);ag.appendChild(O(ad.tag,e.createTextNode(ad.output)));ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);return[O("mrow",ag),ai];case m:F++;ai=p(ai,ad.input.length);al=q(ai,false);F--;ak="";if(al[0].lastChild!=null){ak=al[0].lastChild.firstChild.nodeValue}if(ak=="|"&&ai.charAt(0)!==","){ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0]);return[ac,al[1]]}else{ac=O("mo",e.createTextNode("\u2223"));ac=O("mrow",ac);return[ac,ai]}default:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai]}}function t(ah){var af,ai,ag,ae,ab,ad;ah=p(ah,0);ai=j(ah);ab=G(ah);ae=ab[0];ah=ab[1];af=j(ah);if(af.ttype==i&&af.input!="/"){ah=p(ah,af.input.length);ab=G(ah);if(ab[0]==null){ab[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ab[0])}ah=ab[1];ad=(ai.ttype==L||ai.ttype==K);if(af.input=="_"){ag=j(ah);if(ag.input=="^"){ah=p(ah,ag.input.length);var ac=G(ah);R(ac[0]);ah=ac[1];ae=O((ad?"munderover":"msubsup"),ae);ae.appendChild(ab[0]);ae.appendChild(ac[0]);ae=O("mrow",ae)}else{ae=O((ad?"munder":"msub"),ae);ae.appendChild(ab[0])}}else{if(af.input=="^"&&ad){ae=O("mover",ae);ae.appendChild(ab[0])}else{ae=O(af.tag,ae);ae.appendChild(ab[0])}}if(typeof ai.func!="undefined"&&ai.func){ag=j(ah);if(ag.ttype!=i&&ag.ttype!=h){ab=t(ah);ae=O("mrow",ae);ae.appendChild(ab[0]);ah=ab[1]}}}return[ae,ah]}function q(ak,aj){var ao,al,ag,ar,ah=e.createDocumentFragment();do{ak=p(ak,0);ag=t(ak);al=ag[0];ak=ag[1];ao=j(ak);if(ao.ttype==i&&ao.input=="/"){ak=p(ak,ao.input.length);ag=t(ak);if(ag[0]==null){ag[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ag[0])}ak=ag[1];R(al);al=O(ao.tag,al);al.appendChild(ag[0]);ah.appendChild(al);ao=j(ak)}else{if(al!=undefined){ah.appendChild(al)}}}while((ao.ttype!=h&&(ao.ttype!=m||aj)||F==0)&&ao!=null&&ao.output!="");if(ao.ttype==h||ao.ttype==m){var at=ah.childNodes.length;if(at>0&&ah.childNodes[at-1].nodeName=="mrow"&&ah.childNodes[at-1].lastChild&&ah.childNodes[at-1].lastChild.firstChild){var av=ah.childNodes[at-1].lastChild.firstChild.nodeValue;if(av==")"||av=="]"){var ac=ah.childNodes[at-1].firstChild.firstChild.nodeValue;if(ac=="("&&av==")"&&ao.output!="}"||ac=="["&&av=="]"){var ad=[];var ap=true;var am=ah.childNodes.length;for(ar=0;ap&&ar1){ap=ad[ar].length==ad[ar-2].length}}ap=ap&&(ad.length>1||ad[0].length>0);var af=[];if(ap){var ae,ab,ai,an,au=e.createDocumentFragment();for(ar=0;ar2){ah.removeChild(ah.firstChild);ah.removeChild(ah.firstChild)}au.appendChild(O("mtr",ae))}al=O("mtable",au);al.setAttribute("columnlines",af.join(" "));if(typeof ao.invisible=="boolean"&&ao.invisible){al.setAttribute("columnalign","left")}ah.replaceChild(al,ah.firstChild)}}}}ak=p(ak,ao.input.length);if(typeof ao.invisible!="boolean"||!ao.invisible){al=O("mo",e.createTextNode(ao.output));ah.appendChild(al)}}return[ah,ak]}function M(ad,ac){var ae,ab;F=0;ad=ad.replace(/ /g,"");ad=ad.replace(/>/g,">");ad=ad.replace(/</g,"<");ae=q(ad.replace(/^\s+/g,""),false)[0];ab=O("mstyle",ae);if(C!=""){ab.setAttribute("mathcolor",C)}if(mathfontsize!=""){ab.setAttribute("fontsize",mathfontsize);ab.setAttribute("mathsize",mathfontsize)}if(mathfontfamily!=""){ab.setAttribute("fontfamily",mathfontfamily);ab.setAttribute("mathvariant",mathfontfamily)}if(o){ab.setAttribute("displaystyle","true")}ab=O("math",ab);if(v){ab.setAttribute("title",ad.replace(/\s+/g," "))}return ab}v=false;mathfontfamily="";C="";mathfontsize="";(function(){for(var ac=0,ab=z.length;ac *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-MML-AM_CHTML.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-MML-AM_SVG-full.js b/revisions_report_files/mathjax-27/config/TeX-MML-AM_SVG-full.js new file mode 100644 index 0000000..5b1d7fd --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-MML-AM_SVG-full.js @@ -0,0 +1,73 @@ +/* + * /MathJax/config/TeX-MML-AM_SVG-full.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/SVG/jax.js", + "[MathJax]/jax/output/SVG/autoload/mtable.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +MathJax.Extension.asciimath2jax={version:"2.7.6",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g=ab-1){this.lastChild=ae}this.childNodes[ad]=ae;ae.nextSibling=ac.nextSibling;ac.nextSibling=ac.parent=null;return ac},hasChildNodes:function(ab){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var ab=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ac=ab.apply(this,arguments)||this;ac.childNodes=ac.data;ac.nodeName=ac.type;return ac},appendChild:function(af){if(af.parent){af.parent.removeChild(af)}var ad=arguments;if(af.isa(X)){ad=af.childNodes;af.data=af.childNodes=[];af.firstChild=af.lastChild=null}for(var ae=0,ac=ad.length;ae=ac-1){this.lastChild=af}this.SetData(ae,af);af.nextSibling=ad.nextSibling;ad.nextSibling=ad.parent=null;return ad},hasChildNodes:function(ac){return(this.childNodes.length>0)},setAttribute:function(ac,ad){this[ac]=ad}})};var Q={};var e={getElementById:true,createElementNS:function(ac,ab){var ad=g[ab]();if(ab==="mo"&&aa.config.useMathMLspacing){ad.useMMLspacing=128}return ad},createTextNode:function(ab){return g.chars(ab).With({nodeValue:ab})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var C="blue";var o=true;var v=true;var d=".";var f=true;var l=(J.appName.slice(0,9)=="Microsoft");function E(ab){if(l){return e.createElement(ab)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",ab)}}var W="http://www.w3.org/1998/Math/MathML";function P(ab){if(l){return e.createElement("m:"+ab)}else{return e.createElementNS(W,ab)}}function O(ab,ad){var ac;if(l){ac=e.createElement("m:"+ab)}else{ac=e.createElementNS(W,ab)}if(ad){ac.appendChild(ad)}return ac}function u(ab,ac){z.push({input:ab,tag:"mo",output:ac,tex:null,ttype:V});B()}function r(ab){z.push(ab);B()}var D=["\uD835\uDC9C","\u212C","\uD835\uDC9E","\uD835\uDC9F","\u2130","\u2131","\uD835\uDCA2","\u210B","\u2110","\uD835\uDCA5","\uD835\uDCA6","\u2112","\u2133","\uD835\uDCA9","\uD835\uDCAA","\uD835\uDCAB","\uD835\uDCAC","\u211B","\uD835\uDCAE","\uD835\uDCAF","\uD835\uDCB0","\uD835\uDCB1","\uD835\uDCB2","\uD835\uDCB3","\uD835\uDCB4","\uD835\uDCB5","\uD835\uDCB6","\uD835\uDCB7","\uD835\uDCB8","\uD835\uDCB9","\u212F","\uD835\uDCBB","\u210A","\uD835\uDCBD","\uD835\uDCBE","\uD835\uDCBF","\uD835\uDCC0","\uD835\uDCC1","\uD835\uDCC2","\uD835\uDCC3","\u2134","\uD835\uDCC5","\uD835\uDCC6","\uD835\uDCC7","\uD835\uDCC8","\uD835\uDCC9","\uD835\uDCCA","\uD835\uDCCB","\uD835\uDCCC","\uD835\uDCCD","\uD835\uDCCE","\uD835\uDCCF"];var H=["\uD835\uDD04","\uD835\uDD05","\u212D","\uD835\uDD07","\uD835\uDD08","\uD835\uDD09","\uD835\uDD0A","\u210C","\u2111","\uD835\uDD0D","\uD835\uDD0E","\uD835\uDD0F","\uD835\uDD10","\uD835\uDD11","\uD835\uDD12","\uD835\uDD13","\uD835\uDD14","\u211C","\uD835\uDD16","\uD835\uDD17","\uD835\uDD18","\uD835\uDD19","\uD835\uDD1A","\uD835\uDD1B","\uD835\uDD1C","\u2128","\uD835\uDD1E","\uD835\uDD1F","\uD835\uDD20","\uD835\uDD21","\uD835\uDD22","\uD835\uDD23","\uD835\uDD24","\uD835\uDD25","\uD835\uDD26","\uD835\uDD27","\uD835\uDD28","\uD835\uDD29","\uD835\uDD2A","\uD835\uDD2B","\uD835\uDD2C","\uD835\uDD2D","\uD835\uDD2E","\uD835\uDD2F","\uD835\uDD30","\uD835\uDD31","\uD835\uDD32","\uD835\uDD33","\uD835\uDD34","\uD835\uDD35","\uD835\uDD36","\uD835\uDD37"];var w=["\uD835\uDD38","\uD835\uDD39","\u2102","\uD835\uDD3B","\uD835\uDD3C","\uD835\uDD3D","\uD835\uDD3E","\u210D","\uD835\uDD40","\uD835\uDD41","\uD835\uDD42","\uD835\uDD43","\uD835\uDD44","\u2115","\uD835\uDD46","\u2119","\u211A","\u211D","\uD835\uDD4A","\uD835\uDD4B","\uD835\uDD4C","\uD835\uDD4D","\uD835\uDD4E","\uD835\uDD4F","\uD835\uDD50","\u2124","\uD835\uDD52","\uD835\uDD53","\uD835\uDD54","\uD835\uDD55","\uD835\uDD56","\uD835\uDD57","\uD835\uDD58","\uD835\uDD59","\uD835\uDD5A","\uD835\uDD5B","\uD835\uDD5C","\uD835\uDD5D","\uD835\uDD5E","\uD835\uDD5F","\uD835\uDD60","\uD835\uDD61","\uD835\uDD62","\uD835\uDD63","\uD835\uDD64","\uD835\uDD65","\uD835\uDD66","\uD835\uDD67","\uD835\uDD68","\uD835\uDD69","\uD835\uDD6A","\uD835\uDD6B"];var c=0,A=1,U=2,i=3,b=4,h=5,a=6,L=7,V=8,m=9,Y=10,K=15;var k={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:Y};var z=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:c},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:c},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:c},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:c},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:c},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:c},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:c},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:c},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:c},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:c},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:c},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:c},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"lamda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lamda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:c},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:c},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:c},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:c},{input:"phi",tag:"mi",output:f?"\u03D5":"\u03C6",tex:null,ttype:c},{input:"varphi",tag:"mi",output:f?"\u03C6":"\u03D5",tex:null,ttype:c},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:c},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:c},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:c},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:c},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:c},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:c},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:c},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:c},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:c},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:c},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:c},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:c},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:c},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:c},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:c},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:c},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:c},{input:"**",tag:"mo",output:"\u2217",tex:"ast",ttype:c},{input:"***",tag:"mo",output:"\u22C6",tex:"star",ttype:c},{input:"//",tag:"mo",output:"/",tex:null,ttype:c},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:c},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:c},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:c},{input:"|><",tag:"mo",output:"\u22C9",tex:"ltimes",ttype:c},{input:"><|",tag:"mo",output:"\u22CA",tex:"rtimes",ttype:c},{input:"|><|",tag:"mo",output:"\u22C8",tex:"bowtie",ttype:c},{input:"-:",tag:"mo",output:"\u00F7",tex:"div",ttype:c},{input:"divide",tag:"mo",output:"-:",tex:null,ttype:V},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:c},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:c},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:c},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:c},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:L},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:L},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:c},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:L},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:c},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:L},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:c},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:L},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:c},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:L},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:c},{input:":=",tag:"mo",output:":=",tex:null,ttype:c},{input:"lt",tag:"mo",output:"<",tex:null,ttype:c},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:c},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:c},{input:"gt",tag:"mo",output:">",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:"left(",ttype:b},{input:")",tag:"mo",output:")",tex:"right)",ttype:h},{input:"[",tag:"mo",output:"[",tex:"left[",ttype:b},{input:"]",tag:"mo",output:"]",tex:"right]",ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:m},{input:":|:",tag:"mo",output:"|",tex:null,ttype:c},{input:"|:",tag:"mo",output:"|",tex:null,ttype:b},{input:":|",tag:"mo",output:"|",tex:null,ttype:h},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:":'",tag:"mo",output:"\u2235",tex:"because",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"frown",tag:"mo",output:"\u2322",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"Sin",tag:"mo",output:"Sin",tex:null,ttype:A,func:true},{input:"Cos",tag:"mo",output:"Cos",tex:null,ttype:A,func:true},{input:"Tan",tag:"mo",output:"Tan",tex:null,ttype:A,func:true},{input:"Arcsin",tag:"mo",output:"Arcsin",tex:null,ttype:A,func:true},{input:"Arccos",tag:"mo",output:"Arccos",tex:null,ttype:A,func:true},{input:"Arctan",tag:"mo",output:"Arctan",tex:null,ttype:A,func:true},{input:"Sinh",tag:"mo",output:"Sinh",tex:null,ttype:A,func:true},{input:"Cosh",tag:"mo",output:"Cosh",tex:null,ttype:A,func:true},{input:"Tanh",tag:"mo",output:"Tanh",tex:null,ttype:A,func:true},{input:"Cot",tag:"mo",output:"Cot",tex:null,ttype:A,func:true},{input:"Sec",tag:"mo",output:"Sec",tex:null,ttype:A,func:true},{input:"Csc",tag:"mo",output:"Csc",tex:null,ttype:A,func:true},{input:"Log",tag:"mo",output:"Log",tex:null,ttype:A,func:true},{input:"Ln",tag:"mo",output:"Ln",tex:null,ttype:A,func:true},{input:"Abs",tag:"mo",output:"abs",tex:null,ttype:A,notexcopy:true,rewriteleftright:["|","|"]},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:i},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"overset",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"underset",tag:"munder",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:i},{input:"^",tag:"msup",output:"^",tex:null,ttype:i},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"overarc",tag:"mover",output:"\u23DC",tex:"overparen",ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"id",tag:"mrow",ttype:U},{input:"class",tag:"mrow",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},k,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ac,ab){if(ac.input>ab.input){return 1}else{return -1}}var S=[];function n(){var ac;var ab=z.length;for(ac=0;ac>1;if(ac[ab]=S[ab]}s=y;if(af!=""){y=z[ae].ttype;return z[ae]}y=c;ab=1;ak=ah.slice(0,1);var ai=true;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}if(ak==d){ak=ah.slice(ab,ab+1);if("0"<=ak&&ak<="9"){ai=false;ab++;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}}}if((ai&&ab>1)||ab>2){ak=ah.slice(0,ab-1);aj="mn"}else{ab=2;ak=ah.slice(0,1);aj=(("A">ak||ak>"Z")&&("a">ak||ak>"z")?"mo":"mi")}if(ak=="-"&&s==i){y=i;return{input:ak,tag:aj,output:ak,ttype:A,func:true}}return{input:ak,tag:aj,output:ak,ttype:c}}function R(ac){var ab;if(!ac.hasChildNodes()){return}if(ac.firstChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.firstChild.firstChild.nodeValue;if(ab=="("||ab=="["||ab=="{"){ac.removeChild(ac.firstChild)}}if(ac.lastChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.lastChild.firstChild.nodeValue;if(ab==")"||ab=="]"||ab=="}"){ac.removeChild(ac.lastChild)}}}var F,s,y;function G(ai){var ad,ac,al,af,ak,ag=e.createDocumentFragment();ai=p(ai,0);ad=j(ai);if(ad==null||ad.ttype==h&&F>0){return[null,ai]}if(ad.ttype==V){ai=ad.output+p(ai,ad.input.length);ad=j(ai)}switch(ad.ttype){case L:case c:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai];case b:F++;ai=p(ai,ad.input.length);al=q(ai,true);F--;if(typeof ad.invisible=="boolean"&&ad.invisible){ac=O("mrow",al[0])}else{ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0])}return[ac,al[1]];case Y:if(ad!=k){ai=p(ai,ad.input.length)}if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}else{if(ad==k){af=ai.slice(1).indexOf('"')+1}else{af=0}}}}if(af==-1){af=ai.length}ak=ai.slice(1,af);if(ak.charAt(0)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ag.appendChild(O(ad.tag,e.createTextNode(ak)));if(ak.charAt(ak.length-1)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ai=p(ai,af+1);return[O("mrow",ag),ai];case K:case A:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O(ad.tag,e.createTextNode(ad.output)),ai]}if(typeof ad.func=="boolean"&&ad.func){ak=ai.charAt(0);if(ak=="^"||ak=="_"||ak=="/"||ak=="|"||ak==","||(ad.input.length==1&&ad.input.match(/\w/)&&ak!="(")){return[O(ad.tag,e.createTextNode(ad.output)),ai]}else{ac=O("mrow",O(ad.tag,e.createTextNode(ad.output)));ac.appendChild(al[0]);return[ac,al[1]]}}R(al[0]);if(ad.input=="sqrt"){return[O(ad.tag,al[0]),al[1]]}else{if(typeof ad.rewriteleftright!="undefined"){ac=O("mrow",O("mo",e.createTextNode(ad.rewriteleftright[0])));ac.appendChild(al[0]);ac.appendChild(O("mo",e.createTextNode(ad.rewriteleftright[1])));return[ac,al[1]]}else{if(ad.input=="cancel"){ac=O(ad.tag,al[0]);ac.setAttribute("notation","updiagonalstrike");return[ac,al[1]]}else{if(typeof ad.acc=="boolean"&&ad.acc){ac=O(ad.tag,al[0]);var ah=O("mo",e.createTextNode(ad.output));if(ad.input=="vec"&&((al[0].nodeName=="mrow"&&al[0].childNodes.length==1&&al[0].firstChild.firstChild.nodeValue!==null&&al[0].firstChild.firstChild.nodeValue.length==1)||(al[0].firstChild.nodeValue!==null&&al[0].firstChild.nodeValue.length==1))){ah.setAttribute("stretchy",false)}ac.appendChild(ah);return[ac,al[1]]}else{if(!l&&typeof ad.codes!="undefined"){for(af=0;af64&&ak.charCodeAt(ae)<91){aj=aj+ad.codes[ak.charCodeAt(ae)-65]}else{if(ak.charCodeAt(ae)>96&&ak.charCodeAt(ae)<123){aj=aj+ad.codes[ak.charCodeAt(ae)-71]}else{aj=aj+ak.charAt(ae)}}}if(al[0].nodeName=="mi"){al[0]=O("mo").appendChild(e.createTextNode(aj))}else{al[0].replaceChild(O("mo").appendChild(e.createTextNode(aj)),al[0].childNodes[af])}}}}ac=O(ad.tag,al[0]);ac.setAttribute(ad.atname,ad.atval);return[ac,al[1]]}}}}case U:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(al[0]);var ab=G(al[1]);if(ab[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(ab[0]);if(["color","class","id"].indexOf(ad.input)>=0){if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}}}ak=ai.slice(1,af);ac=O(ad.tag,ab[0]);if(ad.input==="color"){ac.setAttribute("mathcolor",ak)}else{if(ad.input==="class"){ac.setAttribute("class",ak)}else{if(ad.input==="id"){ac.setAttribute("id",ak)}}}return[ac,ab[1]]}if(ad.input=="root"||ad.output=="stackrel"){ag.appendChild(ab[0])}ag.appendChild(al[0]);if(ad.input=="frac"){ag.appendChild(ab[0])}return[O(ad.tag,ag),ab[1]];case i:ai=p(ai,ad.input.length);return[O("mo",e.createTextNode(ad.output)),ai];case a:ai=p(ai,ad.input.length);ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);ag.appendChild(O(ad.tag,e.createTextNode(ad.output)));ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);return[O("mrow",ag),ai];case m:F++;ai=p(ai,ad.input.length);al=q(ai,false);F--;ak="";if(al[0].lastChild!=null){ak=al[0].lastChild.firstChild.nodeValue}if(ak=="|"&&ai.charAt(0)!==","){ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0]);return[ac,al[1]]}else{ac=O("mo",e.createTextNode("\u2223"));ac=O("mrow",ac);return[ac,ai]}default:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai]}}function t(ah){var af,ai,ag,ae,ab,ad;ah=p(ah,0);ai=j(ah);ab=G(ah);ae=ab[0];ah=ab[1];af=j(ah);if(af.ttype==i&&af.input!="/"){ah=p(ah,af.input.length);ab=G(ah);if(ab[0]==null){ab[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ab[0])}ah=ab[1];ad=(ai.ttype==L||ai.ttype==K);if(af.input=="_"){ag=j(ah);if(ag.input=="^"){ah=p(ah,ag.input.length);var ac=G(ah);R(ac[0]);ah=ac[1];ae=O((ad?"munderover":"msubsup"),ae);ae.appendChild(ab[0]);ae.appendChild(ac[0]);ae=O("mrow",ae)}else{ae=O((ad?"munder":"msub"),ae);ae.appendChild(ab[0])}}else{if(af.input=="^"&&ad){ae=O("mover",ae);ae.appendChild(ab[0])}else{ae=O(af.tag,ae);ae.appendChild(ab[0])}}if(typeof ai.func!="undefined"&&ai.func){ag=j(ah);if(ag.ttype!=i&&ag.ttype!=h){ab=t(ah);ae=O("mrow",ae);ae.appendChild(ab[0]);ah=ab[1]}}}return[ae,ah]}function q(ak,aj){var ao,al,ag,ar,ah=e.createDocumentFragment();do{ak=p(ak,0);ag=t(ak);al=ag[0];ak=ag[1];ao=j(ak);if(ao.ttype==i&&ao.input=="/"){ak=p(ak,ao.input.length);ag=t(ak);if(ag[0]==null){ag[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ag[0])}ak=ag[1];R(al);al=O(ao.tag,al);al.appendChild(ag[0]);ah.appendChild(al);ao=j(ak)}else{if(al!=undefined){ah.appendChild(al)}}}while((ao.ttype!=h&&(ao.ttype!=m||aj)||F==0)&&ao!=null&&ao.output!="");if(ao.ttype==h||ao.ttype==m){var at=ah.childNodes.length;if(at>0&&ah.childNodes[at-1].nodeName=="mrow"&&ah.childNodes[at-1].lastChild&&ah.childNodes[at-1].lastChild.firstChild){var av=ah.childNodes[at-1].lastChild.firstChild.nodeValue;if(av==")"||av=="]"){var ac=ah.childNodes[at-1].firstChild.firstChild.nodeValue;if(ac=="("&&av==")"&&ao.output!="}"||ac=="["&&av=="]"){var ad=[];var ap=true;var am=ah.childNodes.length;for(ar=0;ap&&ar1){ap=ad[ar].length==ad[ar-2].length}}ap=ap&&(ad.length>1||ad[0].length>0);var af=[];if(ap){var ae,ab,ai,an,au=e.createDocumentFragment();for(ar=0;ar2){ah.removeChild(ah.firstChild);ah.removeChild(ah.firstChild)}au.appendChild(O("mtr",ae))}al=O("mtable",au);al.setAttribute("columnlines",af.join(" "));if(typeof ao.invisible=="boolean"&&ao.invisible){al.setAttribute("columnalign","left")}ah.replaceChild(al,ah.firstChild)}}}}ak=p(ak,ao.input.length);if(typeof ao.invisible!="boolean"||!ao.invisible){al=O("mo",e.createTextNode(ao.output));ah.appendChild(al)}}return[ah,ak]}function M(ad,ac){var ae,ab;F=0;ad=ad.replace(/ /g,"");ad=ad.replace(/>/g,">");ad=ad.replace(/</g,"<");ae=q(ad.replace(/^\s+/g,""),false)[0];ab=O("mstyle",ae);if(C!=""){ab.setAttribute("mathcolor",C)}if(mathfontsize!=""){ab.setAttribute("fontsize",mathfontsize);ab.setAttribute("mathsize",mathfontsize)}if(mathfontfamily!=""){ab.setAttribute("fontfamily",mathfontfamily);ab.setAttribute("mathvariant",mathfontfamily)}if(o){ab.setAttribute("displaystyle","true")}ab=O("math",ab);if(v){ab.setAttribute("title",ad.replace(/\s+/g," "))}return ab}v=false;mathfontfamily="";C="";mathfontsize="";(function(){for(var ac=0,ab=z.length;ac div":{display:"inline-block"},".mjx-svg-href":{fill:"blue",stroke:"blue"},".MathJax_SVG_Processing":{visibility:"hidden",position:"absolute",top:0,left:0,width:0,height:0,overflow:"hidden",display:"block!important"},".MathJax_SVG_Processed":{display:"none!important"},".MathJax_SVG_test":{"font-style":"normal","font-weight":"normal","font-size":"100%","font-size-adjust":"none","text-indent":0,"text-transform":"none","letter-spacing":"normal","word-spacing":"normal",overflow:"hidden",height:"1px"},".MathJax_SVG_test.mjx-test-display":{display:"table!important"},".MathJax_SVG_test.mjx-test-inline":{display:"inline!important","margin-right":"-1px"},".MathJax_SVG_test.mjx-test-default":{display:"block!important",clear:"both"},".MathJax_SVG_ex_box":{display:"inline-block!important",position:"absolute",overflow:"hidden","min-height":0,"max-height":"none",padding:0,border:0,margin:0,width:"1px",height:"60ex"},".mjx-test-inline .MathJax_SVG_left_box":{display:"inline-block",width:0,"float":"left"},".mjx-test-inline .MathJax_SVG_right_box":{display:"inline-block",width:0,"float":"right"},".mjx-test-display .MathJax_SVG_right_box":{display:"table-cell!important",width:"10000em!important","min-width":0,"max-width":"none",padding:0,border:0,margin:0},"#MathJax_SVG_Tooltip":{position:"absolute",left:0,top:0,width:"auto",height:"auto",display:"none"}}},hideProcessedMath:true,fontNames:["TeX","STIX","STIX-Web","Asana-Math","Gyre-Termes","Gyre-Pagella","Latin-Modern","Neo-Euler"],Config:function(){this.SUPER(arguments).Config.apply(this,arguments);var p=e.config.menuSettings,o=this.config,n=p.font;if(p.scale){o.scale=p.scale}if(n&&n!=="Auto"){n=n.replace(/(Local|Web|Image)$/i,"");n=n.replace(/([a-z])([A-Z])/,"$1-$2");this.fontInUse=n}else{this.fontInUse=o.font||"TeX"}if(this.fontNames.indexOf(this.fontInUse)<0){this.fontInUse="TeX"}this.fontDir+="/"+this.fontInUse;if(!this.require){this.require=[]}this.require.push(this.fontDir+"/fontdata.js");this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){k=MathJax.Extension.MathEvents.Event;c=MathJax.Extension.MathEvents.Touch;f=MathJax.Extension.MathEvents.Hover;this.ContextMenu=k.ContextMenu;this.Mousedown=k.AltContextMenu;this.Mouseover=f.Mouseover;this.Mouseout=f.Mouseout;this.Mousemove=f.Mousemove;this.hiddenDiv=g.Element("div",{style:{visibility:"hidden",overflow:"hidden",position:"absolute",top:0,height:"1px",width:"auto",padding:0,border:0,margin:0,textAlign:"left",textIndent:0,textTransform:"none",lineHeight:"normal",letterSpacing:"normal",wordSpacing:"normal"}});if(!document.body.firstChild){document.body.appendChild(this.hiddenDiv)}else{document.body.insertBefore(this.hiddenDiv,document.body.firstChild)}this.hiddenDiv=g.addElement(this.hiddenDiv,"div",{id:"MathJax_SVG_Hidden"});var n=g.addElement(this.hiddenDiv,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;this.hiddenDiv.removeChild(n);this.textSVG=this.Element("svg");l.GLYPH.defs=this.addElement(this.addElement(this.hiddenDiv.parentNode,"svg"),"defs",{id:"MathJax_SVG_glyphs"});this.TestSpan=g.Element("span",{className:"MathJax_SVG_test"},[["span",{className:"MathJax_SVG_left_box"}],["span",{className:"MathJax_SVG_ex_box"}],["span",{className:"MathJax_SVG_right_box"}]]);return j.Styles(this.config.styles,["InitializeSVG",this])},InitializeSVG:function(){var n=document.body.appendChild(this.TestSpan.cloneNode(true));n.className+=" mjx-test-inline mjx-test-default";this.defaultEx=n.childNodes[1].offsetHeight/60;this.defaultWidth=Math.max(0,n.lastChild.offsetLeft-n.firstChild.offsetLeft-2);document.body.removeChild(n)},preTranslate:function(s){var r=s.jax[this.id],D,z=r.length,y,G,w,C,u,E,p,F,o,v,t=false,A,q=this.config.linebreaks.automatic,x=this.config.linebreaks.width;if(q){t=(x.match(/^\s*(\d+(\.\d*)?%\s*)?container\s*$/)!=null);if(t){x=x.replace(/\s*container\s*/,"")}else{v=this.defaultWidth}if(x===""){x="100%"}}else{v=100000}for(D=0;D=s.SVGlast+s.SVGchunk){this.postTranslate(s,true);s.SVGchunk=Math.floor(s.SVGchunk*this.config.EqnChunkFactor);s.SVGdelay=true}}},postTranslate:function(t,q){var o=t.jax[this.id];if(!this.hideProcessedMath){return}for(var r=t.SVGlast,n=t.SVGeqn;r=55296&&q<56319){v++;q=(((q-55296)<<10)+(D.charCodeAt(v)-56320))+65536;if(this.FONTDATA.RemapPlane1){var y=this.FONTDATA.RemapPlane1(q,u);q=y.n;u=y.variant}}else{o=this.FONTDATA.RANGES;for(p=0,A=o.length;p=o[p].low&&q<=o[p].high){if(o[p].remap&&o[p].remap[q]){q=z+o[p].remap[q]}else{if(o[p].remapOnly){break}q=q-o[p].low+z;if(o[p].add){q+=o[p].add}}if(u["variant"+o[p].offset]){u=this.FONTDATA.VARIANT[u["variant"+o[p].offset]]}break}}}if(u.remap&&u.remap[q]){q=u.remap[q];if(u.remap.variant){u=this.FONTDATA.VARIANT[u.remap.variant]}}else{if(this.FONTDATA.REMAP[q]&&!u.noRemap){q=this.FONTDATA.REMAP[q]}}if(h(q)){u=this.FONTDATA.VARIANT[q[1]];q=q[0]}if(typeof(q)==="string"){D=q+D.substr(v+1);s=D.length;v=-1;continue}r=this.lookupChar(u,q);B=r[q];if(B){if((B[5]&&B[5].space)||(B[5]===""&&B[0]+B[1]===0)){x.w+=B[2]}else{B=[t,r.id+"-"+q.toString(16).toUpperCase()].concat(B);x.Add(l.GLYPH.apply(l,B),x.w,0)}}else{if(this.FONTDATA.DELIMITERS[q]){B=this.createDelimiter(q,0,1,r);x.Add(B,x.w,(this.FONTDATA.DELIMITERS[q].dir==="V"?B.d:0))}else{if(q<=65535){B=String.fromCharCode(q)}else{z=q-65536;B=String.fromCharCode((z>>10)+55296)+String.fromCharCode((z&1023)+56320)}var w=l.TEXT(t*100/a.config.scale,B,{"font-family":u.defaultFamily||a.config.undefinedFamily,"font-style":(u.italic?"italic":""),"font-weight":(u.bold?"bold":"")});if(u.h!=null){w.h=u.h}if(u.d!=null){w.d=u.d}B=l.G();B.Add(w);x.Add(B,x.w,0);e.signal.Post(["SVG Jax - unknown char",q,u])}}}if(a.isChar(D)&&r.skew&&r.skew[q]){x.skew=r.skew[q]*1000}if(x.element.childNodes.length===1&&!x.element.firstChild.getAttribute("x")){x.element=x.element.firstChild;x.removeable=false;x.scale=t}return x},lookupChar:function(r,u){var q,o;if(!r.FONTS){var t=this.FONTDATA.FONTS;var s=(r.fonts||this.FONTDATA.VARIANT.normal.fonts);if(!(s instanceof Array)){s=[s]}if(r.fonts!=s){r.fonts=s}r.FONTS=[];for(q=0,o=s.length;q=55296&&p<56319)},findBlock:function(o,s){if(o.Ranges){for(var r=0,n=o.Ranges.length;r=0;p--){if(o.Ranges[p][2]==q){o.Ranges.splice(p,1)}}this.loadFont(o.directory+"/"+q+".js")}}}},loadFont:function(n){e.RestartAfter(j.Require(this.fontDir+"/"+n))},createDelimiter:function(n,p,s,q){if(!s){s=1}var u=l.G();if(!n){u.Clean();delete u.element;u.w=u.r=this.TeX.nulldelimiterspace*s;return u}if(!(p instanceof Array)){p=[p,p]}var v=p[1];p=p[0];var o={alias:n};while(o.alias){n=o.alias;o=this.FONTDATA.DELIMITERS[n];if(!o){o={HW:[0,this.FONTDATA.VARIANT[i.VARIANT.NORMAL]]}}}if(o.load){e.RestartAfter(j.Require(this.fontDir+"/fontdata-"+o.load+".js"))}for(var t=0,r=o.HW.length;t=p-10-a.config.blacker||(t==r-1&&!o.stretch)){if(o.HW[t][2]){s*=o.HW[t][2]}if(o.HW[t][3]){n=o.HW[t][3]}return this.createChar(s,[n,o.HW[t][1]],q).With({stretched:true})}}if(o.stretch){this["extendDelimiter"+o.dir](u,v,o.stretch,s,q)}return u},createChar:function(u,s,p){var t="",r={fonts:[s[1]],noRemap:true};if(p&&p===i.VARIANT.BOLD){r.fonts=[s[1]+"-bold",s[1]]}if(typeof(s[1])!=="string"){r=s[1]}if(s[0] instanceof Array){for(var q=0,n=s[0].length;qt){var n=this.createChar(q,o.ext,p);var r=(o.mid?2:1),x=(C-t)/r,D=(x+100)/(n.h+n.d);while(r-->0){var v=a.Element("g",{transform:"translate("+n.y+","+(z-D*n.h+50+n.y)+") scale(1,"+D+")"});v.appendChild(n.element.cloneNode(false));u.element.appendChild(v);z-=x;if(o.mid&&r){u.Add(B,0,z-B.h);z-=(B.h+B.d)}}}else{if(o.mid){z+=(t-C)/2;u.Add(B,0,z-B.h);z+=-(B.h+B.d)+(t-C)/2}else{z+=(t-C)}}u.Add(w,0,z-w.h);u.Clean();u.scale=q;u.isMultiChar=true},extendDelimiterH:function(v,q,o,t,p){var r=this.createChar(t,(o.left||o.rep),p);var E=this.createChar(t,(o.right||o.rep),p);v.Add(r,-r.l,0);var D=(r.r-r.l)+(E.r-E.l),B=r.r-r.l;if(o.mid){var C=this.createChar(t,o.mid,p);D+=C.w}if(o.min&&qD){var A=this.createChar(t,o.rep,p),n=o.fuzz||0;var u=(o.mid?2:1),z=(q-D)/u,F=(z+n)/(A.r-A.l);while(u-->0){var y=a.Element("g",{transform:"translate("+(B-n/2-F*A.l+A.x)+","+A.y+") scale("+F+",1)"});y.appendChild(A.element.cloneNode(false));v.element.appendChild(y);B+=z;if(o.mid&&u){v.Add(C,B,0);B+=C.w}}}else{if(o.mid){B-=(D-q)/2;v.Add(C,B,0);B+=C.w-(D-q)/2}else{B-=(D-q)}}v.Add(E,B-E.l,0);v.Clean();v.scale=t;v.isMultiChar=true},MATHSPACE:{veryverythinmathspace:1/18,verythinmathspace:2/18,thinmathspace:3/18,mediummathspace:4/18,thickmathspace:5/18,verythickmathspace:6/18,veryverythickmathspace:7/18,negativeveryverythinmathspace:-1/18,negativeverythinmathspace:-2/18,negativethinmathspace:-3/18,negativemediummathspace:-4/18,negativethickmathspace:-5/18,negativeverythickmathspace:-6/18,negativeveryverythickmathspace:-7/18},TeX:{x_height:430.554,quad:1000,num1:676.508,num2:393.732,num3:443.73,denom1:685.951,denom2:344.841,sup1:412.892,sup2:362.892,sup3:288.888,sub1:150,sub2:247.217,sup_drop:386.108,sub_drop:50,delim1:2390,delim2:1000,axis_height:250,rule_thickness:60,big_op_spacing1:111.111,big_op_spacing2:166.666,big_op_spacing3:200,big_op_spacing4:600,big_op_spacing5:100,scriptspace:100,nulldelimiterspace:120,delimiterfactor:901,delimitershortfall:300,min_rule_thickness:1.25,min_root_space:1.5},BIGDIMEN:10000000,NBSP:"\u00A0"});var l=a.BBOX=MathJax.Object.Subclass({type:"g",removeable:true,Init:function(n){this.h=this.d=-a.BIGDIMEN;this.H=this.D=0;this.w=this.r=0;this.l=a.BIGDIMEN;this.x=this.y=0;this.scale=1;this.n=0;if(this.type){this.element=a.Element(this.type,n)}},With:function(n){return e.Insert(this,n)},Add:function(q,w,v,n,u){if(w){q.x+=w}if(v){q.y+=v}if(q.element){if(q.removeable&&q.element.childNodes.length===1&&q.n===1){var o=q.element.firstChild,s=o.nodeName.toLowerCase();if(s==="use"||s==="rect"){q.element=o;q.scale=q.childScale;var t=q.childX,r=q.childY;q.x+=t;q.y+=r;q.h-=r;q.d+=r;q.H-=r;q.D+=r;q.w-=t;q.r-=t;q.l+=t;q.removeable=false;o.setAttribute("x",Math.floor(q.x/q.scale));o.setAttribute("y",Math.floor(q.y/q.scale))}}if(Math.abs(q.x)<1&&Math.abs(q.y)<1){q.remove=q.removeable}else{s=q.element.nodeName.toLowerCase();if(s==="g"){if(!q.element.firstChild){q.remove=q.removeable}else{q.element.setAttribute("transform","translate("+Math.floor(q.x)+","+Math.floor(q.y)+")")}}else{if(s==="line"||s==="polygon"||s==="path"||s==="a"){var p=q.element.getAttribute("transform")||"";if(p){p=" "+p}p="translate("+Math.floor(q.x)+","+Math.floor(q.y)+")"+p;q.element.setAttribute("transform",p)}else{q.element.setAttribute("x",Math.floor(q.x/q.scale));q.element.setAttribute("y",Math.floor(q.y/q.scale))}}}if(q.remove){this.n+=q.n;while(q.element.firstChild){if(u&&this.element.firstChild){this.element.insertBefore(q.element.firstChild,this.element.firstChild)}else{this.element.appendChild(q.element.firstChild)}}}else{if(u){this.element.insertBefore(q.element,this.element.firstChild)}else{this.element.appendChild(q.element)}}delete q.element}if(q.hasIndent){this.hasIndent=q.hasIndent}if(q.tw!=null){this.tw=q.tw}if(q.d-q.y>this.d){this.d=q.d-q.y;if(this.d>this.D){this.D=this.d}}if(q.y+q.h>this.h){this.h=q.y+q.h;if(this.h>this.H){this.H=this.h}}if(q.D-q.y>this.D){this.D=q.D-q.y}if(q.y+q.H>this.H){this.H=q.y+q.H}if(q.x+q.lthis.r){this.r=q.x+q.r}if(n||q.x+q.w+(q.X||0)>this.w){this.w=q.x+q.w+(q.X||0)}this.childScale=q.scale;this.childX=q.x;this.childY=q.y;this.n++;return q},Align:function(r,s,q,p,o){q=({left:q,center:(this.w-r.w)/2,right:this.w-r.w-q})[s]||0;var n=this.w;this.Add(r,q+(o||0),p);this.w=n},Clean:function(){if(this.h===-a.BIGDIMEN){this.h=this.d=this.l=0}return this}});l.ROW=l.Subclass({Init:function(){this.SUPER(arguments).Init.call(this);this.svg=[];this.sh=this.sd=0},Check:function(o){var n=o.toSVG();this.svg.push(n);if(o.SVGcanStretch("Vertical")){n.mml=o}if(n.h+n.y>this.sh){this.sh=n.h+n.y}if(n.d-n.y>this.sd){this.sd=n.d-n.y}},Stretch:function(){for(var q=0,n=this.svg.length;qo.w&&a.isChar(r)&&!q.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},SVGchildSVG:function(n){return(this.data[n]?this.data[n].toSVG():l())},SVGdataStretched:function(o,n,p){this.SVGdata={HW:n,D:p};if(!this.data[o]){return l()}if(p!=null){return this.data[o].SVGstretchV(n,p)}if(n!=null){return this.data[o].SVGstretchH(n)}return this.data[o].toSVG()},SVGsaveData:function(n){if(!this.SVGdata){this.SVGdata={}}this.SVGdata.w=n.w,this.SVGdata.x=n.x;this.SVGdata.h=n.h,this.SVGdata.d=n.d;if(n.y){this.SVGdata.h+=n.y;this.SVGdata.d-=n.y}if(n.X!=null){this.SVGdata.X=n.X}if(n.tw!=null){this.SVGdata.tw=n.tw}if(n.skew){this.SVGdata.skew=n.skew}if(n.ic){this.SVGdata.ic=n.ic}if(this["class"]){n.removeable=false;a.Element(n.element,{"class":this["class"]})}if(this.id){n.removeable=false;a.Element(n.element,{id:this.id})}if(this.href){this.SVGaddHref(n)}if(a.config.addMMLclasses){this.SVGaddClass(n.element,"mjx-svg-"+this.type);n.removeable=false}var o=this.style;if(o&&n.element){n.element.style.cssText=o;if(n.element.style.fontSize){n.element.style.fontSize=""}n.element.style.border=n.element.style.padding="";if(n.removeable){n.removeable=(n.element.style.cssText==="")}}this.SVGaddAttributes(n)},SVGaddClass:function(p,n){var o=p.getAttribute("class");p.setAttribute("class",(o?o+" ":"")+n)},SVGaddAttributes:function(o){if(this.attrNames){var u=this.attrNames,q=i.nocopyAttributes,t=e.config.ignoreMMLattributes;var r=(this.type==="mstyle"?i.math.prototype.defaults:this.defaults);for(var p=0,n=u.length;p600?"bold":"normal")}return o},SVGhandleSpace:function(q){if(this.hasMMLspacing()){if(this.type!=="mo"){return}var p=this.getValues("scriptlevel","lspace","rspace");if(p.scriptlevel<=0||this.hasValue("lspace")||this.hasValue("rspace")){var o=this.SVGgetMu(q);p.lspace=Math.max(0,a.length2em(p.lspace,o));p.rspace=Math.max(0,a.length2em(p.rspace,o));var n=this,r=this.Parent();while(r&&r.isEmbellished()&&r.Core()===n){n=r;r=r.Parent()}if(p.lspace){q.x+=p.lspace}if(p.rspace){q.X=p.rspace}}}else{var s=this.texSpacing();this.SVGgetScale();if(s!==""){q.x+=a.length2em(s,this.scale)*this.mscale}}},SVGhandleColor:function(r){var A=this.getValues("mathcolor","color");if(this.styles&&this.styles.color&&!A.color){A.color=this.styles.color}if(A.color&&!this.mathcolor){A.mathcolor=A.color}if(A.mathcolor){a.Element(r.element,{fill:A.mathcolor,stroke:A.mathcolor});r.removeable=false}var v=(this.styles||{}).border,y=(this.styles||{}).padding,w=((v||{}).left||0),t=((y||{}).left||0),n;A.background=(this.mathbackground||this.background||(this.styles||{}).background||i.COLOR.TRANSPARENT);if(w+t){var o=l();for(n in r){if(r.hasOwnProperty(n)){o[n]=r[n]}}o.x=0;o.y=0;r.element=a.Element("g");r.removeable=true;r.Add(o,w+t,0)}if(y){r.w+=y.right||0;r.h+=y.top||0;r.d+=y.bottom||0}if(v){r.w+=v.right||0;r.h+=v.top||0;r.d+=v.bottom||0}if(A.background!==i.COLOR.TRANSPARENT){var x=r.element.nodeName.toLowerCase();if(x!=="g"&&x!=="svg"){var s=a.Element("g");s.appendChild(r.element);r.element=s;r.removeable=true}r.Add(l.RECT(r.h,r.d,r.w,{fill:A.background,stroke:"none"}),0,0,false,true)}if(v){var z=5;var p={left:["V",r.h+r.d,-z,-r.d],right:["V",r.h+r.d,r.w-v.right+z,-r.d],top:["H",r.w,0,r.h-v.top+z],bottom:["H",r.w,0,-r.d-z]};for(n in p){if(p.hasOwnProperty(n)){if(v[n]){var u=p[n],q=l[u[0]+"LINE"];r.Add(q(u[1],v[n],v[n+"Style"],v[n+"Color"]),u[2],u[3])}}}}},SVGhandleVariant:function(n,p,o){return a.HandleVariant(n,p,o)},SVGgetVariant:function(){var n=this.getValues("mathvariant","fontfamily","fontweight","fontstyle");var o=n.mathvariant;if(this.variantForm){o="-"+a.fontInUse+"-variant"}n.hasVariant=this.Get("mathvariant",true);if(!n.hasVariant){n.family=n.fontfamily;n.weight=n.fontweight;n.style=n.fontstyle}if(this.styles){if(!n.style&&this.styles.fontStyle){n.style=this.styles.fontStyle}if(!n.weight&&this.styles.fontWeight){n.weight=this.styles.fontWeight}if(!n.family&&this.styles.fontFamily){n.family=this.styles.fontFamily}}if(n.family&&!n.hasVariant){if(!n.weight&&n.mathvariant.match(/bold/)){n.weight="bold"}if(!n.style&&n.mathvariant.match(/italic/)){n.style="italic"}o={forceFamily:true,font:{"font-family":n.family}};if(n.style){o.font["font-style"]=n.style}if(n.weight){o.font["font-weight"]=n.weight}return o}if(n.weight==="bold"){o={normal:i.VARIANT.BOLD,italic:i.VARIANT.BOLDITALIC,fraktur:i.VARIANT.BOLDFRAKTUR,script:i.VARIANT.BOLDSCRIPT,"sans-serif":i.VARIANT.BOLDSANSSERIF,"sans-serif-italic":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.weight==="normal"){o={bold:i.VARIANT.normal,"bold-italic":i.VARIANT.ITALIC,"bold-fraktur":i.VARIANT.FRAKTUR,"bold-script":i.VARIANT.SCRIPT,"bold-sans-serif":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.SANSSERIFITALIC}[o]||o}}if(n.style==="italic"){o={normal:i.VARIANT.ITALIC,bold:i.VARIANT.BOLDITALIC,"sans-serif":i.VARIANT.SANSSERIFITALIC,"bold-sans-serif":i.VARIANT.SANSSERIFBOLDITALIC}[o]||o}else{if(n.style==="normal"){o={italic:i.VARIANT.NORMAL,"bold-italic":i.VARIANT.BOLD,"sans-serif-italic":i.VARIANT.SANSSERIF,"sans-serif-bold-italic":i.VARIANT.BOLDSANSSERIF}[o]||o}}if(!(o in a.FONTDATA.VARIANT)){o="normal"}return a.FONTDATA.VARIANT[o]},SVGgetScale:function(o){var p=1;if(this.mscale){p=this.scale}else{var n=this.getValues("scriptlevel","fontsize");n.mathsize=(this.isToken?this:this.Parent()).Get("mathsize");if((this.styles||{}).fontSize&&!n.fontsize){n.fontsize=this.styles.fontSize}if(n.fontsize&&!this.mathsize){n.mathsize=n.fontsize}if(n.scriptlevel!==0){if(n.scriptlevel>2){n.scriptlevel=2}p=Math.pow(this.Get("scriptsizemultiplier"),n.scriptlevel);n.scriptminsize=a.length2em(this.Get("scriptminsize"))/1000;if(p2){o.scriptlevel=2}n=Math.sqrt(Math.pow(o.scriptsizemultiplier,o.scriptlevel))}return n},SVGnotEmpty:function(n){while(n){if((n.type!=="mrow"&&n.type!=="texatom")||n.data.length>1){return true}n=n.data[0]}return false},SVGcanStretch:function(p){var o=false;if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){o=n.SVGcanStretch(p);if(o&&n.forceStretch){this.forceStretch=true}}}return o},SVGstretchV:function(n,o){return this.toSVG(n,o)},SVGstretchH:function(n){return this.toSVG(n)},SVGlineBreaks:function(){return false}},{SVGemptySVG:function(){var n=this.SVG();n.Clean();this.SVGsaveData(n);return n},SVGautoload:function(){this.constructor.Augment({toSVG:i.mbase.SVGautoloadFail});var n=a.autoloadDir+"/"+this.type+".js";e.RestartAfter(j.Require(n))},SVGautoloadFail:function(){throw Error("SVG can't autoload '"+this.type+"'")},SVGautoloadList:{},SVGautoloadFile:function(n){if(i.mbase.SVGautoloadList.hasOwnProperty(n)){throw Error("SVG can't autoload file '"+n+"'")}i.mbase.SVGautoloadList[n]=true;var o=a.autoloadDir+"/"+n+".js";e.RestartAfter(j.Require(o))}});i.chars.Augment({toSVG:function(o,r,n,p){var q=this.data.join("").replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.entity.Augment({toSVG:function(o,r,n,p){var q=this.toString().replace(/[\u2061-\u2064]/g,"");if(n){q=n(q,p)}return this.SVGhandleVariant(o,r,q)}});i.mo.Augment({toSVG:function(o,n){this.SVGgetStyles();var v=this.svg=this.SVG();var r=this.SVGgetScale(v);this.SVGhandleSpace(v);if(this.data.length==0){v.Clean();this.SVGsaveData(v);return v}if(n!=null){return this.SVGstretchV(o,n)}else{if(o!=null){return this.SVG.strechH(o)}}var t=this.SVGgetVariant();var B=this.getValues("largeop","displaystyle");if(B.largeop){t=a.FONTDATA.VARIANT[B.displaystyle?"-largeOp":"-smallOp"]}var A=this.CoreParent(),s=(A&&A.isa(i.msubsup)&&this!==A.data[0]),p=(s?this.remapChars:null);if(a.isChar(this.data.join(""))&&A&&A.isa(i.munderover)&&a.isChar(this.CoreText(A.data[A.base]))){var w=A.data[A.over],z=A.data[A.under];if(w&&this===w.CoreMO()&&A.Get("accent")){p=a.FONTDATA.REMAPACCENT}else{if(z&&this===z.CoreMO()&&A.Get("accentunder")){p=a.FONTDATA.REMAPACCENTUNDER}}}if(s&&this.data.join("").match(/['`"\u00B4\u2032-\u2037\u2057]/)){t=a.FONTDATA.VARIANT["-"+a.fontInUse+"-variant"]}for(var u=0,q=this.data.length;u10*C.w){y+=-C.l}v.Add(C,y,0,true);if(C.skew){v.skew=C.skew}}}v.Clean();if(!a.isChar(this.data.join(""))){delete v.skew}if(B.largeop){v.y=a.TeX.axis_height-(v.h-v.d)/2/r;if(v.r>v.w){v.ic=v.r-v.w;v.w=v.r}}this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGcanStretch:function(r){if(!this.Get("stretchy")){return false}var s=this.data.join("");if(s.length>1){return false}var o=this.CoreParent();if(o&&o.isa(i.munderover)&&a.isChar(this.CoreText(o.data[o.base]))){var q=o.data[o.over],n=o.data[o.under];if(q&&this===q.CoreMO()&&o.Get("accent")){s=a.FONTDATA.REMAPACCENT[s]||s}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){s=a.FONTDATA.REMAPACCENTUNDER[s]||s}}}s=a.FONTDATA.DELIMITERS[s.charCodeAt(0)];var p=(s&&s.dir==r.substr(0,1));if(!p){delete this.svg}this.forceStretch=p&&(this.Get("minsize",true)||this.Get("maxsize",true));return p},SVGstretchV:function(s,t){var p=this.svg||this.toSVG();var o=this.getValues("symmetric","maxsize","minsize");var r=a.TeX.axis_height*p.scale,n=this.SVGgetMu(p),q;if(o.symmetric){q=2*Math.max(s-r,t+r)}else{q=s+t}o.maxsize=a.length2em(o.maxsize,n,p.h+p.d);o.minsize=a.length2em(o.minsize,n,p.h+p.d);q=Math.max(o.minsize,Math.min(o.maxsize,q));if(q!=o.minsize){q=[Math.max(q*a.TeX.delimiterfactor/1000,q-a.TeX.delimitershortfall),q]}p=a.createDelimiter(this.data.join("").charCodeAt(0),q,p.scale);if(o.symmetric){q=(p.h+p.d)/2+r}else{q=(p.h+p.d)*s/(s+t)}p.y=q-p.h;this.SVGhandleSpace(p);this.SVGhandleColor(p);delete this.svg.element;this.SVGsaveData(p);p.stretched=true;return p},SVGstretchH:function(o){var q=this.svg||this.toSVG(),n=this.SVGgetMu(q);var p=this.getValues("maxsize","minsize","mathvariant","fontweight");if((p.fontweight==="bold"||parseInt(p.fontweight)>=600)&&!this.Get("mathvariant",true)){p.mathvariant=i.VARIANT.BOLD}p.maxsize=a.length2em(p.maxsize,n,q.w);p.minsize=a.length2em(p.minsize,n,q.w);o=Math.max(p.minsize,Math.min(p.maxsize,o));q=a.createDelimiter(this.data.join("").charCodeAt(0),o,q.scale,p.mathvariant);this.SVGhandleSpace(q);this.SVGhandleColor(q);delete this.svg.element;this.SVGsaveData(q);q.stretched=true;return q}});i.mn.Augment({SVGremapMinus:function(n){return n.replace(/^-/,"\u2212")},toSVG:function(){this.SVGgetStyles();var r=this.SVGgetVariant();var o=this.SVG();this.SVGgetScale(o);this.SVGhandleSpace(o);var q=this.SVGremapMinus;for(var p=0,n=this.data.length;po.w&&a.isChar(s)&&!r.noIC){o.ic=o.r-o.w;o.w=o.r}this.SVGhandleColor(o);this.SVGsaveData(o);return o},}),i.mtext.Augment({toSVG:function(){if(a.config.mtextFontInherit||this.Parent().type==="merror"){this.SVGgetStyles();var n=this.SVG(),q=this.SVGgetScale(n);this.SVGhandleSpace(n);var o=this.SVGgetVariant(),p={direction:this.Get("dir")};if(o.bold){p["font-weight"]="bold"}if(o.italic){p["font-style"]="italic"}o=this.Get("mathvariant");if(o==="monospace"){p["class"]="MJX-monospace"}else{if(o.match(/sans-serif/)){p["class"]="MJX-sans-serif"}}n.Add(l.TEXT(q*100/a.config.scale,this.data.join(""),p));n.Clean();this.SVGhandleColor(n);this.SVGsaveData(n);return n}else{return this.SUPER(arguments).toSVG.call(this)}}});i.merror.Augment({toSVG:function(p,n){this.SVGgetStyles();var t=this.SVG(),r=a.length2em(this.styles.fontSize||1)/1000;this.SVGhandleSpace(t);var o=(r!==1?{transform:"scale("+a.Fixed(r)+")"}:{});var v=l(o);v.Add(this.SVGchildSVG(0));v.Clean();if(r!==1){v.removeable=false;var u=["w","h","d","l","r","D","H"];for(var s=0,q=u.length;st.H){t.H=t.h}if(t.d>t.D){t.D=t.d}}this.SVGhandleColor(t);this.SVGsaveData(t);return t},SVGlength2em:function(q,t,o,u,n){if(n==null){n=-a.BIGDIMEN}var r=String(t).match(/width|height|depth/);var s=(r?q[r[0].charAt(0)]:(u?q[u]:0));var p=a.length2em(t,o,s/this.mscale)*this.mscale;if(u&&String(t).match(/^\s*[-+]/)){return Math.max(n,q[u]+p)}else{return p}}});i.mrow.Augment({SVG:l.ROW,toSVG:function(q,s){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(s!=null){o.sh=q;o.sd=s}for(var p=0,n=this.data.length;pa.linebreakWidth)||this.hasNewline()},SVGmultiline:function(n){i.mbase.SVGautoloadFile("multiline")},SVGstretchH:function(o){var p=this.SVG();this.SVGhandleSpace(p);for(var q=0,n=this.data.length;qz){n=((u.h+u.d)-(z-A))/2}w=l.RECT(A,0,r.w);z=r.h+n+A;y=this.SVGaddRoot(v,u,y,u.h+u.d-z,s);v.Add(u,y,z-u.h);v.Add(w,y+u.w,z-w.h);v.Add(r,y+u.w,0);v.Clean();v.h+=A;v.H+=A;this.SVGhandleColor(v);this.SVGsaveData(v);return v},SVGaddRoot:function(o,p,n,r,q){return n}});i.mroot.Augment({toSVG:i.msqrt.prototype.toSVG,SVGaddRoot:function(q,o,t,r,n){var v=(o.isMultiChar?0.55:0.65)*o.w;if(this.data[1]){var s=this.data[1].toSVG();s.x=0;var p=this.SVGrootHeight(o.h+o.d,n,s)-r;var u=Math.min(s.w,s.r);t=Math.max(u,v);q.Add(s,t-u,p)}else{v=t}return t-v},SVGrootHeight:function(p,o,n){return 0.45*(p-900*o)+600*o+Math.max(0,n.d-75)}});i.mfenced.Augment({SVG:l.ROW,toSVG:function(){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data.open){o.Check(this.data.open)}if(this.data[0]!=null){o.Check(this.data[0])}for(var p=1,n=this.data.length;pJ){J=N}if(!L[K]&&J>o){o=J}}}if(E==null&&G!=null){o=G}else{if(o==-a.BIGDIMEN){o=J}}for(K=J=0,H=this.data.length;KJ){J=N}}}var C=a.TeX.rule_thickness*this.mscale;var u,r,z,w,s,B,I,M=0;p=q[this.base]||{w:0,h:0,d:0,H:0,D:0,l:0,r:0,y:0,scale:O};if(p.ic){M=1.3*p.ic+0.05}for(K=0,H=this.data.length;KJ){F.skew+=(J-N-u)/2}}}else{z=a.TeX.big_op_spacing1*O;w=a.TeX.big_op_spacing3*O;I=Math.max(z,w-Math.max(0,v.d))}I=Math.max(I,1500/a.em);u+=M/2;r=p.y+p.h+v.d+I;v.h+=s;if(v.h>v.H){v.H=v.h}}else{if(K==this.under){if(A){I=3*C*O;s=0}else{z=a.TeX.big_op_spacing2*O;w=a.TeX.big_op_spacing4*O;I=Math.max(z,w-v.h)}I=Math.max(I,1500/a.em);u-=M/2;r=p.y-(p.d+v.h+I);v.d+=s;if(v.d>v.D){v.D=v.d}}}F.Add(v,u,r)}}F.Clean();this.SVGhandleColor(F);this.SVGsaveData(F);return F}});i.msubsup.Augment({toSVG:function(M,G){this.SVGgetStyles();var I=this.SVG(),Q=this.SVGgetScale(I);this.SVGhandleSpace(I);var K=this.SVGgetMu(I);var y=I.Add(this.SVGdataStretched(this.base,M,G));var w=(this.data[this.sup]||this.data[this.sub]||this).SVGgetScale();var O=a.TeX.x_height*Q,F=a.TeX.scriptspace*Q;var n,z;if(this.SVGnotEmpty(this.data[this.sup])){n=this.data[this.sup].toSVG();n.w+=F;n.r=Math.max(n.w,n.r)}if(this.SVGnotEmpty(this.data[this.sub])){z=this.data[this.sub].toSVG();z.w+=F;z.r=Math.max(z.w,z.r)}var J=a.TeX.sup_drop*w,H=a.TeX.sub_drop*w;var C=y.h+(y.y||0)-J,B=y.d-(y.y||0)+H,P=0,L;if(y.ic){y.w-=y.ic;P=1.3*y.ic+0.05}if(this.data[this.base]&&(this.data[this.base].type==="mi"||this.data[this.base].type==="mo")){if(a.isChar(this.data[this.base].data.join(""))&&y.scale===1&&!y.stretched&&!this.data[this.base].Get("largeop")){C=B=0}}var N=this.getValues("subscriptshift","superscriptshift");N.subscriptshift=(N.subscriptshift===""?0:a.length2em(N.subscriptshift,K));N.superscriptshift=(N.superscriptshift===""?0:a.length2em(N.superscriptshift,K));var A=y.w+y.x;if(!n){if(z){B=Math.max(B,a.TeX.sub1*Q,z.h-(4/5)*O,N.subscriptshift);I.Add(z,A,-B);this.data[this.sub].SVGdata.dy=-B}}else{if(!z){var o=this.getValues("displaystyle","texprimestyle");L=a.TeX[(o.displaystyle?"sup1":(o.texprimestyle?"sup3":"sup2"))];C=Math.max(C,L*Q,n.d+(1/4)*O,N.superscriptshift);I.Add(n,A+P,C);this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=C}else{B=Math.max(B,a.TeX.sub2*Q);var E=a.TeX.rule_thickness*Q;if((C-n.d)-(z.h-B)<3*E){B=3*E-C+n.d+z.h;J=(4/5)*O-(C-n.d);if(J>0){C+=J;B-=J}}I.Add(n,A+P,Math.max(C,N.superscriptshift));I.Add(z,A,-Math.max(B,N.subscriptshift));this.data[this.sup].SVGdata.dx=P;this.data[this.sup].SVGdata.dy=Math.max(C,N.superscriptshift);this.data[this.sub].SVGdata.dy=-Math.max(B,N.subscriptshift)}}I.Clean();this.SVGhandleColor(I);this.SVGsaveData(I);return I}});i.mmultiscripts.Augment({toSVG:i.mbase.SVGautoload});i.mtable.Augment({toSVG:i.mbase.SVGautoload});i["annotation-xml"].Augment({toSVG:i.mbase.SVGautoload});i.math.Augment({SVG:l.Subclass({type:"svg",removeable:false}),toSVG:function(B,p){var F=a.config;if(this.data[0]){this.SVGgetStyles();i.mbase.prototype.displayAlign=e.config.displayAlign;i.mbase.prototype.displayIndent=e.config.displayIndent;if(String(e.config.displayIndent).match(/^0($|[a-z%])/i)){i.mbase.prototype.displayIndent="0"}var v=l.G();v.Add(this.data[0].toSVG(),0,0,true);v.Clean();this.SVGhandleColor(v);a.Element(v.element,{stroke:"currentColor",fill:"currentColor","stroke-width":0,transform:"matrix(1 0 0 -1 0 0)"});v.removeable=false;var x=this.SVG();x.element.setAttribute("xmlns:xlink",m);if(F.useFontCache&&!F.useGlobalCache){x.element.appendChild(l.GLYPH.defs)}x.Add(v);x.Clean();this.SVGsaveData(x);if(!B){x.element=x.element.firstChild;x.element.removeAttribute("transform");x.removable=true;return x}var u=Math.max(-x.l,0),o=Math.max(x.r-x.w,0);var q=x.element.style,A=a.TeX.x_height/a.ex;var E=(Math.ceil(x.H/A)+1)*A+a.HFUZZ,n=(Math.ceil(x.D/A)+1)*A+a.DFUZZ;var z=u+x.w+o;x.element.setAttribute("width",a.Ex(z));x.element.setAttribute("height",a.Ex(E+n));q.verticalAlign=a.Ex(-n);if(u){q.marginLeft=a.Ex(-u)}if(o){q.marginRight=a.Ex(-o)}x.element.setAttribute("viewBox",a.Fixed(-u,1)+" "+a.Fixed(-E,1)+" "+a.Fixed(z,1)+" "+a.Fixed(E+n,1));if(x.H>x.h){q.marginTop=a.Ex(x.h-E)}if(x.D>x.d){q.marginBottom=a.Ex(x.d-n);q.verticalAlign=a.Ex(-x.d)}if(Math.abs(z-a.cwidth)<10){q.maxWidth=a.Fixed(a.cwidth*a.em/1000*a.config.scale)+"px"}var y=this.Get("alttext");if(y&&!x.element.getAttribute("aria-label")){x.element.setAttribute("aria-label",y)}if(!x.element.getAttribute("role")){x.element.setAttribute("role","img")}x.element.setAttribute("focusable","false");B.appendChild(x.element);x.element=null;if(!this.isMultiline&&this.Get("display")==="block"&&!x.hasIndent){var C=this.getValues("indentalignfirst","indentshiftfirst","indentalign","indentshift");if(C.indentalignfirst!==i.INDENTALIGN.INDENTALIGN){C.indentalign=C.indentalignfirst}if(C.indentalign===i.INDENTALIGN.AUTO){C.indentalign=this.displayAlign}if(C.indentshiftfirst!==i.INDENTSHIFT.INDENTSHIFT){C.indentshift=C.indentshiftfirst}if(C.indentshift==="auto"){C.indentshift="0"}var s=a.length2em(C.indentshift,1,a.cwidth);if(this.displayIndent!=="0"){var t=a.length2em(this.displayIndent,1,a.cwidth);s+=(C.indentalign===i.INDENTALIGN.RIGHT?-t:t)}p.style.textAlign=C.indentalign;if(s){e.Insert(q,({left:{marginLeft:a.Ex(s)},right:{marginRight:a.Ex(-s),marginLeft:a.Ex(Math.max(0,s-z))},center:{marginLeft:a.Ex(s),marginRight:a.Ex(-s)}})[C.indentalign])}}}return B}});i.TeXAtom.Augment({toSVG:function(n,q){this.SVGgetStyles();var o=this.SVG();this.SVGhandleSpace(o);if(this.data[0]!=null){var p=this.SVGdataStretched(0,n,q),r=0;if(this.texClass===i.TEXCLASS.VCENTER){r=a.TeX.axis_height-(p.h+p.d)/2+p.d}o.Add(p,0,r);o.ic=p.ic;o.skew=p.skew}this.SVGhandleColor(o);this.SVGsaveData(o);return o}});i.maligngroup.Augment({toSVG:i.mbase.SVGemptySVG});i.malignmark.Augment({toSVG:i.mbase.SVGemptySVG});i.mprescripts.Augment({toSVG:i.mbase.SVGemptySVG});i.none.Augment({toSVG:i.mbase.SVGemptySVG});e.Register.StartupHook("onLoad",function(){setTimeout(MathJax.Callback(["loadComplete",a,"jax.js"]),0)})});e.Browser.Select({Opera:function(n){a.Augment({operaZoomRefresh:true})}});e.Register.StartupHook("End Cookie",function(){if(e.config.menuSettings.zoom!=="None"){j.Require("[MathJax]/extensions/MathZoom.js")}});if(!document.createElementNS){if(!document.namespaces.svg){document.namespaces.add("svg",b)}a.Augment({Element:function(n,o){var p=(typeof(n)==="string"?document.createElement("svg:"+n):n);p.isMathJax=true;if(o){for(var q in o){if(o.hasOwnProperty(q)){p.setAttribute(q,o[q].toString())}}}return p}})}})(MathJax.Ajax,MathJax.Hub,MathJax.HTML,MathJax.OutputJax.SVG); +MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,d=MathJax.OutputJax.SVG,b=d.BBOX;a.mtable.Augment({toSVG:function(aa){this.SVGgetStyles();var o=this.SVG(),ap=this.SVGgetScale(o);if(this.data.length===0){this.SVGsaveData(o);return o}var aN=this.getValues("columnalign","rowalign","columnspacing","rowspacing","columnwidth","equalcolumns","equalrows","columnlines","rowlines","frame","framespacing","align","useHeight","width","side","minlabelspacing");if(aN.width.match(/%$/)){o.width=aN.width=d.Em((d.cwidth/1000)*(parseFloat(aN.width)/100))}var v=this.SVGgetMu(o);var aK=-1;var z=[],I=[],k=[],O=[],K=[],aI,aG,w=-1,aE,u,az,S,an,E,aA;var ac=d.FONTDATA.lineH*ap*aN.useHeight,ag=d.FONTDATA.lineD*ap*aN.useHeight;for(aI=0,aE=this.data.length;aIw){w=aG}K[aG]=b.G();k[aG]=-d.BIGDIMEN}an=S.data[aG-az];O[aI][aG]=an.toSVG();if(an.isEmbellished()){E=an.CoreMO();var aM=E.Get("minsize",true);if(aM){if(E.SVGcanStretch("Vertical")){aA=E.SVGdata.h+E.SVGdata.d;if(aA){aM=d.length2em(aM,v,aA);if(aM*E.SVGdata.h/aA>z[aI]){z[aI]=aM*E.SVGdata.h/aA}if(aM*E.SVGdata.d/aA>I[aI]){I[aI]=aM*E.SVGdata.d/aA}}}else{if(E.SVGcanStretch("Horizontal")){aM=d.length2em(aM,v,E.SVGdata.w);if(aM>k[aG]){k[aG]=aM}}}}}if(O[aI][aG].h>z[aI]){z[aI]=O[aI][aG].h}if(O[aI][aG].d>I[aI]){I[aI]=O[aI][aG].d}if(O[aI][aG].w>k[aG]){k[aG]=O[aI][aG].w}}}var ao=MathJax.Hub.SplitList;var am=ao(aN.columnspacing),T=ao(aN.rowspacing),ai=ao(aN.columnalign),L=ao(aN.rowalign),N=ao(aN.columnlines),h=ao(aN.rowlines),ar=ao(aN.columnwidth),aw=[];for(aI=0,aE=am.length;aIO.length){aD=O.length}}g=0;ay=-(aA+ab)+z[0];for(aI=0,aE=aD-1;aI0.98){aj=X/(V+X);at=V+X}else{at=V/(1-ax)}}else{at=Math.max(V+X,d.length2em(aN.width,v));for(aI=0,aE=Math.min(w,am.length);aI0.01){if(aJ&&at>V){at=(at-V)/aJ;for(aI=0,aE=B.length;aIq+az*ak){R.indentalign=ai[aK];ak=az*(al+az*aO);aH+=al+Math.max(0,ak)}}else{if(ai[aK]===R.indentalign){if(e<0){aO=az*e;e=0}ak+=az*e;if(al>az*ak){ak=az*al}ak+=aO;aH+=az*ak}else{ak-=az*e;if(aH-az*ak+al>d.cwidth){ak=az*(aH+al-d.cwidth);if(az*ak>0){aH=d.cwidth+az*ak;ak=0}}}}var G=o;o=this.SVG();o.hasIndent=true;o.w=o.r=Math.max(aH,d.cwidth);o.Align(K[aK],ai[aK],0,0,aO);o.Align(G,R.indentalign,0,0,ak);o.tw=aH}this.SVGsaveData(o);return o},SVGhandleSpace:function(e){if(!this.hasFrame&&!e.width){e.x=e.X=167}this.SUPER(arguments).SVGhandleSpace.call(this,e)}});a.mtd.Augment({toSVG:function(e,g){var f=this.svg=this.SVG();if(this.data[0]){f.Add(this.SVGdataStretched(0,e,g));f.Clean()}this.SVGhandleColor(f);this.SVGsaveData(f);return f}});MathJax.Hub.Startup.signal.Post("SVG mtable Ready");MathJax.Ajax.loadComplete(d.autoloadDir+"/mtable.js")}); +(function(i,b,e,g){var h;var j,a,d;var f="'Times New Roman',Times,STIXGeneral,serif";var m={".MJXp-script":{"font-size":".8em"},".MJXp-right":{"-webkit-transform-origin":"right","-moz-transform-origin":"right","-ms-transform-origin":"right","-o-transform-origin":"right","transform-origin":"right"},".MJXp-bold":{"font-weight":"bold"},".MJXp-italic":{"font-style":"italic"},".MJXp-scr":{"font-family":"MathJax_Script,"+f},".MJXp-frak":{"font-family":"MathJax_Fraktur,"+f},".MJXp-sf":{"font-family":"MathJax_SansSerif,"+f},".MJXp-cal":{"font-family":"MathJax_Caligraphic,"+f},".MJXp-mono":{"font-family":"MathJax_Typewriter,"+f},".MJXp-largeop":{"font-size":"150%"},".MJXp-largeop.MJXp-int":{"vertical-align":"-.2em"},".MJXp-math":{display:"inline-block","line-height":"1.2","text-indent":"0","font-family":f,"white-space":"nowrap","border-collapse":"collapse"},".MJXp-display":{display:"block","text-align":"center",margin:"1em 0"},".MJXp-math span":{display:"inline-block"},".MJXp-box":{display:"block!important","text-align":"center"},".MJXp-box:after":{content:'" "'},".MJXp-rule":{display:"block!important","margin-top":".1em"},".MJXp-char":{display:"block!important"},".MJXp-mo":{margin:"0 .15em"},".MJXp-mfrac":{margin:"0 .125em","vertical-align":".25em"},".MJXp-denom":{display:"inline-table!important",width:"100%"},".MJXp-denom > *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-MML-AM_SVG-full.js"); diff --git a/revisions_report_files/mathjax-27/config/TeX-MML-AM_SVG.js b/revisions_report_files/mathjax-27/config/TeX-MML-AM_SVG.js new file mode 100644 index 0000000..71ddcd2 --- /dev/null +++ b/revisions_report_files/mathjax-27/config/TeX-MML-AM_SVG.js @@ -0,0 +1,69 @@ +/* + * /MathJax/config/TeX-MML-AM_SVG.js + * + * Copyright (c) 2010-2018 The MathJax Consortium + * + * Part of the MathJax library. + * See http://www.mathjax.org for details. + * + * Licensed under the Apache License, Version 2.0; + * you may not use this file except in compliance with the License. + * + * http://www.apache.org/licenses/LICENSE-2.0 + */ + +MathJax.Ajax.Preloading( + "[MathJax]/jax/input/TeX/config.js", + "[MathJax]/jax/input/MathML/config.js", + "[MathJax]/jax/input/AsciiMath/config.js", + "[MathJax]/jax/output/SVG/config.js", + "[MathJax]/jax/output/PreviewHTML/config.js", + "[MathJax]/extensions/tex2jax.js", + "[MathJax]/extensions/mml2jax.js", + "[MathJax]/extensions/asciimath2jax.js", + "[MathJax]/extensions/MathEvents.js", + "[MathJax]/extensions/MathZoom.js", + "[MathJax]/extensions/MathMenu.js", + "[MathJax]/jax/element/mml/jax.js", + "[MathJax]/extensions/toMathML.js", + "[MathJax]/extensions/TeX/noErrors.js", + "[MathJax]/extensions/TeX/noUndefined.js", + "[MathJax]/jax/input/TeX/jax.js", + "[MathJax]/extensions/TeX/AMSmath.js", + "[MathJax]/extensions/TeX/AMSsymbols.js", + "[MathJax]/jax/input/MathML/jax.js", + "[MathJax]/jax/input/AsciiMath/jax.js", + "[MathJax]/jax/output/PreviewHTML/jax.js", + "[MathJax]/extensions/fast-preview.js", + "[MathJax]/extensions/AssistiveMML.js", + "[MathJax]/extensions/a11y/accessibility-menu.js" +); + +MathJax.Hub.Config({ + extensions: ['[a11y]/accessibility-menu.js'] +}); + +MathJax.InputJax.TeX=MathJax.InputJax({id:"TeX",version:"2.7.6",directory:MathJax.InputJax.directory+"/TeX",extensionDir:MathJax.InputJax.extensionDir+"/TeX",config:{TagSide:"right",TagIndent:"0.8em",MultLineWidth:"85%",equationNumbers:{autoNumber:"none",formatNumber:function(a){return a},formatTag:function(a){return"("+a+")"},formatID:function(a){return"mjx-eqn-"+String(a).replace(/\s/g,"_")},formatURL:function(b,a){return a+"#"+encodeURIComponent(b)},useLabelIds:true}},resetEquationNumbers:function(){}});MathJax.InputJax.TeX.Register("math/tex");MathJax.InputJax.TeX.loadComplete("config.js"); +MathJax.InputJax.MathML=MathJax.InputJax({id:"MathML",version:"2.7.6",directory:MathJax.InputJax.directory+"/MathML",extensionDir:MathJax.InputJax.extensionDir+"/MathML",entityDir:MathJax.InputJax.directory+"/MathML/entities",config:{useMathMLspacing:false}});MathJax.InputJax.MathML.Register("math/mml");MathJax.InputJax.MathML.loadComplete("config.js"); +MathJax.InputJax.AsciiMath=MathJax.InputJax({id:"AsciiMath",version:"2.7.6",directory:MathJax.InputJax.directory+"/AsciiMath",extensionDir:MathJax.InputJax.extensionDir+"/AsciiMath",config:{fixphi:true,useMathMLspacing:true,displaystyle:true,decimalsign:"."}});MathJax.InputJax.AsciiMath.Register("math/asciimath");MathJax.InputJax.AsciiMath.loadComplete("config.js"); +MathJax.OutputJax.SVG=MathJax.OutputJax({id:"SVG",version:"2.7.6",directory:MathJax.OutputJax.directory+"/SVG",extensionDir:MathJax.OutputJax.extensionDir+"/SVG",autoloadDir:MathJax.OutputJax.directory+"/SVG/autoload",fontDir:MathJax.OutputJax.directory+"/SVG/fonts",config:{scale:100,minScaleAdjust:50,font:"TeX",blacker:1,mtextFontInherit:false,undefinedFamily:"STIXGeneral,'Arial Unicode MS',serif",addMMLclasses:false,useFontCache:true,useGlobalCache:true,EqnChunk:(MathJax.Hub.Browser.isMobile?10:50),EqnChunkFactor:1.5,EqnChunkDelay:100,linebreaks:{automatic:false,width:"container"},merrorStyle:{fontSize:"90%",color:"#C00",background:"#FF8",border:"1px solid #C00",padding:"3px"},styles:{".MathJax_SVG_Display":{"text-align":"center",margin:"1em 0em"},".MathJax_SVG .MJX-monospace":{"font-family":"monospace"},".MathJax_SVG .MJX-sans-serif":{"font-family":"sans-serif"},"#MathJax_SVG_Tooltip":{"background-color":"InfoBackground",color:"InfoText",border:"1px solid black","box-shadow":"2px 2px 5px #AAAAAA","-webkit-box-shadow":"2px 2px 5px #AAAAAA","-moz-box-shadow":"2px 2px 5px #AAAAAA","-khtml-box-shadow":"2px 2px 5px #AAAAAA",padding:"3px 4px","z-index":401}}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.SVG.Register("jax/mml")}MathJax.OutputJax.SVG.loadComplete("config.js"); +MathJax.OutputJax.PreviewHTML=MathJax.OutputJax({id:"PreviewHTML",version:"2.7.6",directory:MathJax.OutputJax.directory+"/PreviewHTML",extensionDir:MathJax.OutputJax.extensionDir+"/PreviewHTML",noFastPreview:true,config:{scale:100,minScaleAdjust:50,mtextFontInherit:false,linebreaks:{automatic:false,width:"container"}}});if(!MathJax.Hub.config.delayJaxRegistration){MathJax.OutputJax.PreviewHTML.Register("jax/mml")}MathJax.OutputJax.PreviewHTML.loadComplete("config.js"); +MathJax.Extension.tex2jax={version:"2.7.6",config:{inlineMath:[["\\(","\\)"]],displayMath:[["$$","$$"],["\\[","\\]"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"tex2jax_ignore",processClass:"tex2jax_process",processEscapes:false,processEnvironments:true,processRefs:true,preview:"TeX"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("tex2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}if(typeof(this.config.previewTeX)!=="undefined"&&!this.config.previewTeX){this.config.preview="none"}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],e=[],c,a,b=this.config;this.match={};for(c=0,a=b.inlineMath.length;c0)},patternQuote:function(a){return a.replace(/([\^$(){}+*?\-|\[\]\:\\])/g,"\\$1")},endPattern:function(a){return new RegExp(this.patternQuote(a)+"|\\\\.|[{}]","g")},sortLength:function(d,c){if(d.length!==c.length){return c.length-d.length}return(d==c?0:(d/i,"").replace(/<\?xml:namespace .*?\/>/i,"");b=b.replace(/ /g," ")}MathJax.HTML.setScript(a,b);d.removeChild(e)}else{var c=MathJax.HTML.Element("span");c.appendChild(e);MathJax.HTML.setScript(a,c.innerHTML)}if(this.config.preview!=="none"){this.createPreview(e,a)}},ProcessMathFlattened:function(f){var d=f.parentNode;if(!d||d.className===MathJax.Hub.config.preRemoveClass){return}var b=document.createElement("script");b.type="math/mml";d.insertBefore(b,f);var c="",e,a=f;while(f&&f.nodeName!=="/MATH"){e=f;f=f.nextSibling;c+=this.NodeHTML(e);e.parentNode.removeChild(e)}if(f&&f.nodeName==="/MATH"){f.parentNode.removeChild(f)}b.text=c+"";if(this.config.preview!=="none"){this.createPreview(a,b)}},NodeHTML:function(e){var c,b,a;if(e.nodeName==="#text"){c=this.quoteHTML(e.nodeValue)}else{if(e.nodeName==="#comment"){c=""}else{c="<"+e.nodeName.toLowerCase();for(b=0,a=e.attributes.length;b";if(e.outerHTML!=null&&e.outerHTML.match(/(.<\/[A-Z]+>|\/>)$/)){for(b=0,a=e.childNodes.length;b"}}}return c},OuterHTML:function(d){if(d.nodeName.charAt(0)==="#"){return this.NodeHTML(d)}if(!this.AttributeBug){return d.outerHTML}var c=this.NodeHTML(d);for(var b=0,a=d.childNodes.length;b";return c},quoteHTML:function(a){if(a==null){a=""}return a.replace(/&/g,"&").replace(//g,">").replace(/\"/g,""")},createPreview:function(g,f){var e=this.config.preview;if(e==="none"){return}var i=false;var c=MathJax.Hub.config.preRemoveClass;if((f.previousSibling||{}).className===c){return}if(e==="mathml"){i=true;if(this.MathTagBug){e="alttext"}else{e=g.cloneNode(true)}}if(e==="alttext"||e==="altimg"){i=true;var d=this.filterPreview(g.getAttribute("alttext"));if(e==="alttext"){if(d!=null){e=MathJax.HTML.TextNode(d)}else{e=null}}else{var a=g.getAttribute("altimg");if(a!=null){var b={width:g.getAttribute("altimg-width"),height:g.getAttribute("altimg-height")};e=MathJax.HTML.Element("img",{src:a,alt:d,style:b})}else{e=null}}}if(e){var h;if(i){h=MathJax.HTML.Element("span",{className:c});h.appendChild(e)}else{h=MathJax.HTML.Element("span",{className:c},e)}f.parentNode.insertBefore(h,f)}},filterPreview:function(a){return a},InitBrowser:function(){var b=MathJax.HTML.Element("span",{id:"<",className:"mathjax",innerHTML:"x"});var a=b.outerHTML||"";this.AttributeBug=a!==""&&!(a.match(/id="<"/)&&a.match(/class="mathjax"/)&&a.match(/<\/math>/));this.MathTagBug=b.childNodes.length>1;this.CleanupHTML=MathJax.Hub.Browser.isMSIE}};MathJax.Hub.Register.PreProcessor(["PreProcess",MathJax.Extension.mml2jax],5);MathJax.Ajax.loadComplete("[MathJax]/extensions/mml2jax.js"); +MathJax.Extension.asciimath2jax={version:"2.7.6",config:{delimiters:[["`","`"]],skipTags:["script","noscript","style","textarea","pre","code","annotation","annotation-xml"],ignoreClass:"asciimath2jax_ignore",processClass:"asciimath2jax_process",preview:"AsciiMath"},ignoreTags:{br:(MathJax.Hub.Browser.isMSIE&&document.documentMode<9?"\n":" "),wbr:"","#comment":""},PreProcess:function(a){if(!this.configured){this.config=MathJax.Hub.CombineConfig("asciimath2jax",this.config);if(this.config.Augment){MathJax.Hub.Insert(this,this.config.Augment)}this.configured=true}if(typeof(a)==="string"){a=document.getElementById(a)}if(!a){a=document.body}if(this.createPatterns()){this.scanElement(a,a.nextSibling)}},createPatterns:function(){var d=[],c,a,b=this.config;this.match={};if(b.delimiters.length===0){return false}for(c=0,a=b.delimiters.length;c0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.lastt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;x0||this.Get("scriptlevel")>0)&&g>=0){return""}return this.TEXSPACELENGTH[Math.abs(g)]},TEXSPACELENGTH:["",a.LENGTH.THINMATHSPACE,a.LENGTH.MEDIUMMATHSPACE,a.LENGTH.THICKMATHSPACE],TEXSPACE:[[0,-1,2,3,0,0,0,1],[-1,-1,0,3,0,0,0,1],[2,2,0,0,2,0,0,2],[3,3,0,0,3,0,0,3],[0,0,0,0,0,0,0,0],[0,-1,2,3,0,0,0,1],[1,1,0,1,1,1,1,1],[1,-1,2,3,1,0,1,1]],autoDefault:function(e){return""},isSpacelike:function(){return false},isEmbellished:function(){return false},Core:function(){return this},CoreMO:function(){return this},childIndex:function(g){if(g==null){return}for(var f=0,e=this.data.length;f=55296&&e.charCodeAt(0)<56320)?a.VARIANT.ITALIC:a.VARIANT.NORMAL)}return""},setTeXclass:function(f){this.getPrevClass(f);var e=this.data.join("");if(e.length>1&&e.match(/^[a-z][a-z0-9]*$/i)&&this.texClass===a.TEXCLASS.ORD){this.texClass=a.TEXCLASS.OP;this.autoOP=true}return this}});a.mn=a.mbase.Subclass({type:"mn",isToken:true,texClass:a.TEXCLASS.ORD,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT}});a.mo=a.mbase.Subclass({type:"mo",isToken:true,defaults:{mathvariant:a.INHERIT,mathsize:a.INHERIT,mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,form:a.AUTO,fence:a.AUTO,separator:a.AUTO,lspace:a.AUTO,rspace:a.AUTO,stretchy:a.AUTO,symmetric:a.AUTO,maxsize:a.AUTO,minsize:a.AUTO,largeop:a.AUTO,movablelimits:a.AUTO,accent:a.AUTO,linebreak:a.LINEBREAK.AUTO,lineleading:a.INHERIT,linebreakstyle:a.AUTO,linebreakmultchar:a.INHERIT,indentalign:a.INHERIT,indentshift:a.INHERIT,indenttarget:a.INHERIT,indentalignfirst:a.INHERIT,indentshiftfirst:a.INHERIT,indentalignlast:a.INHERIT,indentshiftlast:a.INHERIT,texClass:a.AUTO},defaultDef:{form:a.FORM.INFIX,fence:false,separator:false,lspace:a.LENGTH.THICKMATHSPACE,rspace:a.LENGTH.THICKMATHSPACE,stretchy:false,symmetric:false,maxsize:a.SIZE.INFINITY,minsize:"0em",largeop:false,movablelimits:false,accent:false,linebreak:a.LINEBREAK.AUTO,lineleading:"1ex",linebreakstyle:"before",indentalign:a.INDENTALIGN.AUTO,indentshift:"0",indenttarget:"",indentalignfirst:a.INDENTALIGN.INDENTALIGN,indentshiftfirst:a.INDENTSHIFT.INDENTSHIFT,indentalignlast:a.INDENTALIGN.INDENTALIGN,indentshiftlast:a.INDENTSHIFT.INDENTSHIFT,texClass:a.TEXCLASS.REL},SPACE_ATTR:{lspace:1,rspace:2},useMMLspacing:3,hasMMLspacing:function(){if(this.useMMLspacing){return true}return this.form&&(this.OPTABLE[this.form]||{})[this.data.join("")]},autoDefault:function(g,n){var l=this.def;if(!l){if(g==="form"){return this.getForm()}var k=this.data.join("");var f=[this.Get("form"),a.FORM.INFIX,a.FORM.POSTFIX,a.FORM.PREFIX];for(var h=0,e=f.length;h=55296&&k<56320){k=(((k-55296)<<10)+(j.charCodeAt(1)-56320))+65536}for(var g=0,e=this.RANGES.length;g=0;e--){if(this.data[0]&&!this.data[e].isSpacelike()){return this.data[e]}}return null},Core:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core]},CoreMO:function(){if(!(this.isEmbellished())||typeof(this.core)==="undefined"){return this}return this.data[this.core].CoreMO()},toString:function(){if(this.inferred){return"["+this.data.join(",")+"]"}return this.SUPER(arguments).toString.call(this)},setTeXclass:function(g){var f,e=this.data.length;if((this.open||this.close)&&(!g||!g.fnOP)){this.getPrevClass(g);g=null;for(f=0;f0){e++}return e},adjustChild_texprimestyle:function(e){if(e==this.den){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.msqrt=a.mbase.Subclass({type:"msqrt",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD,setTeXclass:a.mbase.setSeparateTeXclasses,adjustChild_texprimestyle:function(e){return true}});a.mroot=a.mbase.Subclass({type:"mroot",linebreakContainer:true,texClass:a.TEXCLASS.ORD,adjustChild_displaystyle:function(e){if(e===1){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f===1){e+=2}return e},adjustChild_texprimestyle:function(e){if(e===0){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setSeparateTeXclasses});a.mstyle=a.mbase.Subclass({type:"mstyle",isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,inferRow:true,defaults:{scriptlevel:a.INHERIT,displaystyle:a.INHERIT,scriptsizemultiplier:Math.sqrt(1/2),scriptminsize:"8pt",mathbackground:a.INHERIT,mathcolor:a.INHERIT,dir:a.INHERIT,infixlinebreakstyle:a.LINEBREAKSTYLE.BEFORE,decimalseparator:"."},adjustChild_scriptlevel:function(g){var f=this.scriptlevel;if(f==null){f=this.Get("scriptlevel")}else{if(String(f).match(/^ *[-+]/)){var e=this.Get("scriptlevel",null,true);f=e+parseInt(f)}}return f},inheritFromMe:true,noInherit:{mpadded:{width:true,height:true,depth:true,lspace:true,voffset:true},mtable:{width:true,height:true,depth:true,align:true}},getRemoved:{fontfamily:"fontFamily",fontweight:"fontWeight",fontstyle:"fontStyle",fontsize:"fontSize"},setTeXclass:a.mbase.setChildTeXclass});a.merror=a.mbase.Subclass({type:"merror",inferRow:true,linebreakContainer:true,texClass:a.TEXCLASS.ORD});a.mpadded=a.mbase.Subclass({type:"mpadded",inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,width:"",height:"",depth:"",lspace:0,voffset:0},setTeXclass:a.mbase.setChildTeXclass});a.mphantom=a.mbase.Subclass({type:"mphantom",texClass:a.TEXCLASS.ORD,inferRow:true,isSpacelike:a.mbase.childrenSpacelike,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,setTeXclass:a.mbase.setChildTeXclass});a.mfenced=a.mbase.Subclass({type:"mfenced",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,open:"(",close:")",separators:","},addFakeNodes:function(){var f=this.getValues("open","close","separators");f.open=f.open.replace(/[ \t\n\r]/g,"");f.close=f.close.replace(/[ \t\n\r]/g,"");f.separators=f.separators.replace(/[ \t\n\r]/g,"");if(f.open!==""){this.SetData("open",a.mo(f.open).With({fence:true,form:a.FORM.PREFIX,texClass:a.TEXCLASS.OPEN}))}if(f.separators!==""){while(f.separators.length0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(f){var e=this.Get("scriptlevel");if(f>0){e++}return e},adjustChild_texprimestyle:function(e){if(e===this.sub){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.msub=a.msubsup.Subclass({type:"msub"});a.msup=a.msubsup.Subclass({type:"msup",sub:2,sup:1});a.mmultiscripts=a.msubsup.Subclass({type:"mmultiscripts",adjustChild_texprimestyle:function(e){if(e%2===1){return true}return this.Get("texprimestyle")}});a.mprescripts=a.mbase.Subclass({type:"mprescripts"});a.none=a.mbase.Subclass({type:"none"});a.munderover=a.mbase.Subclass({type:"munderover",base:0,under:1,over:2,sub:1,sup:2,ACCENTS:["","accentunder","accent"],linebreakContainer:true,isEmbellished:a.mbase.childEmbellished,Core:a.mbase.childCore,CoreMO:a.mbase.childCoreMO,defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,accent:a.AUTO,accentunder:a.AUTO,align:a.ALIGN.CENTER,texClass:a.AUTO,subscriptshift:"",superscriptshift:""},autoDefault:function(e){if(e==="texClass"){return(this.isEmbellished()?this.CoreMO().Get(e):a.TEXCLASS.ORD)}if(e==="accent"&&this.data[this.over]){return this.data[this.over].CoreMO().Get("accent")}if(e==="accentunder"&&this.data[this.under]){return this.data[this.under].CoreMO().Get("accent")}return false},adjustChild_displaystyle:function(e){if(e>0){return false}return this.Get("displaystyle")},adjustChild_scriptlevel:function(g){var f=this.Get("scriptlevel");var e=(this.data[this.base]&&!this.Get("displaystyle")&&this.data[this.base].CoreMO().Get("movablelimits"));if(g==this.under&&(e||!this.Get("accentunder"))){f++}if(g==this.over&&(e||!this.Get("accent"))){f++}return f},adjustChild_texprimestyle:function(e){if(e===this.base&&this.data[this.over]){return true}return this.Get("texprimestyle")},setTeXclass:a.mbase.setBaseTeXclasses});a.munder=a.munderover.Subclass({type:"munder"});a.mover=a.munderover.Subclass({type:"mover",over:1,under:2,sup:1,sub:2,ACCENTS:["","accent","accentunder"]});a.mtable=a.mbase.Subclass({type:"mtable",defaults:{mathbackground:a.INHERIT,mathcolor:a.INHERIT,align:a.ALIGN.AXIS,rowalign:a.ALIGN.BASELINE,columnalign:a.ALIGN.CENTER,groupalign:"{left}",alignmentscope:true,columnwidth:a.WIDTH.AUTO,width:a.WIDTH.AUTO,rowspacing:"1ex",columnspacing:".8em",rowlines:a.LINES.NONE,columnlines:a.LINES.NONE,frame:a.LINES.NONE,framespacing:"0.4em 0.5ex",equalrows:false,equalcolumns:false,displaystyle:false,side:a.SIDE.RIGHT,minlabelspacing:"0.8em",texClass:a.TEXCLASS.ORD,useHeight:1},adjustChild_displaystyle:function(){return(this.displaystyle!=null?this.displaystyle:this.defaults.displaystyle)},inheritFromMe:true,noInherit:{mover:{align:true},munder:{align:true},munderover:{align:true},mtable:{align:true,rowalign:true,columnalign:true,groupalign:true,alignmentscope:true,columnwidth:true,width:true,rowspacing:true,columnspacing:true,rowlines:true,columnlines:true,frame:true,framespacing:true,equalrows:true,equalcolumns:true,displaystyle:true,side:true,minlabelspacing:true,texClass:true,useHeight:1}},linebreakContainer:true,Append:function(){for(var f=0,e=arguments.length;f>10)+55296)+String.fromCharCode((e&1023)+56320)}});a.xml=a.mbase.Subclass({type:"xml",Init:function(){this.div=document.createElement("div");return this.SUPER(arguments).Init.apply(this,arguments)},Append:function(){for(var f=0,e=arguments.length;f":d.REL,"?":[1,1,b.CLOSE],"\\":d.ORD,"^":d.ORD11,_:d.ORD11,"|":[2,2,b.ORD,{fence:true,stretchy:true,symmetric:true}],"#":d.ORD,"$":d.ORD,"\u002E":[0,3,b.PUNCT,{separator:true}],"\u02B9":d.ORD,"\u0300":d.ACCENT,"\u0301":d.ACCENT,"\u0303":d.WIDEACCENT,"\u0304":d.ACCENT,"\u0306":d.ACCENT,"\u0307":d.ACCENT,"\u0308":d.ACCENT,"\u030C":d.ACCENT,"\u0332":d.WIDEACCENT,"\u0338":d.REL4,"\u2015":[0,0,b.ORD,{stretchy:true}],"\u2017":[0,0,b.ORD,{stretchy:true}],"\u2020":d.BIN3,"\u2021":d.BIN3,"\u20D7":d.ACCENT,"\u2111":d.ORD,"\u2113":d.ORD,"\u2118":d.ORD,"\u211C":d.ORD,"\u2205":d.ORD,"\u221E":d.ORD,"\u2305":d.BIN3,"\u2306":d.BIN3,"\u2322":d.REL4,"\u2323":d.REL4,"\u2329":d.OPEN,"\u232A":d.CLOSE,"\u23AA":d.ORD,"\u23AF":[0,0,b.ORD,{stretchy:true}],"\u23B0":d.OPEN,"\u23B1":d.CLOSE,"\u2500":d.ORD,"\u25EF":d.BIN3,"\u2660":d.ORD,"\u2661":d.ORD,"\u2662":d.ORD,"\u2663":d.ORD,"\u3008":d.OPEN,"\u3009":d.CLOSE,"\uFE37":d.WIDEACCENT,"\uFE38":d.WIDEACCENT}}},{OPTYPES:d});var c=a.mo.prototype.OPTABLE;c.infix["^"]=d.WIDEREL;c.infix._=d.WIDEREL;c.prefix["\u2223"]=d.OPEN;c.prefix["\u2225"]=d.OPEN;c.postfix["\u2223"]=d.CLOSE;c.postfix["\u2225"]=d.CLOSE})(MathJax.ElementJax.mml);MathJax.ElementJax.mml.loadComplete("jax.js"); +MathJax.Hub.Register.LoadHook("[MathJax]/jax/element/mml/jax.js",function(){var c="2.7.6";var a=MathJax.ElementJax.mml,b=MathJax.Hub.config.menuSettings;a.mbase.Augment({toMathML:function(l){var h=(this.inferred&&this.parent.inferRow);if(l==null){l=""}var f=this.type,e=this.toMathMLattributes();if(f==="mspace"){return l+"<"+f+e+" />"}var k=[],j=(this.isToken?"":l+(h?"":" "));for(var g=0,d=this.data.length;g")}}}if(this.isToken||this.isChars){return l+"<"+f+e+">"+k.join("")+""}if(h){return k.join("\n")}if(k.length===0||(k.length===1&&k[0]==="")){return l+"<"+f+e+" />"}return l+"<"+f+e+">\n"+k.join("\n")+"\n"+l+""},toMathMLattributes:function(){var j=(this.type==="mstyle"?a.math.prototype.defaults:this.defaults);var h=(this.attrNames||a.copyAttributeNames),g=a.skipAttributes,l=a.copyAttributes;var e=[];if(this.type==="math"&&(!this.attr||!("xmlns" in this.attr))){e.push('xmlns="http://www.w3.org/1998/Math/MathML"')}if(!this.attrNames){for(var k in j){if(!g[k]&&!l[k]&&j.hasOwnProperty(k)){if(this[k]!=null&&this[k]!==j[k]){if(this.Get(k,null,1)!==this[k]){e.push(k+'="'+this.toMathMLattribute(this[k])+'"')}}}}}for(var f=0,d=h.length;f126||(k<32&&k!==10&&k!==13&&k!==9)){f[g]="&#x"+k.toString(16).toUpperCase()+";"}else{var j={"&":"&","<":"<",">":">",'"':"""}[f[g]];if(j){f[g]=j}}}else{if(g+11);var p=this.type,k=this.toMathMLattributes();var j=[],o=d+(g?" "+(n?" ":""):"")+" ";for(var h=0,f=this.data.length;h")}}if(j.length===0||(j.length===1&&j[0]==="")){if(!g){return"<"+p+k+" />"}j.push(o+"")}if(g){if(n){j.unshift(d+" ");j.push(d+" ")}j.unshift(d+" ");var l=e.originalText.replace(/[&<>]/g,function(i){return{">":">","<":"<","&":"&"}[i]});j.push(d+' '+l+"");j.push(d+" ")}return d+"<"+p+k+">\n"+j.join("\n")+"\n"+d+""}});a.msubsup.Augment({toMathML:function(j){var f=this.type;if(this.data[this.sup]==null){f="msub"}if(this.data[this.sub]==null){f="msup"}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+j+""}});a.munderover.Augment({toMathML:function(k){var f=this.type;var j=this.data[this.base];if(j&&j.isa(a.TeXAtom)&&j.movablelimits&&!j.Get("displaystyle")){type="msubsup";if(this.data[this.under]==null){f="msup"}if(this.data[this.over]==null){f="msub"}}else{if(this.data[this.under]==null){f="mover"}if(this.data[this.over]==null){f="munder"}}var e=this.toMathMLattributes();delete this.data[0].inferred;var h=[];for(var g=0,d=this.data.length;g\n"+h.join("\n")+"\n"+k+""}});a.TeXAtom.Augment({toMathML:function(e){var d=this.toMathMLattributes();if(!d&&this.data[0].data.length===1){return e.substr(2)+this.data[0].toMathML(e)}return e+"\n"+this.data[0].toMathML(e+" ")+"\n"+e+""}});a.chars.Augment({toMathML:function(d){return(d||"")+this.toMathMLquote(this.toString())}});a.entity.Augment({toMathML:function(d){return(d||"")+"&"+this.toMathMLquote(this.data[0])+";"}});a.xml.Augment({toMathML:function(d){return(d||"")+this.toString()}});MathJax.Hub.Register.StartupHook("TeX mathchoice Ready",function(){a.TeXmathchoice.Augment({toMathML:function(d){return this.Core().toMathML(d)}})});MathJax.Hub.Startup.signal.Post("toMathML Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/toMathML.js"); +(function(b,e){var d="2.7.6";var a=b.CombineConfig("TeX.noErrors",{disabled:false,multiLine:true,inlineDelimiters:["",""],style:{"font-size":"90%","text-align":"left",color:"black",padding:"1px 3px",border:"1px solid"}});var c="\u00A0";MathJax.Extension["TeX/noErrors"]={version:d,config:a};b.Register.StartupHook("TeX Jax Ready",function(){var f=MathJax.InputJax.TeX.formatError;MathJax.InputJax.TeX.Augment({formatError:function(j,i,k,g){if(a.disabled){return f.apply(this,arguments)}var h=j.message.replace(/\n.*/,"");b.signal.Post(["TeX Jax - parse error",h,i,k,g]);var m=a.inlineDelimiters;var l=(k||a.multiLine);if(!k){i=m[0]+i+m[1]}if(l){i=i.replace(/ /g,c)}else{i=i.replace(/\n/g," ")}return MathJax.ElementJax.mml.merror(i).With({isError:true,multiLine:l})}})});b.Register.StartupHook("HTML-CSS Jax Config",function(){b.Config({"HTML-CSS":{styles:{".MathJax .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("HTML-CSS Jax Ready",function(){var g=MathJax.ElementJax.mml;var h=MathJax.OutputJax["HTML-CSS"];var f=g.math.prototype.toHTML,i=g.merror.prototype.toHTML;g.math.Augment({toHTML:function(j,k){var l=this.data[0];if(l&&l.data[0]&&l.data[0].isError){j.style.fontSize="";j=this.HTMLcreateSpan(j);j.bbox=l.data[0].toHTML(j).bbox}else{j=f.apply(this,arguments)}return j}});g.merror.Augment({toHTML:function(p){if(!this.isError){return i.apply(this,arguments)}p=this.HTMLcreateSpan(p);p.className="noError";if(this.multiLine){p.style.display="inline-block"}var r=this.data[0].data[0].data.join("").split(/\n/);for(var o=0,l=r.length;o1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); +(function(d,c,j){var i,h="\u00A0";var k=function(m){return MathJax.Localization._.apply(MathJax.Localization,[["TeX",m]].concat([].slice.call(arguments,1)))};var f=MathJax.Object.isArray;var e=MathJax.Object.Subclass({Init:function(n,m){this.global={isInner:m};this.data=[b.start(this.global)];if(n){this.data[0].env=n}this.env=this.data[0].env},Push:function(){var o,n,p,q;for(o=0,n=arguments.length;o":"27E9","\\lt":"27E8","\\gt":"27E9","/":"/","|":["|",{texClass:i.TEXCLASS.ORD}],".":"","\\\\":"\\","\\lmoustache":"23B0","\\rmoustache":"23B1","\\lgroup":"27EE","\\rgroup":"27EF","\\arrowvert":"23D0","\\Arrowvert":"2016","\\bracevert":"23AA","\\Vert":["2016",{texClass:i.TEXCLASS.ORD}],"\\|":["2016",{texClass:i.TEXCLASS.ORD}],"\\vert":["|",{texClass:i.TEXCLASS.ORD}],"\\uparrow":"2191","\\downarrow":"2193","\\updownarrow":"2195","\\Uparrow":"21D1","\\Downarrow":"21D3","\\Updownarrow":"21D5","\\backslash":"\\","\\rangle":"27E9","\\langle":"27E8","\\rbrace":"}","\\lbrace":"{","\\}":"}","\\{":"{","\\rceil":"2309","\\lceil":"2308","\\rfloor":"230B","\\lfloor":"230A","\\lbrack":"[","\\rbrack":"]"},macros:{displaystyle:["SetStyle","D",true,0],textstyle:["SetStyle","T",false,0],scriptstyle:["SetStyle","S",false,1],scriptscriptstyle:["SetStyle","SS",false,2],rm:["SetFont",i.VARIANT.NORMAL],mit:["SetFont",i.VARIANT.ITALIC],oldstyle:["SetFont",i.VARIANT.OLDSTYLE],cal:["SetFont",i.VARIANT.CALIGRAPHIC],it:["SetFont","-tex-mathit"],bf:["SetFont",i.VARIANT.BOLD],bbFont:["SetFont",i.VARIANT.DOUBLESTRUCK],scr:["SetFont",i.VARIANT.SCRIPT],frak:["SetFont",i.VARIANT.FRAKTUR],sf:["SetFont",i.VARIANT.SANSSERIF],tt:["SetFont",i.VARIANT.MONOSPACE],tiny:["SetSize",0.5],Tiny:["SetSize",0.6],scriptsize:["SetSize",0.7],small:["SetSize",0.85],normalsize:["SetSize",1],large:["SetSize",1.2],Large:["SetSize",1.44],LARGE:["SetSize",1.73],huge:["SetSize",2.07],Huge:["SetSize",2.49],arcsin:["NamedFn"],arccos:["NamedFn"],arctan:["NamedFn"],arg:["NamedFn"],cos:["NamedFn"],cosh:["NamedFn"],cot:["NamedFn"],coth:["NamedFn"],csc:["NamedFn"],deg:["NamedFn"],det:"NamedOp",dim:["NamedFn"],exp:["NamedFn"],gcd:"NamedOp",hom:["NamedFn"],inf:"NamedOp",ker:["NamedFn"],lg:["NamedFn"],lim:"NamedOp",liminf:["NamedOp","lim inf"],limsup:["NamedOp","lim sup"],ln:["NamedFn"],log:["NamedFn"],max:"NamedOp",min:"NamedOp",Pr:"NamedOp",sec:["NamedFn"],sin:["NamedFn"],sinh:["NamedFn"],sup:"NamedOp",tan:["NamedFn"],tanh:["NamedFn"],limits:["Limits",1],nolimits:["Limits",0],overline:["UnderOver","00AF",null,1],underline:["UnderOver","005F"],overbrace:["UnderOver","23DE",1],underbrace:["UnderOver","23DF",1],overparen:["UnderOver","23DC"],underparen:["UnderOver","23DD"],overrightarrow:["UnderOver","2192"],underrightarrow:["UnderOver","2192"],overleftarrow:["UnderOver","2190"],underleftarrow:["UnderOver","2190"],overleftrightarrow:["UnderOver","2194"],underleftrightarrow:["UnderOver","2194"],overset:"Overset",underset:"Underset",stackrel:["Macro","\\mathrel{\\mathop{#2}\\limits^{#1}}",2],over:"Over",overwithdelims:"Over",atop:"Over",atopwithdelims:"Over",above:"Over",abovewithdelims:"Over",brace:["Over","{","}"],brack:["Over","[","]"],choose:["Over","(",")"],frac:"Frac",sqrt:"Sqrt",root:"Root",uproot:["MoveRoot","upRoot"],leftroot:["MoveRoot","leftRoot"],left:"LeftRight",right:"LeftRight",middle:"Middle",llap:"Lap",rlap:"Lap",raise:"RaiseLower",lower:"RaiseLower",moveleft:"MoveLeftRight",moveright:"MoveLeftRight",",":["Spacer",i.LENGTH.THINMATHSPACE],":":["Spacer",i.LENGTH.MEDIUMMATHSPACE],">":["Spacer",i.LENGTH.MEDIUMMATHSPACE],";":["Spacer",i.LENGTH.THICKMATHSPACE],"!":["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],enspace:["Spacer",".5em"],quad:["Spacer","1em"],qquad:["Spacer","2em"],thinspace:["Spacer",i.LENGTH.THINMATHSPACE],negthinspace:["Spacer",i.LENGTH.NEGATIVETHINMATHSPACE],hskip:"Hskip",hspace:"Hskip",kern:"Hskip",mskip:"Hskip",mspace:"Hskip",mkern:"Hskip",rule:"rule",Rule:["Rule"],Space:["Rule","blank"],big:["MakeBig",i.TEXCLASS.ORD,0.85],Big:["MakeBig",i.TEXCLASS.ORD,1.15],bigg:["MakeBig",i.TEXCLASS.ORD,1.45],Bigg:["MakeBig",i.TEXCLASS.ORD,1.75],bigl:["MakeBig",i.TEXCLASS.OPEN,0.85],Bigl:["MakeBig",i.TEXCLASS.OPEN,1.15],biggl:["MakeBig",i.TEXCLASS.OPEN,1.45],Biggl:["MakeBig",i.TEXCLASS.OPEN,1.75],bigr:["MakeBig",i.TEXCLASS.CLOSE,0.85],Bigr:["MakeBig",i.TEXCLASS.CLOSE,1.15],biggr:["MakeBig",i.TEXCLASS.CLOSE,1.45],Biggr:["MakeBig",i.TEXCLASS.CLOSE,1.75],bigm:["MakeBig",i.TEXCLASS.REL,0.85],Bigm:["MakeBig",i.TEXCLASS.REL,1.15],biggm:["MakeBig",i.TEXCLASS.REL,1.45],Biggm:["MakeBig",i.TEXCLASS.REL,1.75],mathord:["TeXAtom",i.TEXCLASS.ORD],mathop:["TeXAtom",i.TEXCLASS.OP],mathopen:["TeXAtom",i.TEXCLASS.OPEN],mathclose:["TeXAtom",i.TEXCLASS.CLOSE],mathbin:["TeXAtom",i.TEXCLASS.BIN],mathrel:["TeXAtom",i.TEXCLASS.REL],mathpunct:["TeXAtom",i.TEXCLASS.PUNCT],mathinner:["TeXAtom",i.TEXCLASS.INNER],vcenter:["TeXAtom",i.TEXCLASS.VCENTER],mathchoice:["Extension","mathchoice"],buildrel:"BuildRel",hbox:["HBox",0],text:"HBox",mbox:["HBox",0],fbox:"FBox",strut:"Strut",mathstrut:["Macro","\\vphantom{(}"],phantom:"Phantom",vphantom:["Phantom",1,0],hphantom:["Phantom",0,1],smash:"Smash",acute:["Accent","00B4"],grave:["Accent","0060"],ddot:["Accent","00A8"],tilde:["Accent","007E"],bar:["Accent","00AF"],breve:["Accent","02D8"],check:["Accent","02C7"],hat:["Accent","005E"],vec:["Accent","2192"],dot:["Accent","02D9"],widetilde:["Accent","007E",1],widehat:["Accent","005E",1],matrix:"Matrix",array:"Matrix",pmatrix:["Matrix","(",")"],cases:["Matrix","{","","left left",null,".1em",null,true],eqalign:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D"],displaylines:["Matrix",null,null,"center",null,".5em","D"],cr:"Cr","\\":"CrLaTeX",newline:"Cr",hline:["HLine","solid"],hdashline:["HLine","dashed"],eqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"right"],leqalignno:["Matrix",null,null,"right left",i.LENGTH.THICKMATHSPACE,".5em","D",null,"left"],hfill:"HFill",hfil:"HFill",hfilll:"HFill",bmod:["Macro",'\\mmlToken{mo}[lspace="thickmathspace" rspace="thickmathspace"]{mod}'],pmod:["Macro","\\pod{\\mmlToken{mi}{mod}\\kern 6mu #1}",1],mod:["Macro","\\mathchoice{\\kern18mu}{\\kern12mu}{\\kern12mu}{\\kern12mu}\\mmlToken{mi}{mod}\\,\\,#1",1],pod:["Macro","\\mathchoice{\\kern18mu}{\\kern8mu}{\\kern8mu}{\\kern8mu}(#1)",1],iff:["Macro","\\;\\Longleftrightarrow\\;"],skew:["Macro","{{#2{#3\\mkern#1mu}\\mkern-#1mu}{}}",3],mathcal:["Macro","{\\cal #1}",1],mathscr:["Macro","{\\scr #1}",1],mathrm:["Macro","{\\rm #1}",1],mathbf:["Macro","{\\bf #1}",1],mathbb:["Macro","{\\bbFont #1}",1],Bbb:["Macro","{\\bbFont #1}",1],mathit:["Macro","{\\it #1}",1],mathfrak:["Macro","{\\frak #1}",1],mathsf:["Macro","{\\sf #1}",1],mathtt:["Macro","{\\tt #1}",1],textrm:["Macro","\\mathord{\\rm\\text{#1}}",1],textit:["Macro","\\mathord{\\it\\text{#1}}",1],textbf:["Macro","\\mathord{\\bf\\text{#1}}",1],textsf:["Macro","\\mathord{\\sf\\text{#1}}",1],texttt:["Macro","\\mathord{\\tt\\text{#1}}",1],pmb:["Macro","\\rlap{#1}\\kern1px{#1}",1],TeX:["Macro","T\\kern-.14em\\lower.5ex{E}\\kern-.115em X"],LaTeX:["Macro","L\\kern-.325em\\raise.21em{\\scriptstyle{A}}\\kern-.17em\\TeX"]," ":["Macro","\\text{ }"],not:"Not",dots:"Dots",space:"Tilde","\u00A0":"Tilde",begin:"BeginEnd",end:"BeginEnd",newcommand:["Extension","newcommand"],renewcommand:["Extension","newcommand"],newenvironment:["Extension","newcommand"],renewenvironment:["Extension","newcommand"],def:["Extension","newcommand"],let:["Extension","newcommand"],verb:["Extension","verb"],boldsymbol:["Extension","boldsymbol"],tag:["Extension","AMSmath"],notag:["Extension","AMSmath"],label:["Extension","AMSmath"],ref:["Extension","AMSmath"],eqref:["Extension","AMSmath"],nonumber:["Macro","\\notag"],unicode:["Extension","unicode"],color:"Color",href:["Extension","HTML"],"class":["Extension","HTML"],style:["Extension","HTML"],cssId:["Extension","HTML"],bbox:["Extension","bbox"],mmlToken:"MmlToken",require:"Require"},environment:{array:["AlignedArray"],matrix:["Array",null,null,null,"c"],pmatrix:["Array",null,"(",")","c"],bmatrix:["Array",null,"[","]","c"],Bmatrix:["Array",null,"\\{","\\}","c"],vmatrix:["Array",null,"\\vert","\\vert","c"],Vmatrix:["Array",null,"\\Vert","\\Vert","c"],cases:["Array",null,"\\{",".","ll",null,".2em","T"],equation:[null,"Equation"],"equation*":[null,"Equation"],eqnarray:["ExtensionEnv",null,"AMSmath"],"eqnarray*":["ExtensionEnv",null,"AMSmath"],align:["ExtensionEnv",null,"AMSmath"],"align*":["ExtensionEnv",null,"AMSmath"],aligned:["ExtensionEnv",null,"AMSmath"],multline:["ExtensionEnv",null,"AMSmath"],"multline*":["ExtensionEnv",null,"AMSmath"],split:["ExtensionEnv",null,"AMSmath"],gather:["ExtensionEnv",null,"AMSmath"],"gather*":["ExtensionEnv",null,"AMSmath"],gathered:["ExtensionEnv",null,"AMSmath"],alignat:["ExtensionEnv",null,"AMSmath"],"alignat*":["ExtensionEnv",null,"AMSmath"],alignedat:["ExtensionEnv",null,"AMSmath"]},p_height:1.2/0.85});if(this.config.Macros){var m=this.config.Macros;for(var n in m){if(m.hasOwnProperty(n)){if(typeof(m[n])==="string"){g.macros[n]=["Macro",m[n]]}else{g.macros[n]=["Macro"].concat(m[n])}g.macros[n].isUser=true}}}};var a=MathJax.Object.Subclass({Init:function(n,o){this.string=n;this.i=0;this.macroCount=0;var m;if(o){m={};for(var p in o){if(o.hasOwnProperty(p)){m[p]=o[p]}}}this.stack=d.Stack(m,!!o);this.Parse();this.Push(b.stop())},Parse:function(){var o,m;while(this.i=55296&&m<56320){o+=this.string.charAt(this.i++)}if(g.special.hasOwnProperty(o)){this[g.special[o]](o)}else{if(g.letter.test(o)){this.Variable(o)}else{if(g.digit.test(o)){this.Number(o)}else{this.Other(o)}}}}},Push:function(){this.stack.Push.apply(this.stack,arguments)},mml:function(){if(this.stack.Top().type!=="mml"){return null}return this.stack.Top().data[0]},mmlToken:function(m){return m},ControlSequence:function(p){var m=this.GetCS(),o=this.csFindMacro(m);if(o){if(!f(o)){o=[o]}var n=o[0];if(!(n instanceof Function)){n=this[n]}n.apply(this,[p+m].concat(o.slice(1)))}else{if(g.mathchar0mi.hasOwnProperty(m)){this.csMathchar0mi(m,g.mathchar0mi[m])}else{if(g.mathchar0mo.hasOwnProperty(m)){this.csMathchar0mo(m,g.mathchar0mo[m])}else{if(g.mathchar7.hasOwnProperty(m)){this.csMathchar7(m,g.mathchar7[m])}else{if(g.delimiter.hasOwnProperty("\\"+m)){this.csDelimiter(m,g.delimiter["\\"+m])}else{this.csUndefined(p+m)}}}}}},csFindMacro:function(m){return(g.macros.hasOwnProperty(m)?g.macros[m]:null)},csMathchar0mi:function(m,o){var n={mathvariant:i.VARIANT.ITALIC};if(f(o)){n=o[1];o=o[0]}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csMathchar0mo:function(m,o){var n={stretchy:false};if(f(o)){n=o[1];n.stretchy=false;o=o[0]}this.Push(this.mmlToken(i.mo(i.entity("#x"+o)).With(n)))},csMathchar7:function(m,o){var n={mathvariant:i.VARIANT.NORMAL};if(f(o)){n=o[1];o=o[0]}if(this.stack.env.font){n.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.entity("#x"+o)).With(n)))},csDelimiter:function(m,o){var n={};if(f(o)){n=o[1];o=o[0]}if(o.length===4){o=i.entity("#x"+o)}else{o=i.chars(o)}this.Push(this.mmlToken(i.mo(o).With({fence:false,stretchy:false}).With(n)))},csUndefined:function(m){d.Error(["UndefinedControlSequence","Undefined control sequence %1",m])},Variable:function(n){var m={};if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(i.mi(i.chars(n)).With(m)))},Number:function(p){var m,o=this.string.slice(this.i-1).match(g.number);if(o){m=i.mn(o[0].replace(/[{}]/g,""));this.i+=o[0].length-1}else{m=i.mo(i.chars(p))}if(this.stack.env.font){m.mathvariant=this.stack.env.font}this.Push(this.mmlToken(m))},Open:function(m){this.Push(b.open())},Close:function(m){this.Push(b.close())},Tilde:function(m){this.Push(i.mtext(i.chars(h)))},Space:function(m){},Superscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sup;if((o.type==="msubsup"&&o.data[o.sup])||(o.type==="munderover"&&o.data[o.over]&&!o.subsupOK)){d.Error(["DoubleExponent","Double exponent: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.over]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.over}else{o=i.msubsup(o,null,null);m=o.sup}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},Subscript:function(r){if(this.GetNext().match(/\d/)){this.string=this.string.substr(0,this.i+1)+" "+this.string.substr(this.i+1)}var q,o,p=this.stack.Top();if(p.type==="prime"){o=p.data[0];q=p.data[1];this.stack.Pop()}else{o=this.stack.Prev();if(!o){o=i.mi("")}}if(o.isEmbellishedWrapper){o=o.data[0].data[0]}var n=o.movesupsub,m=o.sub;if((o.type==="msubsup"&&o.data[o.sub])||(o.type==="munderover"&&o.data[o.under]&&!o.subsupOK)){d.Error(["DoubleSubscripts","Double subscripts: use braces to clarify"])}if(o.type!=="msubsup"){if(n){if(o.type!=="munderover"||o.data[o.under]){if(o.movablelimits&&o.isa(i.mi)){o=this.mi2mo(o)}o=i.munderover(o,null,null).With({movesupsub:true})}m=o.under}else{o=i.msubsup(o,null,null);m=o.sub}}this.Push(b.subsup(o).With({position:m,primes:q,movesupsub:n}))},PRIME:"\u2032",SMARTQUOTE:"\u2019",Prime:function(o){var n=this.stack.Prev();if(!n){n=i.mi()}if(n.type==="msubsup"&&n.data[n.sup]){d.Error(["DoubleExponentPrime","Prime causes double exponent: use braces to clarify"])}var m="";this.i--;do{m+=this.PRIME;this.i++,o=this.GetNext()}while(o==="'"||o===this.SMARTQUOTE);m=["","\u2032","\u2033","\u2034","\u2057"][m.length]||m;this.Push(b.prime(n,this.mmlToken(i.mo(m))))},mi2mo:function(m){var n=i.mo();n.Append.apply(n,m.data);var o;for(o in n.defaults){if(n.defaults.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}for(o in i.copyAttributes){if(i.copyAttributes.hasOwnProperty(o)&&m[o]!=null){n[o]=m[o]}}n.lspace=n.rspace="0";n.useMMLspacing&=~(n.SPACE_ATTR.lspace|n.SPACE_ATTR.rspace);return n},Comment:function(m){while(this.id.config.MAXMACROS){d.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},Matrix:function(n,p,v,r,u,o,m,w,t){var s=this.GetNext();if(s===""){d.Error(["MissingArgFor","Missing argument for %1",n])}if(s==="{"){this.i++}else{this.string=s+"}"+this.string.slice(this.i+1);this.i=0}var q=b.array().With({requireClose:true,arraydef:{rowspacing:(o||"4pt"),columnspacing:(u||"1em")}});if(w){q.isCases=true}if(t){q.isNumbered=true;q.arraydef.side=t}if(p||v){q.open=p;q.close=v}if(m==="D"){q.arraydef.displaystyle=true}if(r!=null){q.arraydef.columnalign=r}this.Push(q)},Entry:function(p){this.Push(b.cell().With({isEntry:true,name:p}));if(this.stack.Top().isCases){var o=this.string;var t=0,s=-1,q=this.i,n=o.length;while(qd.config.MAXMACROS){d.Error(["MaxMacroSub2","MathJax maximum substitution count exceeded; is there a recursive latex environment?"])}if(q[0]&&this[q[0]]){n=this[q[0]].apply(this,[n].concat(q.slice(2)))}}this.Push(n)},envFindName:function(m){return(g.environment.hasOwnProperty(m)?g.environment[m]:null)},Equation:function(m,n){return n},ExtensionEnv:function(n,m){this.Extension(n.name,m,"environment")},Array:function(n,p,u,s,t,o,m,q){if(!s){s=this.GetArgument("\\begin{"+n.name+"}")}var v=("c"+s).replace(/[^clr|:]/g,"").replace(/[^|:]([|:])+/g,"$1");s=s.replace(/[^clr]/g,"").split("").join(" ");s=s.replace(/l/g,"left").replace(/r/g,"right").replace(/c/g,"center");var r=b.array().With({arraydef:{columnalign:s,columnspacing:(t||"1em"),rowspacing:(o||"4pt")}});if(v.match(/[|:]/)){if(v.charAt(0).match(/[|:]/)){r.frame.push("left");r.frame.dashed=v.charAt(0)===":"}if(v.charAt(v.length-1).match(/[|:]/)){r.frame.push("right")}v=v.substr(1,v.length-2);r.arraydef.columnlines=v.split("").join(" ").replace(/[^|: ]/g,"none").replace(/\|/g,"solid").replace(/:/g,"dashed")}if(p){r.open=this.convertDelimiter(p)}if(u){r.close=this.convertDelimiter(u)}if(m==="D"){r.arraydef.displaystyle=true}else{if(m){r.arraydef.displaystyle=false}}if(m==="S"){r.arraydef.scriptlevel=1}if(q){r.arraydef.useHeight=false}this.Push(n);return r},AlignedArray:function(m){var n=this.GetBrackets("\\begin{"+m.name+"}");return this.setArrayAlign(this.Array.apply(this,arguments),n)},setArrayAlign:function(n,m){m=this.trimSpaces(m||"");if(m==="t"){n.arraydef.align="baseline 1"}else{if(m==="b"){n.arraydef.align="baseline -1"}else{if(m==="c"){n.arraydef.align="center"}else{if(m){n.arraydef.align=m}}}}return n},convertDelimiter:function(m){if(m){m=(g.delimiter.hasOwnProperty(m)?g.delimiter[m]:null)}if(m==null){return null}if(f(m)){m=m[0]}if(m.length===4){m=String.fromCharCode(parseInt(m,16))}return m},trimSpaces:function(n){if(typeof(n)!="string"){return n}var m=n.replace(/^\s+|\s+$/g,"");if(m.match(/\\$/)&&n.match(/ $/)){m+=" "}return m},nextIsSpace:function(){return this.string.charAt(this.i).match(/\s/)},GetNext:function(){while(this.nextIsSpace()){this.i++}return this.string.charAt(this.i)},GetCS:function(){var m=this.string.slice(this.i).match(/^([a-z]+|.) ?/i);if(m){this.i+=m[1].length;return m[1]}else{this.i++;return" "}},GetArgument:function(n,o){switch(this.GetNext()){case"":if(!o){d.Error(["MissingArgFor","Missing argument for %1",n])}return null;case"}":if(!o){d.Error(["ExtraCloseMissingOpen","Extra close brace or missing open brace"])}return null;case"\\":this.i++;return"\\"+this.GetCS();case"{":var m=++this.i,p=1;while(this.i1){n=[i.mrow.apply(i,n)]}}return n},InternalText:function(n,m){n=n.replace(/^\s+/,h).replace(/\s+$/,h);return i.mtext(i.chars(n)).With(m)},setDef:function(m,n){n.isUser=true;g.macros[m]=n},setEnv:function(m,n){n.isUser=true;g.environment[m]=n},SubstituteArgs:function(n,m){var q="";var p="";var r;var o=0;while(on.length){d.Error(["IllegalMacroParam","Illegal macro parameter reference"])}p=this.AddArgs(this.AddArgs(p,q),n[r-1]);q=""}}else{q+=r}}}return this.AddArgs(p,q)},AddArgs:function(n,m){if(m.match(/^[a-z]/i)&&n.match(/(^|[^\\])(\\\\)*\\[a-z]+$/i)){n+=" "}if(n.length+m.length>d.config.MAXBUFFER){d.Error(["MaxBufferSize","MathJax internal buffer size exceeded; is there a recursive macro call?"])}return n+m}});d.Augment({Stack:e,Parse:a,Definitions:g,Startup:l,config:{MAXMACROS:10000,MAXBUFFER:5*1024},sourceMenuTitle:["TeXCommands","TeX Commands"],annotationEncoding:"application/x-tex",prefilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Config:function(){this.SUPER(arguments).Config.apply(this,arguments);if(this.config.equationNumbers.autoNumber!=="none"){if(!this.config.extensions){this.config.extensions=[]}this.config.extensions.push("AMSmath.js")}},Translate:function(m){var n,o=false,q=MathJax.HTML.getScript(m);var s=(m.type.replace(/\n/g," ").match(/(;|\s|\n)mode\s*=\s*display(;|\s|\n|$)/)!=null);var r={math:q,display:s,script:m};var t=this.prefilterHooks.Execute(r);if(t){return t}q=r.math;try{n=d.Parse(q).mml()}catch(p){if(!p.texError){throw p}n=this.formatError(p,q,s,m);o=true}if(n.isa(i.mtable)&&n.displaystyle==="inherit"){n.displaystyle=s}if(n.inferred){n=i.apply(MathJax.ElementJax,n.data)}else{n=i(n)}if(s){n.root.display="block"}if(o){n.texError=true}r.math=n;return this.postfilterHooks.Execute(r)||r.math},prefilterMath:function(n,o,m){return n},postfilterMath:function(n,o,m){this.combineRelations(n.root);return n},formatError:function(p,o,q,m){var n=p.message.replace(/\n.*/,"");c.signal.Post(["TeX Jax - parse error",n,o,q,m]);return i.Error(n)},Error:function(m){if(f(m)){m=k.apply(k,m)}throw c.Insert(Error(m),{texError:true})},Macro:function(m,n,o){g.macros[m]=["Macro"].concat([].slice.call(arguments,1));g.macros[m].isUser=true},fenced:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.INNER});m.Append(i.mo(o).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.OPEN}));if(n.type==="mrow"&&n.inferred){m.Append.apply(m,n.data)}else{m.Append(n)}m.Append(i.mo(p).With({fence:true,stretchy:true,symmetric:true,texClass:i.TEXCLASS.CLOSE}));return m},fixedFence:function(o,n,p){var m=i.mrow().With({open:o,close:p,texClass:i.TEXCLASS.ORD});if(o){m.Append(this.mathPalette(o,"l"))}if(n.type==="mrow"){m.Append.apply(m,n.data)}else{m.Append(n)}if(p){m.Append(this.mathPalette(p,"r"))}return m},mathPalette:function(p,n){if(p==="{"||p==="}"){p="\\"+p}var o="{\\bigg"+n+" "+p+"}",m="{\\big"+n+" "+p+"}";return d.Parse("\\mathchoice"+o+m+m+m,{}).mml()},combineRelations:function(q){var r,n,p,o;for(r=0,n=q.data.length;r0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k element, not %1","<"+j.firstChild.nodeName+">"])}var i={math:j.firstChild,script:e};c.DOMfilterHooks.Execute(i);this.mml=this.MakeMML(i.math)},MakeMML:function(h){var i=String(h.getAttribute("class")||"");var f,g=h.nodeName.toLowerCase().replace(/^[a-z]+:/,"");var e=(i.match(/(^| )MJX-TeXAtom-([^ ]*)/));if(e){f=this.TeXAtom(e[2],e[2]==="OP"&&!i.match(/MJX-fixedlimits/))}else{if(!(a[g]&&a[g].isa&&a[g].isa(a.mbase))){MathJax.Hub.signal.Post(["MathML Jax - unknown node type",g]);return a.Error(b("UnknownNodeType","Unknown node type: %1",g))}else{f=a[g]()}}this.AddAttributes(f,h);this.CheckClass(f,f["class"]);this.AddChildren(f,h);if(c.config.useMathMLspacing){f.useMMLspacing=8}return f},TeXAtom:function(g,f){var e=a.TeXAtom().With({texClass:a.TEXCLASS[g]});if(f){e.movesupsub=e.movablelimits=true}return e},CheckClass:function(f,h){h=(h||"").split(/ /);var j=[];for(var g=0,e=h.length;g=2){var l=e.data[0],n=e.data[e.data.length-1];if(l.type==="mo"&&l.Get("fence")&&n.type==="mo"&&n.Get("fence")){if(l.data[0]){e.open=l.data.join("")}if(n.data[0]){e.close=n.data.join("")}}}},preProcessMath:function(f){if(f.match(/^<[a-z]+:/i)&&!f.match(/^<[^<>]* xmlns:/)){f=f.replace(/^<([a-z]+)(:math)/i,'<$1$2 xmlns:$1="http://www.w3.org/1998/Math/MathML"')}var e=f.match(/^(])+)>)/i);if(e&&e[2].match(/ (?!xmlns=)[a-z]+=\"http:/i)){f=e[1].replace(/ (?!xmlns=)([a-z]+=(['"])http:.*?\2)/ig," xmlns:$1 $1")+f.substr(e[0].length)}if(f.match(/^]/i)&&!f.match(/^<[^<>]* xmlns=/)){f=f.replace(/^<(math)/i,'\s*$/,"$2");return f.replace(/&([a-z][a-z0-9]*);/ig,this.replaceEntity)},trimSpace:function(e){return e.replace(/[\t\n\r]/g," ").replace(/^ +/,"").replace(/ +$/,"").replace(/ +/g," ")},replaceEntity:function(g,f){if(f.match(/^(lt|amp|quot)$/)){return g}if(c.Parse.Entity[f]){return c.Parse.Entity[f]}var h=f.charAt(0).toLowerCase();var e=f.match(/^[a-zA-Z](fr|scr|opf)$/);if(e){h=e[1]}if(!c.Parse.loaded[h]){c.Parse.loaded[h]=true;MathJax.Hub.RestartAfter(MathJax.Ajax.Require(c.entityDir+"/"+h+".js"))}return g}},{loaded:[]});c.Augment({sourceMenuTitle:["OriginalMathML","Original MathML"],prefilterHooks:MathJax.Callback.Hooks(true),DOMfilterHooks:MathJax.Callback.Hooks(true),postfilterHooks:MathJax.Callback.Hooks(true),Translate:function(e){if(!this.ParseXML){this.ParseXML=this.createParser()}var f,h,i={script:e};if(e.firstChild&&e.firstChild.nodeName.toLowerCase().replace(/^[a-z]+:/,"")==="math"){i.math=e.firstChild}else{h=MathJax.HTML.getScript(e);if(d.isMSIE){h=h.replace(/( )+$/,"")}i.math=h}var j=this.prefilterHooks.Execute(i);if(j){return j}h=i.math;try{f=c.Parse(h,e).mml}catch(g){if(!g.mathmlError){throw g}f=this.formatError(g,h,e)}i.math=a(f);return this.postfilterHooks.Execute(i)||i.math},prefilterMath:function(f,e){return f},prefilterMathML:function(f,e){return f},formatError:function(h,g,e){var f=h.message.replace(/\n.*/,"");MathJax.Hub.signal.Post(["MathML Jax - parse error",f,g,e]);return a.Error(f)},Error:function(e){if(MathJax.Object.isArray(e)){e=b.apply(b,e)}throw MathJax.Hub.Insert(Error(e),{mathmlError:true})},parseDOM:function(e){return this.parser.parseFromString(e,"text/xml")},parseMS:function(e){return(this.parser.loadXML(e)?this.parser:null)},parseDIV:function(e){this.div.innerHTML="
"+e.replace(/<([a-z]+)([^>]*)\/>/g,"<$1$2>")+"
";var f=this.div.firstChild;this.div.innerHTML="";return f},parseError:function(e){return null},createMSParser:function(){var j=null;var f=["MSXML2.DOMDocument.6.0","MSXML2.DOMDocument.5.0","MSXML2.DOMDocument.4.0","MSXML2.DOMDocument.3.0","MSXML2.DOMDocument.2.0","Microsoft.XMLDOM"];for(var g=0,e=f.length;g=ab-1){this.lastChild=ae}this.childNodes[ad]=ae;ae.nextSibling=ac.nextSibling;ac.nextSibling=ac.parent=null;return ac},hasChildNodes:function(ab){return(this.childNodes.length>0)},toString:function(){return"{"+this.childNodes.join("")+"}"}});var x=function(){g=MathJax.ElementJax.mml;var ab=g.mbase.prototype.Init;g.mbase.Augment({firstChild:null,lastChild:null,nodeValue:null,nextSibling:null,Init:function(){var ac=ab.apply(this,arguments)||this;ac.childNodes=ac.data;ac.nodeName=ac.type;return ac},appendChild:function(af){if(af.parent){af.parent.removeChild(af)}var ad=arguments;if(af.isa(X)){ad=af.childNodes;af.data=af.childNodes=[];af.firstChild=af.lastChild=null}for(var ae=0,ac=ad.length;ae=ac-1){this.lastChild=af}this.SetData(ae,af);af.nextSibling=ad.nextSibling;ad.nextSibling=ad.parent=null;return ad},hasChildNodes:function(ac){return(this.childNodes.length>0)},setAttribute:function(ac,ad){this[ac]=ad}})};var Q={};var e={getElementById:true,createElementNS:function(ac,ab){var ad=g[ab]();if(ab==="mo"&&aa.config.useMathMLspacing){ad.useMMLspacing=128}return ad},createTextNode:function(ab){return g.chars(ab).With({nodeValue:ab})},createDocumentFragment:function(){return X()}};var J={appName:"MathJax"};var C="blue";var o=true;var v=true;var d=".";var f=true;var l=(J.appName.slice(0,9)=="Microsoft");function E(ab){if(l){return e.createElement(ab)}else{return e.createElementNS("http://www.w3.org/1999/xhtml",ab)}}var W="http://www.w3.org/1998/Math/MathML";function P(ab){if(l){return e.createElement("m:"+ab)}else{return e.createElementNS(W,ab)}}function O(ab,ad){var ac;if(l){ac=e.createElement("m:"+ab)}else{ac=e.createElementNS(W,ab)}if(ad){ac.appendChild(ad)}return ac}function u(ab,ac){z.push({input:ab,tag:"mo",output:ac,tex:null,ttype:V});B()}function r(ab){z.push(ab);B()}var D=["\uD835\uDC9C","\u212C","\uD835\uDC9E","\uD835\uDC9F","\u2130","\u2131","\uD835\uDCA2","\u210B","\u2110","\uD835\uDCA5","\uD835\uDCA6","\u2112","\u2133","\uD835\uDCA9","\uD835\uDCAA","\uD835\uDCAB","\uD835\uDCAC","\u211B","\uD835\uDCAE","\uD835\uDCAF","\uD835\uDCB0","\uD835\uDCB1","\uD835\uDCB2","\uD835\uDCB3","\uD835\uDCB4","\uD835\uDCB5","\uD835\uDCB6","\uD835\uDCB7","\uD835\uDCB8","\uD835\uDCB9","\u212F","\uD835\uDCBB","\u210A","\uD835\uDCBD","\uD835\uDCBE","\uD835\uDCBF","\uD835\uDCC0","\uD835\uDCC1","\uD835\uDCC2","\uD835\uDCC3","\u2134","\uD835\uDCC5","\uD835\uDCC6","\uD835\uDCC7","\uD835\uDCC8","\uD835\uDCC9","\uD835\uDCCA","\uD835\uDCCB","\uD835\uDCCC","\uD835\uDCCD","\uD835\uDCCE","\uD835\uDCCF"];var H=["\uD835\uDD04","\uD835\uDD05","\u212D","\uD835\uDD07","\uD835\uDD08","\uD835\uDD09","\uD835\uDD0A","\u210C","\u2111","\uD835\uDD0D","\uD835\uDD0E","\uD835\uDD0F","\uD835\uDD10","\uD835\uDD11","\uD835\uDD12","\uD835\uDD13","\uD835\uDD14","\u211C","\uD835\uDD16","\uD835\uDD17","\uD835\uDD18","\uD835\uDD19","\uD835\uDD1A","\uD835\uDD1B","\uD835\uDD1C","\u2128","\uD835\uDD1E","\uD835\uDD1F","\uD835\uDD20","\uD835\uDD21","\uD835\uDD22","\uD835\uDD23","\uD835\uDD24","\uD835\uDD25","\uD835\uDD26","\uD835\uDD27","\uD835\uDD28","\uD835\uDD29","\uD835\uDD2A","\uD835\uDD2B","\uD835\uDD2C","\uD835\uDD2D","\uD835\uDD2E","\uD835\uDD2F","\uD835\uDD30","\uD835\uDD31","\uD835\uDD32","\uD835\uDD33","\uD835\uDD34","\uD835\uDD35","\uD835\uDD36","\uD835\uDD37"];var w=["\uD835\uDD38","\uD835\uDD39","\u2102","\uD835\uDD3B","\uD835\uDD3C","\uD835\uDD3D","\uD835\uDD3E","\u210D","\uD835\uDD40","\uD835\uDD41","\uD835\uDD42","\uD835\uDD43","\uD835\uDD44","\u2115","\uD835\uDD46","\u2119","\u211A","\u211D","\uD835\uDD4A","\uD835\uDD4B","\uD835\uDD4C","\uD835\uDD4D","\uD835\uDD4E","\uD835\uDD4F","\uD835\uDD50","\u2124","\uD835\uDD52","\uD835\uDD53","\uD835\uDD54","\uD835\uDD55","\uD835\uDD56","\uD835\uDD57","\uD835\uDD58","\uD835\uDD59","\uD835\uDD5A","\uD835\uDD5B","\uD835\uDD5C","\uD835\uDD5D","\uD835\uDD5E","\uD835\uDD5F","\uD835\uDD60","\uD835\uDD61","\uD835\uDD62","\uD835\uDD63","\uD835\uDD64","\uD835\uDD65","\uD835\uDD66","\uD835\uDD67","\uD835\uDD68","\uD835\uDD69","\uD835\uDD6A","\uD835\uDD6B"];var c=0,A=1,U=2,i=3,b=4,h=5,a=6,L=7,V=8,m=9,Y=10,K=15;var k={input:'"',tag:"mtext",output:"mbox",tex:null,ttype:Y};var z=[{input:"alpha",tag:"mi",output:"\u03B1",tex:null,ttype:c},{input:"beta",tag:"mi",output:"\u03B2",tex:null,ttype:c},{input:"chi",tag:"mi",output:"\u03C7",tex:null,ttype:c},{input:"delta",tag:"mi",output:"\u03B4",tex:null,ttype:c},{input:"Delta",tag:"mo",output:"\u0394",tex:null,ttype:c},{input:"epsi",tag:"mi",output:"\u03B5",tex:"epsilon",ttype:c},{input:"varepsilon",tag:"mi",output:"\u025B",tex:null,ttype:c},{input:"eta",tag:"mi",output:"\u03B7",tex:null,ttype:c},{input:"gamma",tag:"mi",output:"\u03B3",tex:null,ttype:c},{input:"Gamma",tag:"mo",output:"\u0393",tex:null,ttype:c},{input:"iota",tag:"mi",output:"\u03B9",tex:null,ttype:c},{input:"kappa",tag:"mi",output:"\u03BA",tex:null,ttype:c},{input:"lambda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lambda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"lamda",tag:"mi",output:"\u03BB",tex:null,ttype:c},{input:"Lamda",tag:"mo",output:"\u039B",tex:null,ttype:c},{input:"mu",tag:"mi",output:"\u03BC",tex:null,ttype:c},{input:"nu",tag:"mi",output:"\u03BD",tex:null,ttype:c},{input:"omega",tag:"mi",output:"\u03C9",tex:null,ttype:c},{input:"Omega",tag:"mo",output:"\u03A9",tex:null,ttype:c},{input:"phi",tag:"mi",output:f?"\u03D5":"\u03C6",tex:null,ttype:c},{input:"varphi",tag:"mi",output:f?"\u03C6":"\u03D5",tex:null,ttype:c},{input:"Phi",tag:"mo",output:"\u03A6",tex:null,ttype:c},{input:"pi",tag:"mi",output:"\u03C0",tex:null,ttype:c},{input:"Pi",tag:"mo",output:"\u03A0",tex:null,ttype:c},{input:"psi",tag:"mi",output:"\u03C8",tex:null,ttype:c},{input:"Psi",tag:"mi",output:"\u03A8",tex:null,ttype:c},{input:"rho",tag:"mi",output:"\u03C1",tex:null,ttype:c},{input:"sigma",tag:"mi",output:"\u03C3",tex:null,ttype:c},{input:"Sigma",tag:"mo",output:"\u03A3",tex:null,ttype:c},{input:"tau",tag:"mi",output:"\u03C4",tex:null,ttype:c},{input:"theta",tag:"mi",output:"\u03B8",tex:null,ttype:c},{input:"vartheta",tag:"mi",output:"\u03D1",tex:null,ttype:c},{input:"Theta",tag:"mo",output:"\u0398",tex:null,ttype:c},{input:"upsilon",tag:"mi",output:"\u03C5",tex:null,ttype:c},{input:"xi",tag:"mi",output:"\u03BE",tex:null,ttype:c},{input:"Xi",tag:"mo",output:"\u039E",tex:null,ttype:c},{input:"zeta",tag:"mi",output:"\u03B6",tex:null,ttype:c},{input:"*",tag:"mo",output:"\u22C5",tex:"cdot",ttype:c},{input:"**",tag:"mo",output:"\u2217",tex:"ast",ttype:c},{input:"***",tag:"mo",output:"\u22C6",tex:"star",ttype:c},{input:"//",tag:"mo",output:"/",tex:null,ttype:c},{input:"\\\\",tag:"mo",output:"\\",tex:"backslash",ttype:c},{input:"setminus",tag:"mo",output:"\\",tex:null,ttype:c},{input:"xx",tag:"mo",output:"\u00D7",tex:"times",ttype:c},{input:"|><",tag:"mo",output:"\u22C9",tex:"ltimes",ttype:c},{input:"><|",tag:"mo",output:"\u22CA",tex:"rtimes",ttype:c},{input:"|><|",tag:"mo",output:"\u22C8",tex:"bowtie",ttype:c},{input:"-:",tag:"mo",output:"\u00F7",tex:"div",ttype:c},{input:"divide",tag:"mo",output:"-:",tex:null,ttype:V},{input:"@",tag:"mo",output:"\u2218",tex:"circ",ttype:c},{input:"o+",tag:"mo",output:"\u2295",tex:"oplus",ttype:c},{input:"ox",tag:"mo",output:"\u2297",tex:"otimes",ttype:c},{input:"o.",tag:"mo",output:"\u2299",tex:"odot",ttype:c},{input:"sum",tag:"mo",output:"\u2211",tex:null,ttype:L},{input:"prod",tag:"mo",output:"\u220F",tex:null,ttype:L},{input:"^^",tag:"mo",output:"\u2227",tex:"wedge",ttype:c},{input:"^^^",tag:"mo",output:"\u22C0",tex:"bigwedge",ttype:L},{input:"vv",tag:"mo",output:"\u2228",tex:"vee",ttype:c},{input:"vvv",tag:"mo",output:"\u22C1",tex:"bigvee",ttype:L},{input:"nn",tag:"mo",output:"\u2229",tex:"cap",ttype:c},{input:"nnn",tag:"mo",output:"\u22C2",tex:"bigcap",ttype:L},{input:"uu",tag:"mo",output:"\u222A",tex:"cup",ttype:c},{input:"uuu",tag:"mo",output:"\u22C3",tex:"bigcup",ttype:L},{input:"!=",tag:"mo",output:"\u2260",tex:"ne",ttype:c},{input:":=",tag:"mo",output:":=",tex:null,ttype:c},{input:"lt",tag:"mo",output:"<",tex:null,ttype:c},{input:"<=",tag:"mo",output:"\u2264",tex:"le",ttype:c},{input:"lt=",tag:"mo",output:"\u2264",tex:"leq",ttype:c},{input:"gt",tag:"mo",output:">",tex:null,ttype:c},{input:">=",tag:"mo",output:"\u2265",tex:"ge",ttype:c},{input:"gt=",tag:"mo",output:"\u2265",tex:"geq",ttype:c},{input:"-<",tag:"mo",output:"\u227A",tex:"prec",ttype:c},{input:"-lt",tag:"mo",output:"\u227A",tex:null,ttype:c},{input:">-",tag:"mo",output:"\u227B",tex:"succ",ttype:c},{input:"-<=",tag:"mo",output:"\u2AAF",tex:"preceq",ttype:c},{input:">-=",tag:"mo",output:"\u2AB0",tex:"succeq",ttype:c},{input:"in",tag:"mo",output:"\u2208",tex:null,ttype:c},{input:"!in",tag:"mo",output:"\u2209",tex:"notin",ttype:c},{input:"sub",tag:"mo",output:"\u2282",tex:"subset",ttype:c},{input:"sup",tag:"mo",output:"\u2283",tex:"supset",ttype:c},{input:"sube",tag:"mo",output:"\u2286",tex:"subseteq",ttype:c},{input:"supe",tag:"mo",output:"\u2287",tex:"supseteq",ttype:c},{input:"-=",tag:"mo",output:"\u2261",tex:"equiv",ttype:c},{input:"~=",tag:"mo",output:"\u2245",tex:"cong",ttype:c},{input:"~~",tag:"mo",output:"\u2248",tex:"approx",ttype:c},{input:"prop",tag:"mo",output:"\u221D",tex:"propto",ttype:c},{input:"and",tag:"mtext",output:"and",tex:null,ttype:a},{input:"or",tag:"mtext",output:"or",tex:null,ttype:a},{input:"not",tag:"mo",output:"\u00AC",tex:"neg",ttype:c},{input:"=>",tag:"mo",output:"\u21D2",tex:"implies",ttype:c},{input:"if",tag:"mo",output:"if",tex:null,ttype:a},{input:"<=>",tag:"mo",output:"\u21D4",tex:"iff",ttype:c},{input:"AA",tag:"mo",output:"\u2200",tex:"forall",ttype:c},{input:"EE",tag:"mo",output:"\u2203",tex:"exists",ttype:c},{input:"_|_",tag:"mo",output:"\u22A5",tex:"bot",ttype:c},{input:"TT",tag:"mo",output:"\u22A4",tex:"top",ttype:c},{input:"|--",tag:"mo",output:"\u22A2",tex:"vdash",ttype:c},{input:"|==",tag:"mo",output:"\u22A8",tex:"models",ttype:c},{input:"(",tag:"mo",output:"(",tex:"left(",ttype:b},{input:")",tag:"mo",output:")",tex:"right)",ttype:h},{input:"[",tag:"mo",output:"[",tex:"left[",ttype:b},{input:"]",tag:"mo",output:"]",tex:"right]",ttype:h},{input:"{",tag:"mo",output:"{",tex:null,ttype:b},{input:"}",tag:"mo",output:"}",tex:null,ttype:h},{input:"|",tag:"mo",output:"|",tex:null,ttype:m},{input:":|:",tag:"mo",output:"|",tex:null,ttype:c},{input:"|:",tag:"mo",output:"|",tex:null,ttype:b},{input:":|",tag:"mo",output:"|",tex:null,ttype:h},{input:"(:",tag:"mo",output:"\u2329",tex:"langle",ttype:b},{input:":)",tag:"mo",output:"\u232A",tex:"rangle",ttype:h},{input:"<<",tag:"mo",output:"\u2329",tex:null,ttype:b},{input:">>",tag:"mo",output:"\u232A",tex:null,ttype:h},{input:"{:",tag:"mo",output:"{:",tex:null,ttype:b,invisible:true},{input:":}",tag:"mo",output:":}",tex:null,ttype:h,invisible:true},{input:"int",tag:"mo",output:"\u222B",tex:null,ttype:c},{input:"dx",tag:"mi",output:"{:d x:}",tex:null,ttype:V},{input:"dy",tag:"mi",output:"{:d y:}",tex:null,ttype:V},{input:"dz",tag:"mi",output:"{:d z:}",tex:null,ttype:V},{input:"dt",tag:"mi",output:"{:d t:}",tex:null,ttype:V},{input:"oint",tag:"mo",output:"\u222E",tex:null,ttype:c},{input:"del",tag:"mo",output:"\u2202",tex:"partial",ttype:c},{input:"grad",tag:"mo",output:"\u2207",tex:"nabla",ttype:c},{input:"+-",tag:"mo",output:"\u00B1",tex:"pm",ttype:c},{input:"O/",tag:"mo",output:"\u2205",tex:"emptyset",ttype:c},{input:"oo",tag:"mo",output:"\u221E",tex:"infty",ttype:c},{input:"aleph",tag:"mo",output:"\u2135",tex:null,ttype:c},{input:"...",tag:"mo",output:"...",tex:"ldots",ttype:c},{input:":.",tag:"mo",output:"\u2234",tex:"therefore",ttype:c},{input:":'",tag:"mo",output:"\u2235",tex:"because",ttype:c},{input:"/_",tag:"mo",output:"\u2220",tex:"angle",ttype:c},{input:"/_\\",tag:"mo",output:"\u25B3",tex:"triangle",ttype:c},{input:"'",tag:"mo",output:"\u2032",tex:"prime",ttype:c},{input:"tilde",tag:"mover",output:"~",tex:null,ttype:A,acc:true},{input:"\\ ",tag:"mo",output:"\u00A0",tex:null,ttype:c},{input:"frown",tag:"mo",output:"\u2322",tex:null,ttype:c},{input:"quad",tag:"mo",output:"\u00A0\u00A0",tex:null,ttype:c},{input:"qquad",tag:"mo",output:"\u00A0\u00A0\u00A0\u00A0",tex:null,ttype:c},{input:"cdots",tag:"mo",output:"\u22EF",tex:null,ttype:c},{input:"vdots",tag:"mo",output:"\u22EE",tex:null,ttype:c},{input:"ddots",tag:"mo",output:"\u22F1",tex:null,ttype:c},{input:"diamond",tag:"mo",output:"\u22C4",tex:null,ttype:c},{input:"square",tag:"mo",output:"\u25A1",tex:null,ttype:c},{input:"|__",tag:"mo",output:"\u230A",tex:"lfloor",ttype:c},{input:"__|",tag:"mo",output:"\u230B",tex:"rfloor",ttype:c},{input:"|~",tag:"mo",output:"\u2308",tex:"lceiling",ttype:c},{input:"~|",tag:"mo",output:"\u2309",tex:"rceiling",ttype:c},{input:"CC",tag:"mo",output:"\u2102",tex:null,ttype:c},{input:"NN",tag:"mo",output:"\u2115",tex:null,ttype:c},{input:"QQ",tag:"mo",output:"\u211A",tex:null,ttype:c},{input:"RR",tag:"mo",output:"\u211D",tex:null,ttype:c},{input:"ZZ",tag:"mo",output:"\u2124",tex:null,ttype:c},{input:"f",tag:"mi",output:"f",tex:null,ttype:A,func:true},{input:"g",tag:"mi",output:"g",tex:null,ttype:A,func:true},{input:"lim",tag:"mo",output:"lim",tex:null,ttype:L},{input:"Lim",tag:"mo",output:"Lim",tex:null,ttype:L},{input:"sin",tag:"mo",output:"sin",tex:null,ttype:A,func:true},{input:"cos",tag:"mo",output:"cos",tex:null,ttype:A,func:true},{input:"tan",tag:"mo",output:"tan",tex:null,ttype:A,func:true},{input:"sinh",tag:"mo",output:"sinh",tex:null,ttype:A,func:true},{input:"cosh",tag:"mo",output:"cosh",tex:null,ttype:A,func:true},{input:"tanh",tag:"mo",output:"tanh",tex:null,ttype:A,func:true},{input:"cot",tag:"mo",output:"cot",tex:null,ttype:A,func:true},{input:"sec",tag:"mo",output:"sec",tex:null,ttype:A,func:true},{input:"csc",tag:"mo",output:"csc",tex:null,ttype:A,func:true},{input:"arcsin",tag:"mo",output:"arcsin",tex:null,ttype:A,func:true},{input:"arccos",tag:"mo",output:"arccos",tex:null,ttype:A,func:true},{input:"arctan",tag:"mo",output:"arctan",tex:null,ttype:A,func:true},{input:"coth",tag:"mo",output:"coth",tex:null,ttype:A,func:true},{input:"sech",tag:"mo",output:"sech",tex:null,ttype:A,func:true},{input:"csch",tag:"mo",output:"csch",tex:null,ttype:A,func:true},{input:"exp",tag:"mo",output:"exp",tex:null,ttype:A,func:true},{input:"abs",tag:"mo",output:"abs",tex:null,ttype:A,rewriteleftright:["|","|"]},{input:"norm",tag:"mo",output:"norm",tex:null,ttype:A,rewriteleftright:["\u2225","\u2225"]},{input:"floor",tag:"mo",output:"floor",tex:null,ttype:A,rewriteleftright:["\u230A","\u230B"]},{input:"ceil",tag:"mo",output:"ceil",tex:null,ttype:A,rewriteleftright:["\u2308","\u2309"]},{input:"log",tag:"mo",output:"log",tex:null,ttype:A,func:true},{input:"ln",tag:"mo",output:"ln",tex:null,ttype:A,func:true},{input:"det",tag:"mo",output:"det",tex:null,ttype:A,func:true},{input:"dim",tag:"mo",output:"dim",tex:null,ttype:c},{input:"mod",tag:"mo",output:"mod",tex:null,ttype:c},{input:"gcd",tag:"mo",output:"gcd",tex:null,ttype:A,func:true},{input:"lcm",tag:"mo",output:"lcm",tex:null,ttype:A,func:true},{input:"lub",tag:"mo",output:"lub",tex:null,ttype:c},{input:"glb",tag:"mo",output:"glb",tex:null,ttype:c},{input:"min",tag:"mo",output:"min",tex:null,ttype:L},{input:"max",tag:"mo",output:"max",tex:null,ttype:L},{input:"Sin",tag:"mo",output:"Sin",tex:null,ttype:A,func:true},{input:"Cos",tag:"mo",output:"Cos",tex:null,ttype:A,func:true},{input:"Tan",tag:"mo",output:"Tan",tex:null,ttype:A,func:true},{input:"Arcsin",tag:"mo",output:"Arcsin",tex:null,ttype:A,func:true},{input:"Arccos",tag:"mo",output:"Arccos",tex:null,ttype:A,func:true},{input:"Arctan",tag:"mo",output:"Arctan",tex:null,ttype:A,func:true},{input:"Sinh",tag:"mo",output:"Sinh",tex:null,ttype:A,func:true},{input:"Cosh",tag:"mo",output:"Cosh",tex:null,ttype:A,func:true},{input:"Tanh",tag:"mo",output:"Tanh",tex:null,ttype:A,func:true},{input:"Cot",tag:"mo",output:"Cot",tex:null,ttype:A,func:true},{input:"Sec",tag:"mo",output:"Sec",tex:null,ttype:A,func:true},{input:"Csc",tag:"mo",output:"Csc",tex:null,ttype:A,func:true},{input:"Log",tag:"mo",output:"Log",tex:null,ttype:A,func:true},{input:"Ln",tag:"mo",output:"Ln",tex:null,ttype:A,func:true},{input:"Abs",tag:"mo",output:"abs",tex:null,ttype:A,notexcopy:true,rewriteleftright:["|","|"]},{input:"uarr",tag:"mo",output:"\u2191",tex:"uparrow",ttype:c},{input:"darr",tag:"mo",output:"\u2193",tex:"downarrow",ttype:c},{input:"rarr",tag:"mo",output:"\u2192",tex:"rightarrow",ttype:c},{input:"->",tag:"mo",output:"\u2192",tex:"to",ttype:c},{input:">->",tag:"mo",output:"\u21A3",tex:"rightarrowtail",ttype:c},{input:"->>",tag:"mo",output:"\u21A0",tex:"twoheadrightarrow",ttype:c},{input:">->>",tag:"mo",output:"\u2916",tex:"twoheadrightarrowtail",ttype:c},{input:"|->",tag:"mo",output:"\u21A6",tex:"mapsto",ttype:c},{input:"larr",tag:"mo",output:"\u2190",tex:"leftarrow",ttype:c},{input:"harr",tag:"mo",output:"\u2194",tex:"leftrightarrow",ttype:c},{input:"rArr",tag:"mo",output:"\u21D2",tex:"Rightarrow",ttype:c},{input:"lArr",tag:"mo",output:"\u21D0",tex:"Leftarrow",ttype:c},{input:"hArr",tag:"mo",output:"\u21D4",tex:"Leftrightarrow",ttype:c},{input:"sqrt",tag:"msqrt",output:"sqrt",tex:null,ttype:A},{input:"root",tag:"mroot",output:"root",tex:null,ttype:U},{input:"frac",tag:"mfrac",output:"/",tex:null,ttype:U},{input:"/",tag:"mfrac",output:"/",tex:null,ttype:i},{input:"stackrel",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"overset",tag:"mover",output:"stackrel",tex:null,ttype:U},{input:"underset",tag:"munder",output:"stackrel",tex:null,ttype:U},{input:"_",tag:"msub",output:"_",tex:null,ttype:i},{input:"^",tag:"msup",output:"^",tex:null,ttype:i},{input:"hat",tag:"mover",output:"\u005E",tex:null,ttype:A,acc:true},{input:"bar",tag:"mover",output:"\u00AF",tex:"overline",ttype:A,acc:true},{input:"vec",tag:"mover",output:"\u2192",tex:null,ttype:A,acc:true},{input:"dot",tag:"mover",output:".",tex:null,ttype:A,acc:true},{input:"ddot",tag:"mover",output:"..",tex:null,ttype:A,acc:true},{input:"overarc",tag:"mover",output:"\u23DC",tex:"overparen",ttype:A,acc:true},{input:"ul",tag:"munder",output:"\u0332",tex:"underline",ttype:A,acc:true},{input:"ubrace",tag:"munder",output:"\u23DF",tex:"underbrace",ttype:K,acc:true},{input:"obrace",tag:"mover",output:"\u23DE",tex:"overbrace",ttype:K,acc:true},{input:"text",tag:"mtext",output:"text",tex:null,ttype:Y},{input:"mbox",tag:"mtext",output:"mbox",tex:null,ttype:Y},{input:"color",tag:"mstyle",ttype:U},{input:"id",tag:"mrow",ttype:U},{input:"class",tag:"mrow",ttype:U},{input:"cancel",tag:"menclose",output:"cancel",tex:null,ttype:A},k,{input:"bb",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"bb",tex:null,ttype:A},{input:"mathbf",tag:"mstyle",atname:"mathvariant",atval:"bold",output:"mathbf",tex:null,ttype:A},{input:"sf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"sf",tex:null,ttype:A},{input:"mathsf",tag:"mstyle",atname:"mathvariant",atval:"sans-serif",output:"mathsf",tex:null,ttype:A},{input:"bbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"bbb",tex:null,ttype:A,codes:w},{input:"mathbb",tag:"mstyle",atname:"mathvariant",atval:"double-struck",output:"mathbb",tex:null,ttype:A,codes:w},{input:"cc",tag:"mstyle",atname:"mathvariant",atval:"script",output:"cc",tex:null,ttype:A,codes:D},{input:"mathcal",tag:"mstyle",atname:"mathvariant",atval:"script",output:"mathcal",tex:null,ttype:A,codes:D},{input:"tt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"tt",tex:null,ttype:A},{input:"mathtt",tag:"mstyle",atname:"mathvariant",atval:"monospace",output:"mathtt",tex:null,ttype:A},{input:"fr",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"fr",tex:null,ttype:A,codes:H},{input:"mathfrak",tag:"mstyle",atname:"mathvariant",atval:"fraktur",output:"mathfrak",tex:null,ttype:A,codes:H}];function T(ac,ab){if(ac.input>ab.input){return 1}else{return -1}}var S=[];function n(){var ac;var ab=z.length;for(ac=0;ac>1;if(ac[ab]=S[ab]}s=y;if(af!=""){y=z[ae].ttype;return z[ae]}y=c;ab=1;ak=ah.slice(0,1);var ai=true;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}if(ak==d){ak=ah.slice(ab,ab+1);if("0"<=ak&&ak<="9"){ai=false;ab++;while("0"<=ak&&ak<="9"&&ab<=ah.length){ak=ah.slice(ab,ab+1);ab++}}}if((ai&&ab>1)||ab>2){ak=ah.slice(0,ab-1);aj="mn"}else{ab=2;ak=ah.slice(0,1);aj=(("A">ak||ak>"Z")&&("a">ak||ak>"z")?"mo":"mi")}if(ak=="-"&&s==i){y=i;return{input:ak,tag:aj,output:ak,ttype:A,func:true}}return{input:ak,tag:aj,output:ak,ttype:c}}function R(ac){var ab;if(!ac.hasChildNodes()){return}if(ac.firstChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.firstChild.firstChild.nodeValue;if(ab=="("||ab=="["||ab=="{"){ac.removeChild(ac.firstChild)}}if(ac.lastChild.hasChildNodes()&&(ac.nodeName=="mrow"||ac.nodeName=="M:MROW")){ab=ac.lastChild.firstChild.nodeValue;if(ab==")"||ab=="]"||ab=="}"){ac.removeChild(ac.lastChild)}}}var F,s,y;function G(ai){var ad,ac,al,af,ak,ag=e.createDocumentFragment();ai=p(ai,0);ad=j(ai);if(ad==null||ad.ttype==h&&F>0){return[null,ai]}if(ad.ttype==V){ai=ad.output+p(ai,ad.input.length);ad=j(ai)}switch(ad.ttype){case L:case c:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai];case b:F++;ai=p(ai,ad.input.length);al=q(ai,true);F--;if(typeof ad.invisible=="boolean"&&ad.invisible){ac=O("mrow",al[0])}else{ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0])}return[ac,al[1]];case Y:if(ad!=k){ai=p(ai,ad.input.length)}if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}else{if(ad==k){af=ai.slice(1).indexOf('"')+1}else{af=0}}}}if(af==-1){af=ai.length}ak=ai.slice(1,af);if(ak.charAt(0)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ag.appendChild(O(ad.tag,e.createTextNode(ak)));if(ak.charAt(ak.length-1)==" "){ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac)}ai=p(ai,af+1);return[O("mrow",ag),ai];case K:case A:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O(ad.tag,e.createTextNode(ad.output)),ai]}if(typeof ad.func=="boolean"&&ad.func){ak=ai.charAt(0);if(ak=="^"||ak=="_"||ak=="/"||ak=="|"||ak==","||(ad.input.length==1&&ad.input.match(/\w/)&&ak!="(")){return[O(ad.tag,e.createTextNode(ad.output)),ai]}else{ac=O("mrow",O(ad.tag,e.createTextNode(ad.output)));ac.appendChild(al[0]);return[ac,al[1]]}}R(al[0]);if(ad.input=="sqrt"){return[O(ad.tag,al[0]),al[1]]}else{if(typeof ad.rewriteleftright!="undefined"){ac=O("mrow",O("mo",e.createTextNode(ad.rewriteleftright[0])));ac.appendChild(al[0]);ac.appendChild(O("mo",e.createTextNode(ad.rewriteleftright[1])));return[ac,al[1]]}else{if(ad.input=="cancel"){ac=O(ad.tag,al[0]);ac.setAttribute("notation","updiagonalstrike");return[ac,al[1]]}else{if(typeof ad.acc=="boolean"&&ad.acc){ac=O(ad.tag,al[0]);var ah=O("mo",e.createTextNode(ad.output));if(ad.input=="vec"&&((al[0].nodeName=="mrow"&&al[0].childNodes.length==1&&al[0].firstChild.firstChild.nodeValue!==null&&al[0].firstChild.firstChild.nodeValue.length==1)||(al[0].firstChild.nodeValue!==null&&al[0].firstChild.nodeValue.length==1))){ah.setAttribute("stretchy",false)}ac.appendChild(ah);return[ac,al[1]]}else{if(!l&&typeof ad.codes!="undefined"){for(af=0;af64&&ak.charCodeAt(ae)<91){aj=aj+ad.codes[ak.charCodeAt(ae)-65]}else{if(ak.charCodeAt(ae)>96&&ak.charCodeAt(ae)<123){aj=aj+ad.codes[ak.charCodeAt(ae)-71]}else{aj=aj+ak.charAt(ae)}}}if(al[0].nodeName=="mi"){al[0]=O("mo").appendChild(e.createTextNode(aj))}else{al[0].replaceChild(O("mo").appendChild(e.createTextNode(aj)),al[0].childNodes[af])}}}}ac=O(ad.tag,al[0]);ac.setAttribute(ad.atname,ad.atval);return[ac,al[1]]}}}}case U:ai=p(ai,ad.input.length);al=G(ai);if(al[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(al[0]);var ab=G(al[1]);if(ab[0]==null){return[O("mo",e.createTextNode(ad.input)),ai]}R(ab[0]);if(["color","class","id"].indexOf(ad.input)>=0){if(ai.charAt(0)=="{"){af=ai.indexOf("}")}else{if(ai.charAt(0)=="("){af=ai.indexOf(")")}else{if(ai.charAt(0)=="["){af=ai.indexOf("]")}}}ak=ai.slice(1,af);ac=O(ad.tag,ab[0]);if(ad.input==="color"){ac.setAttribute("mathcolor",ak)}else{if(ad.input==="class"){ac.setAttribute("class",ak)}else{if(ad.input==="id"){ac.setAttribute("id",ak)}}}return[ac,ab[1]]}if(ad.input=="root"||ad.output=="stackrel"){ag.appendChild(ab[0])}ag.appendChild(al[0]);if(ad.input=="frac"){ag.appendChild(ab[0])}return[O(ad.tag,ag),ab[1]];case i:ai=p(ai,ad.input.length);return[O("mo",e.createTextNode(ad.output)),ai];case a:ai=p(ai,ad.input.length);ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);ag.appendChild(O(ad.tag,e.createTextNode(ad.output)));ac=O("mspace");ac.setAttribute("width","1ex");ag.appendChild(ac);return[O("mrow",ag),ai];case m:F++;ai=p(ai,ad.input.length);al=q(ai,false);F--;ak="";if(al[0].lastChild!=null){ak=al[0].lastChild.firstChild.nodeValue}if(ak=="|"&&ai.charAt(0)!==","){ac=O("mo",e.createTextNode(ad.output));ac=O("mrow",ac);ac.appendChild(al[0]);return[ac,al[1]]}else{ac=O("mo",e.createTextNode("\u2223"));ac=O("mrow",ac);return[ac,ai]}default:ai=p(ai,ad.input.length);return[O(ad.tag,e.createTextNode(ad.output)),ai]}}function t(ah){var af,ai,ag,ae,ab,ad;ah=p(ah,0);ai=j(ah);ab=G(ah);ae=ab[0];ah=ab[1];af=j(ah);if(af.ttype==i&&af.input!="/"){ah=p(ah,af.input.length);ab=G(ah);if(ab[0]==null){ab[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ab[0])}ah=ab[1];ad=(ai.ttype==L||ai.ttype==K);if(af.input=="_"){ag=j(ah);if(ag.input=="^"){ah=p(ah,ag.input.length);var ac=G(ah);R(ac[0]);ah=ac[1];ae=O((ad?"munderover":"msubsup"),ae);ae.appendChild(ab[0]);ae.appendChild(ac[0]);ae=O("mrow",ae)}else{ae=O((ad?"munder":"msub"),ae);ae.appendChild(ab[0])}}else{if(af.input=="^"&&ad){ae=O("mover",ae);ae.appendChild(ab[0])}else{ae=O(af.tag,ae);ae.appendChild(ab[0])}}if(typeof ai.func!="undefined"&&ai.func){ag=j(ah);if(ag.ttype!=i&&ag.ttype!=h){ab=t(ah);ae=O("mrow",ae);ae.appendChild(ab[0]);ah=ab[1]}}}return[ae,ah]}function q(ak,aj){var ao,al,ag,ar,ah=e.createDocumentFragment();do{ak=p(ak,0);ag=t(ak);al=ag[0];ak=ag[1];ao=j(ak);if(ao.ttype==i&&ao.input=="/"){ak=p(ak,ao.input.length);ag=t(ak);if(ag[0]==null){ag[0]=O("mo",e.createTextNode("\u25A1"))}else{R(ag[0])}ak=ag[1];R(al);al=O(ao.tag,al);al.appendChild(ag[0]);ah.appendChild(al);ao=j(ak)}else{if(al!=undefined){ah.appendChild(al)}}}while((ao.ttype!=h&&(ao.ttype!=m||aj)||F==0)&&ao!=null&&ao.output!="");if(ao.ttype==h||ao.ttype==m){var at=ah.childNodes.length;if(at>0&&ah.childNodes[at-1].nodeName=="mrow"&&ah.childNodes[at-1].lastChild&&ah.childNodes[at-1].lastChild.firstChild){var av=ah.childNodes[at-1].lastChild.firstChild.nodeValue;if(av==")"||av=="]"){var ac=ah.childNodes[at-1].firstChild.firstChild.nodeValue;if(ac=="("&&av==")"&&ao.output!="}"||ac=="["&&av=="]"){var ad=[];var ap=true;var am=ah.childNodes.length;for(ar=0;ap&&ar1){ap=ad[ar].length==ad[ar-2].length}}ap=ap&&(ad.length>1||ad[0].length>0);var af=[];if(ap){var ae,ab,ai,an,au=e.createDocumentFragment();for(ar=0;ar2){ah.removeChild(ah.firstChild);ah.removeChild(ah.firstChild)}au.appendChild(O("mtr",ae))}al=O("mtable",au);al.setAttribute("columnlines",af.join(" "));if(typeof ao.invisible=="boolean"&&ao.invisible){al.setAttribute("columnalign","left")}ah.replaceChild(al,ah.firstChild)}}}}ak=p(ak,ao.input.length);if(typeof ao.invisible!="boolean"||!ao.invisible){al=O("mo",e.createTextNode(ao.output));ah.appendChild(al)}}return[ah,ak]}function M(ad,ac){var ae,ab;F=0;ad=ad.replace(/ /g,"");ad=ad.replace(/>/g,">");ad=ad.replace(/</g,"<");ae=q(ad.replace(/^\s+/g,""),false)[0];ab=O("mstyle",ae);if(C!=""){ab.setAttribute("mathcolor",C)}if(mathfontsize!=""){ab.setAttribute("fontsize",mathfontsize);ab.setAttribute("mathsize",mathfontsize)}if(mathfontfamily!=""){ab.setAttribute("fontfamily",mathfontfamily);ab.setAttribute("mathvariant",mathfontfamily)}if(o){ab.setAttribute("displaystyle","true")}ab=O("math",ab);if(v){ab.setAttribute("title",ad.replace(/\s+/g," "))}return ab}v=false;mathfontfamily="";C="";mathfontsize="";(function(){for(var ac=0,ab=z.length;ac *":{display:"table-row!important"},".MJXp-surd":{"vertical-align":"top"},".MJXp-surd > *":{display:"block!important"},".MJXp-script-box > * ":{display:"table!important",height:"50%"},".MJXp-script-box > * > *":{display:"table-cell!important","vertical-align":"top"},".MJXp-script-box > *:last-child > *":{"vertical-align":"bottom"},".MJXp-script-box > * > * > *":{display:"block!important"},".MJXp-mphantom":{visibility:"hidden"},".MJXp-munderover, .MJXp-munder":{display:"inline-table!important"},".MJXp-over":{display:"inline-block!important","text-align":"center"},".MJXp-over > *":{display:"block!important"},".MJXp-munderover > *, .MJXp-munder > *":{display:"table-row!important"},".MJXp-mtable":{"vertical-align":".25em",margin:"0 .125em"},".MJXp-mtable > *":{display:"inline-table!important","vertical-align":"middle"},".MJXp-mtr":{display:"table-row!important"},".MJXp-mtd":{display:"table-cell!important","text-align":"center",padding:".5em 0 0 .5em"},".MJXp-mtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-mlabeledtr":{display:"table-row!important"},".MJXp-mlabeledtr > .MJXp-mtd:first-child":{"padding-left":0},".MJXp-mlabeledtr:first-child > .MJXp-mtd":{"padding-top":0},".MJXp-merror":{"background-color":"#FFFF88",color:"#CC0000",border:"1px solid #CC0000",padding:"1px 3px","font-style":"normal","font-size":"90%"}};(function(){for(var n=0;n<10;n++){var o="scaleX(."+n+")";m[".MJXp-scale"+n]={"-webkit-transform":o,"-moz-transform":o,"-ms-transform":o,"-o-transform":o,transform:o}}})();var k=1000000;var c="V",l="H";g.Augment({settings:b.config.menuSettings,config:{styles:m},hideProcessedMath:false,maxStretchyParts:1000,Config:function(){if(!this.require){this.require=[]}this.SUPER(arguments).Config.call(this);var n=this.settings;if(n.scale){this.config.scale=n.scale}this.require.push(MathJax.OutputJax.extensionDir+"/MathEvents.js")},Startup:function(){j=MathJax.Extension.MathEvents.Event;a=MathJax.Extension.MathEvents.Touch;d=MathJax.Extension.MathEvents.Hover;this.ContextMenu=j.ContextMenu;this.Mousedown=j.AltContextMenu;this.Mouseover=d.Mouseover;this.Mouseout=d.Mouseout;this.Mousemove=d.Mousemove;var n=e.addElement(document.body,"div",{style:{width:"5in"}});this.pxPerInch=n.offsetWidth/5;n.parentNode.removeChild(n);return i.Styles(this.config.styles,["InitializePHTML",this])},InitializePHTML:function(){},preTranslate:function(p){var s=p.jax[this.id],t,q=s.length,u,r,v,o,n;for(t=0;tthis.PHTML.h){this.PHTML.h=q.PHTML.h}if(q.PHTML.d>this.PHTML.d){this.PHTML.d=q.PHTML.d}if(q.PHTML.t>this.PHTML.t){this.PHTML.t=q.PHTML.t}if(q.PHTML.b>this.PHTML.b){this.PHTML.b=q.PHTML.b}}}else{if(n.forceChild){e.addElement(p,"span")}}},PHTMLstretchChild:function(q,p,s){var r=this.data[q];if(r&&r.PHTMLcanStretch("Vertical",p,s)){var t=this.PHTML,o=r.PHTML,n=o.w;r.PHTMLstretchV(p,s);t.w+=o.w-n;if(o.h>t.h){t.h=o.h}if(o.d>t.d){t.d=o.d}}},PHTMLcreateSpan:function(n){if(!this.PHTML){this.PHTML={}}this.PHTML={w:0,h:0,d:0,l:0,r:0,t:0,b:0};if(this.inferred){return n}if(this.type==="mo"&&this.data.join("")==="\u222B"){g.lastIsInt=true}else{if(this.type!=="mspace"||this.width!=="negativethinmathspace"){g.lastIsInt=false}}if(!this.PHTMLspanID){this.PHTMLspanID=g.GetID()}var o=(this.id||"MJXp-Span-"+this.PHTMLspanID);return e.addElement(n,"span",{className:"MJXp-"+this.type,id:o})},PHTMLspanElement:function(){if(!this.PHTMLspanID){return null}return document.getElementById(this.id||"MJXp-Span-"+this.PHTMLspanID)},PHTMLhandleToken:function(o){var n=this.getValues("mathvariant");if(n.mathvariant!==h.VARIANT.NORMAL){o.className+=" "+g.VARIANT[n.mathvariant]}},PHTMLhandleStyle:function(n){if(this.style){n.style.cssText=this.style}},PHTMLhandleColor:function(n){if(this.mathcolor){n.style.color=this.mathcolor}if(this.mathbackground){n.style.backgroundColor=this.mathbackground}},PHTMLhandleScriptlevel:function(n){var o=this.Get("scriptlevel");if(o){n.className+=" MJXp-script"}},PHTMLhandleText:function(y,A){var v,p;var z=0,o=0,q=0;for(var s=0,r=A.length;s=55296&&p<56319){s++;p=(((p-55296)<<10)+(A.charCodeAt(s)-56320))+65536}var t=0.7,u=0.22,x=0.5;if(p<127){if(v.match(/[A-Za-ehik-or-xz0-9]/)){u=0}if(v.match(/[A-HK-Z]/)){x=0.67}else{if(v.match(/[IJ]/)){x=0.36}}if(v.match(/[acegm-su-z]/)){t=0.45}else{if(v.match(/[ij]/)){t=0.75}}if(v.match(/[ijlt]/)){x=0.28}}if(g.DELIMITERS[v]){x=g.DELIMITERS[v].w||0.4}if(t>z){z=t}if(u>o){o=u}q+=x}if(!this.CHML){this.PHTML={}}this.PHTML={h:0.9,d:0.3,w:q,l:0,r:0,t:z,b:o};e.addText(y,A)},PHTMLbboxFor:function(o){if(this.data[o]&&this.data[o].PHTML){return this.data[o].PHTML}return{w:0,h:0,d:0,l:0,r:0,t:0,b:0}},PHTMLcanStretch:function(q,o,p){if(this.isEmbellished()){var n=this.Core();if(n&&n!==this){return n.PHTMLcanStretch(q,o,p)}}return false},PHTMLstretchV:function(n,o){},PHTMLstretchH:function(n){},CoreParent:function(){var n=this;while(n&&n.isEmbellished()&&n.CoreMO()===this&&!n.isa(h.math)){n=n.Parent()}return n},CoreText:function(n){if(!n){return""}if(n.isEmbellished()){return n.CoreMO().data.join("")}while((n.isa(h.mrow)||n.isa(h.TeXAtom)||n.isa(h.mstyle)||n.isa(h.mphantom))&&n.data.length===1&&n.data[0]){n=n.data[0]}if(!n.isToken){return""}else{return n.data.join("")}}});h.chars.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.entity.Augment({toPreviewHTML:function(n){var o=this.toString().replace(/[\u2061-\u2064]/g,"");this.PHTMLhandleText(n,o)}});h.math.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n);if(this.Get("display")==="block"){n.className+=" MJXp-display"}return n}});h.mo.Augment({toPreviewHTML:function(o){o=this.PHTMLdefaultSpan(o);this.PHTMLadjustAccent(o);var n=this.getValues("lspace","rspace","scriptlevel","displaystyle","largeop");if(n.scriptlevel===0){this.PHTML.l=g.length2em(n.lspace);this.PHTML.r=g.length2em(n.rspace);o.style.marginLeft=g.Em(this.PHTML.l);o.style.marginRight=g.Em(this.PHTML.r)}else{this.PHTML.l=0.15;this.PHTML.r=0.1}if(n.displaystyle&&n.largeop){var p=e.Element("span",{className:"MJXp-largeop"});p.appendChild(o.firstChild);o.appendChild(p);this.PHTML.h*=1.2;this.PHTML.d*=1.2;if(this.data.join("")==="\u222B"){p.className+=" MJXp-int"}}return o},PHTMLadjustAccent:function(p){var o=this.CoreParent();if(o&&o.isa(h.munderover)&&this.CoreText(o.data[o.base]).length===1){var q=o.data[o.over],n=o.data[o.under];var s=this.data.join(""),r;if(q&&this===q.CoreMO()&&o.Get("accent")){r=g.REMAPACCENT[s]}else{if(n&&this===n.CoreMO()&&o.Get("accentunder")){r=g.REMAPACCENTUNDER[s]}}if(r){s=p.innerHTML=r}if(s.match(/[\u02C6-\u02DC\u00A8]/)){this.PHTML.acc=-0.52}else{if(s==="\u2192"){this.PHTML.acc=-0.15;this.PHTML.vec=true}}}},PHTMLcanStretch:function(q,o,p){if(!this.Get("stretchy")){return false}var r=this.data.join("");if(r.length>1){return false}r=g.DELIMITERS[r];var n=(r&&r.dir===q.substr(0,1));if(n){n=(this.PHTML.h!==o||this.PHTML.d!==p||(this.Get("minsize",true)||this.Get("maxsize",true)))}return n},PHTMLstretchV:function(p,u){var o=this.PHTMLspanElement(),t=this.PHTML;var n=this.getValues("symmetric","maxsize","minsize");if(n.symmetric){l=2*Math.max(p-0.25,u+0.25)}else{l=p+u}n.maxsize=g.length2em(n.maxsize,t.h+t.d);n.minsize=g.length2em(n.minsize,t.h+t.d);l=Math.max(n.minsize,Math.min(n.maxsize,l));var s=l/(t.h+t.d-0.3);var q=e.Element("span",{style:{"font-size":g.Em(s)}});if(s>1.25){var r=Math.ceil(1.25/s*10);q.className="MJXp-right MJXp-scale"+r;q.style.marginLeft=g.Em(t.w*(r/10-1)+0.07);t.w*=s*r/10}q.appendChild(o.firstChild);o.appendChild(q);if(n.symmetric){o.style.verticalAlign=g.Em(0.25*(1-s))}}});h.mspace.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q);var o=this.getValues("height","depth","width");var n=g.length2em(o.width),p=g.length2em(o.height),s=g.length2em(o.depth);var r=this.PHTML;r.w=n;r.h=p;r.d=s;if(n<0){if(!g.lastIsInt){q.style.marginLeft=g.Em(n)}n=0}q.style.width=g.Em(n);q.style.height=g.Em(p+s);if(s){q.style.verticalAlign=g.Em(-s)}return q}});h.mpadded.Augment({toPreviewHTML:function(u){u=this.PHTMLdefaultSpan(u,{childSpans:true,className:"MJXp-box",forceChild:true});var o=u.firstChild;var v=this.getValues("width","height","depth","lspace","voffset");var s=this.PHTMLdimen(v.lspace);var q=0,n=0,t=s.len,r=-s.len,p=0;if(v.width!==""){s=this.PHTMLdimen(v.width,"w",0);if(s.pm){r+=s.len}else{u.style.width=g.Em(s.len)}}if(v.height!==""){s=this.PHTMLdimen(v.height,"h",0);if(!s.pm){q+=-this.PHTMLbboxFor(0).h}q+=s.len}if(v.depth!==""){s=this.PHTMLdimen(v.depth,"d",0);if(!s.pm){n+=-this.PHTMLbboxFor(0).d;p+=-s.len}n+=s.len}if(v.voffset!==""){s=this.PHTMLdimen(v.voffset);q-=s.len;n+=s.len;p+=s.len}if(q){o.style.marginTop=g.Em(q)}if(n){o.style.marginBottom=g.Em(n)}if(t){o.style.marginLeft=g.Em(t)}if(r){o.style.marginRight=g.Em(r)}if(p){u.style.verticalAlign=g.Em(p)}return u},PHTMLdimen:function(q,r,n){if(n==null){n=-k}q=String(q);var o=q.match(/width|height|depth/);var p=(o?this.PHTML[o[0].charAt(0)]:(r?this.PHTML[r]:0));return{len:g.length2em(q,p)||0,pm:!!q.match(/^[-+]/)}}});h.munderover.Augment({toPreviewHTML:function(r){var t=this.getValues("displaystyle","accent","accentunder","align");var n=this.data[this.base];if(!t.displaystyle&&n!=null&&(n.movablelimits||n.CoreMO().Get("movablelimits"))){r=h.msubsup.prototype.toPreviewHTML.call(this,r);r.className=r.className.replace(/munderover/,"msubsup");return r}r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"",noBBox:true});var p=this.PHTMLbboxFor(this.over),v=this.PHTMLbboxFor(this.under),u=this.PHTMLbboxFor(this.base),s=this.PHTML,o=p.acc;if(this.data[this.over]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=p.l=r.lastChild.firstChild.style.marginRight=p.r=0}var q=e.Element("span",{},[["span",{className:"MJXp-over"}]]);q.firstChild.appendChild(r.lastChild);if(r.childNodes.length>(this.data[this.under]?1:0)){q.firstChild.appendChild(r.firstChild)}this.data[this.over].PHTMLhandleScriptlevel(q.firstChild.firstChild);if(o!=null){if(p.vec){q.firstChild.firstChild.firstChild.style.fontSize="60%";p.h*=0.6;p.d*=0.6;p.w*=0.6}o=o-p.d+0.1;if(u.t!=null){o+=u.t-u.h}q.firstChild.firstChild.style.marginBottom=g.Em(o)}if(r.firstChild){r.insertBefore(q,r.firstChild)}else{r.appendChild(q)}}if(this.data[this.under]){if(r.lastChild.firstChild){r.lastChild.firstChild.style.marginLeft=v.l=r.lastChild.firstChild.marginRight=v.r=0}this.data[this.under].PHTMLhandleScriptlevel(r.lastChild)}s.w=Math.max(0.8*p.w,0.8*v.w,u.w);s.h=0.8*(p.h+p.d+(o||0))+u.h;s.d=u.d+0.8*(v.h+v.d);return r}});h.msubsup.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{noBBox:true});if(!this.data[this.base]){if(q.firstChild){q.insertBefore(e.Element("span"),q.firstChild)}else{q.appendChild(e.Element("span"))}}var s=this.data[this.base],p=this.data[this.sub],n=this.data[this.sup];if(!s){s={bbox:{h:0.8,d:0.2}}}q.firstChild.style.marginRight=".05em";var o=Math.max(0.4,s.PHTML.h-0.4),u=Math.max(0.2,s.PHTML.d+0.1);var t=this.PHTML;if(n&&p){var r=e.Element("span",{className:"MJXp-script-box",style:{height:g.Em(o+n.PHTML.h*0.8+u+p.PHTML.d*0.8),"vertical-align":g.Em(-u-p.PHTML.d*0.8)}},[["span",{},[["span",{},[["span",{style:{"margin-bottom":g.Em(-(n.PHTML.d-0.05))}}]]]]],["span",{},[["span",{},[["span",{style:{"margin-top":g.Em(-(n.PHTML.h-0.05))}}]]]]]]);p.PHTMLhandleScriptlevel(r.firstChild);n.PHTMLhandleScriptlevel(r.lastChild);r.firstChild.firstChild.firstChild.appendChild(q.lastChild);r.lastChild.firstChild.firstChild.appendChild(q.lastChild);q.appendChild(r);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+Math.max(n.PHTML.w,p.PHTML.w)+0.07}else{if(n){q.lastChild.style.verticalAlign=g.Em(o);n.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,n.PHTML.h*0.8+o);t.d=Math.max(s.PHTML.d,n.PHTML.d*0.8-o);t.w=s.PHTML.w+n.PHTML.w+0.07}else{if(p){q.lastChild.style.verticalAlign=g.Em(-u);p.PHTMLhandleScriptlevel(q.lastChild);t.h=Math.max(s.PHTML.h,p.PHTML.h*0.8-u);t.d=Math.max(s.PHTML.d,p.PHTML.d*0.8+u);t.w=s.PHTML.w+p.PHTML.w+0.07}}}return q}});h.mfrac.Augment({toPreviewHTML:function(r){r=this.PHTMLdefaultSpan(r,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var o=this.getValues("linethickness","displaystyle");if(!o.displaystyle){if(this.data[0]){this.data[0].PHTMLhandleScriptlevel(r.firstChild)}if(this.data[1]){this.data[1].PHTMLhandleScriptlevel(r.lastChild)}}var n=e.Element("span",{className:"MJXp-box"},[["span",{className:"MJXp-denom"},[["span",{},[["span",{className:"MJXp-rule",style:{height:"1em"}}]]],["span"]]]]);n.firstChild.lastChild.appendChild(r.lastChild);r.appendChild(n);var s=this.PHTMLbboxFor(0),p=this.PHTMLbboxFor(1),v=this.PHTML;v.w=Math.max(s.w,p.w)*0.8;v.h=s.h+s.d+0.1+0.25;v.d=p.h+p.d-0.25;v.l=v.r=0.125;o.linethickness=Math.max(0,g.length2em(o.linethickness||"0",0));if(o.linethickness){var u=n.firstChild.firstChild.firstChild;var q=g.Em(o.linethickness);u.style.borderTop="none";u.style.borderBottom=(o.linethickness<0.15?"1px":q)+" solid";u.style.margin=q+" 0";q=o.linethickness;n.style.marginTop=g.Em(3*q-1.2);r.style.verticalAlign=g.Em(1.5*q+0.1);v.h+=1.5*q-0.1;v.d+=1.5*q}else{n.style.marginTop="-.7em"}return r}});h.msqrt.Augment({toPreviewHTML:function(n){n=this.PHTMLdefaultSpan(n,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});this.PHTMLlayoutRoot(n,n.firstChild);return n},PHTMLlayoutRoot:function(u,n){var v=this.PHTMLbboxFor(0);var q=Math.ceil((v.h+v.d+0.14)*100),w=g.Em(14/q);var r=e.Element("span",{className:"MJXp-surd"},[["span",{style:{"font-size":q+"%","margin-top":w}},["\u221A"]]]);var s=e.Element("span",{className:"MJXp-root"},[["span",{className:"MJXp-rule",style:{"border-top":".08em solid"}}]]);var p=(1.2/2.2)*q/100;if(q>150){var o=Math.ceil(150/q*10);r.firstChild.className="MJXp-right MJXp-scale"+o;r.firstChild.style.marginLeft=g.Em(p*(o/10-1)/q*100);p=p*o/10;s.firstChild.style.borderTopWidth=g.Em(0.08/Math.sqrt(o/10))}s.appendChild(n);u.appendChild(r);u.appendChild(s);this.PHTML.h=v.h+0.18;this.PHTML.d=v.d;this.PHTML.w=v.w+p;return u}});h.mroot.Augment({toPreviewHTML:function(q){q=this.PHTMLdefaultSpan(q,{childSpans:true,className:"MJXp-box",forceChild:true,noBBox:true});var p=this.PHTMLbboxFor(1),n=q.removeChild(q.lastChild);var t=this.PHTMLlayoutRoot(e.Element("span"),q.firstChild);n.className="MJXp-script";var u=parseInt(t.firstChild.firstChild.style.fontSize);var o=0.55*(u/120)+p.d*0.8,s=-0.6*(u/120);if(u>150){s*=0.95*Math.ceil(150/u*10)/10}n.style.marginRight=g.Em(s);n.style.verticalAlign=g.Em(o);if(-s>p.w*0.8){n.style.marginLeft=g.Em(-s-p.w*0.8)}q.appendChild(n);q.appendChild(t);this.PHTML.w+=Math.max(0,p.w*0.8+s);this.PHTML.h=Math.max(this.PHTML.h,p.h*0.8+o);return q},PHTMLlayoutRoot:h.msqrt.prototype.PHTMLlayoutRoot});h.mfenced.Augment({toPreviewHTML:function(q){q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);this.addFakeNodes();this.PHTMLaddChild(q,"open",{});for(var p=0,n=this.data.length;ps){s=x.w}}}var o=this.PHTML;o.w=s;o.h=y/2+0.25;o.d=y/2-0.25;o.l=o.r=0.125;return E}});h.mlabeledtr.Augment({PHTMLdefaultSpan:function(q,o){if(!o){o={}}q=this.PHTMLcreateSpan(q);this.PHTMLhandleStyle(q);this.PHTMLhandleColor(q);if(this.isToken){this.PHTMLhandleToken(q)}for(var p=1,n=this.data.length;p/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); +!function(a,b){var c,d,e=a.config.menuSettings,f=Function.prototype.bind?function(a,b){return a.bind(b)}:function(a,b){return function(){a.apply(b,arguments)}},g=Object.keys||function(a){var b=[];for(var c in a)a.hasOwnProperty(c)&&b.push(c);return b},h=MathJax.Ajax.config.path;h.a11y||(h.a11y=a.config.root+"/extensions/a11y");var i=b["accessibility-menu"]={version:"1.5.0",prefix:"",defaults:{},modules:[],MakeOption:function(a){return i.prefix+a},GetOption:function(a){return e[i.MakeOption(a)]},AddDefaults:function(){for(var a,b=g(i.defaults),c=0;a=b[c];c++){var d=i.MakeOption(a);void 0===e[d]&&(e[d]=i.defaults[a])}},AddMenu:function(){for(var a,b=Array(this.modules.length),e=0;a=this.modules[e];e++)b[e]=a.placeHolder;var f=d.FindId("Accessibility");if(f)b.unshift(c.RULE()),f.submenu.items.push.apply(f.submenu.items,b);else{var g=(d.FindId("Settings","Renderer")||{}).submenu;g&&(b.unshift(c.RULE()),b.unshift(g.items.pop()),b.unshift(g.items.pop())),b.unshift("Accessibility");var f=c.SUBMENU.apply(c.SUBMENU,b),h=d.IndexOfId("Locale");h?d.items.splice(h,0,f):d.items.push(c.RULE(),f)}},Register:function(a){i.defaults[a.option]=!1,i.modules.push(a)},Startup:function(){c=MathJax.Menu.ITEM,d=MathJax.Menu.menu;for(var a,b=0;a=this.modules[b];b++)a.CreateMenu();this.AddMenu()},LoadExtensions:function(){for(var b,c=[],d=0;b=this.modules[d];d++)e[b.option]&&c.push(b.module);return c.length?a.Startup.loadArray(c):null}},j=MathJax.Extension.ModuleLoader=MathJax.Object.Subclass({option:"",name:["",""],module:"",placeHolder:null,submenu:!1,extension:null,Init:function(a,b,c,d,e){this.option=a,this.name=[b.replace(/ /g,""),b],this.module=c,this.extension=d,this.submenu=e||!1},CreateMenu:function(){var a=f(this.Load,this);this.submenu?this.placeHolder=c.SUBMENU(this.name,c.CHECKBOX(["Activate","Activate"],i.MakeOption(this.option),{action:a}),c.RULE(),c.COMMAND(["OptionsWhenActive","(Options when Active)"],null,{disabled:!0})):this.placeHolder=c.CHECKBOX(this.name,i.MakeOption(this.option),{action:a})},Load:function(){a.Queue(["Require",MathJax.Ajax,this.module,["Enable",this]])},Enable:function(a){var b=MathJax.Extension[this.extension];b&&(b.Enable(!0,!0),MathJax.Menu.saveCookie())}});i.Register(j("collapsible","Collapsible Math","[a11y]/collapsible.js","collapsible")),i.Register(j("autocollapse","Auto Collapse","[a11y]/auto-collapse.js","auto-collapse")),i.Register(j("explorer","Explorer","[a11y]/explorer.js","explorer",!0)),i.AddDefaults(),a.Register.StartupHook("End Extensions",function(){a.Register.StartupHook("MathMenu Ready",function(){i.Startup(),a.Startup.signal.Post("Accessibility Menu Ready")},5)},5),MathJax.Hub.Register.StartupHook("End Cookie",function(){MathJax.Callback.Queue(["LoadExtensions",i],["loadComplete",MathJax.Ajax,"[a11y]/accessibility-menu.js"])})}(MathJax.Hub,MathJax.Extension);MathJax.Ajax.loadComplete("[MathJax]/config/TeX-MML-AM_SVG.js"); diff --git a/revisions_report_files/mathjax-27/extensions/AssistiveMML.js b/revisions_report_files/mathjax-27/extensions/AssistiveMML.js new file mode 100644 index 0000000..77c51fe --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/AssistiveMML.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/AssistiveMML.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +(function(a,e,b,f){var c=b.config.menuSettings;var d=MathJax.Extension.AssistiveMML={version:"2.7.6",config:b.CombineConfig("AssistiveMML",{disabled:false,styles:{".MJX_Assistive_MathML":{position:"absolute!important",top:0,left:0,clip:(b.Browser.isMSIE&&(document.documentMode||0)<8?"rect(1px 1px 1px 1px)":"rect(1px, 1px, 1px, 1px)"),padding:"1px 0 0 0!important",border:"0!important",height:"1px!important",width:"1px!important",overflow:"hidden!important",display:"block!important","-webkit-touch-callout":"none","-webkit-user-select":"none","-khtml-user-select":"none","-moz-user-select":"none","-ms-user-select":"none","user-select":"none"},".MJX_Assistive_MathML.MJX_Assistive_MathML_Block":{width:"100%!important"}}}),Config:function(){if(!this.config.disabled&&c.assistiveMML==null){b.Config({menuSettings:{assistiveMML:true}})}a.Styles(this.config.styles);b.Register.MessageHook("End Math",function(g){if(c.assistiveMML){return d.AddAssistiveMathML(g[1])}})},AddAssistiveMathML:function(g){var h={jax:b.getAllJax(g),i:0,callback:MathJax.Callback({})};this.HandleMML(h);return h.callback},RemoveAssistiveMathML:function(k){var h=b.getAllJax(k),l;for(var j=0,g=h.length;j/g,"")}catch(k){if(!k.restart){throw k}return MathJax.Callback.After(["HandleMML",this,l],k.restart)}n.setAttribute("data-mathml",i);j=f.addElement(n,"span",{isMathJax:true,unselectable:"on",className:"MJX_Assistive_MathML"+(h.root.Get("display")==="block"?" MJX_Assistive_MathML_Block":"")});try{j.innerHTML=i}catch(k){}n.style.position="relative";n.setAttribute("role","presentation");n.firstChild.setAttribute("aria-hidden","true");j.setAttribute("role","presentation")}l.i++}l.callback()}};b.Startup.signal.Post("AssistiveMML Ready")})(MathJax.Ajax,MathJax.Callback,MathJax.Hub,MathJax.HTML);MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/toMathML.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/AssistiveMML.js"],function(){MathJax.Hub.Register.StartupHook("End Config",["Config",MathJax.Extension.AssistiveMML])}); diff --git a/revisions_report_files/mathjax-27/extensions/CHTML-preview.js b/revisions_report_files/mathjax-27/extensions/CHTML-preview.js new file mode 100644 index 0000000..bd60209 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/CHTML-preview.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/CHTML-preview.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Callback.Queue(["Require",MathJax.Ajax,"[MathJax]/extensions/fast-preview.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/CHTML-preview.js"]); diff --git a/revisions_report_files/mathjax-27/extensions/FontWarnings.js b/revisions_report_files/mathjax-27/extensions/FontWarnings.js new file mode 100644 index 0000000..bbfec14 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/FontWarnings.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/FontWarnings.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +(function(b,d){var i="2.7.6";var a="http://www.stixfonts.org/";var f="https://github.com/mathjax/MathJax/tree/master/fonts/HTML-CSS/TeX/otf";var h=b.CombineConfig("FontWarnings",{messageStyle:{position:"fixed",bottom:"4em",left:"3em",width:"40em",border:"3px solid #880000","background-color":"#E0E0E0",color:"black",padding:"1em","font-size":"small","white-space":"normal","border-radius":".75em","-webkit-border-radius":".75em","-moz-border-radius":".75em","-khtml-border-radius":".75em","box-shadow":"4px 4px 10px #AAAAAA","-webkit-box-shadow":"4px 4px 10px #AAAAAA","-moz-box-shadow":"4px 4px 10px #AAAAAA","-khtml-box-shadow":"4px 4px 10px #AAAAAA",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=3, OffY=3, Color='gray', Positive='true')"},Message:{webFont:[["closeBox"],["webFont","MathJax is using web-based fonts to display the mathematics on this page. These take time to download, so the page would render faster if you installed math fonts directly in your system's font folder."],["fonts"]],imageFonts:[["closeBox"],["imageFonts","MathJax is using its image fonts rather than local or web-based fonts. This will render slower than usual, and the mathematics may not print at the full resolution of your printer."],["fonts"],["webFonts"]],noFonts:[["closeBox"],["noFonts","MathJax is unable to locate a font to use to display its mathematics, and image fonts are not available, so it is falling back on generic unicode characters in hopes that your browser will be able to display them. Some characters may not show up properly, or possibly not at all."],["fonts"],["webFonts"]]},HTML:{closeBox:[["div",{style:{position:"absolute",overflow:"hidden",top:".1em",right:".1em",border:"1px outset",width:"1em",height:"1em","text-align":"center",cursor:"pointer","background-color":"#EEEEEE",color:"#606060","border-radius":".5em","-webkit-border-radius":".5em","-moz-border-radius":".5em","-khtml-border-radius":".5em"},onclick:function(){if(c.div&&c.fade===0){if(c.timer){clearTimeout(c.timer)}c.div.style.display="none"}}},[["span",{style:{position:"relative",bottom:".2em"}},["x"]]]]],webFonts:[["p"],["webFonts","Most modern browsers allow for fonts to be downloaded over the web. Updating to a more recent version of your browser (or changing browsers) could improve the quality of the mathematics on this page."]],fonts:[["p"],["fonts","MathJax can use either the [STIX fonts](%1) or the [MathJax TeX fonts](%2). Download and install one of those fonts to improve your MathJax experience.",a,f]],STIXfonts:[["p"],["STIXPage","This page is designed to use the [STIX fonts](%1). Download and install those fonts to improve your MathJax experience.",a]],TeXfonts:[["p"],["TeXPage","This page is designed to use the [MathJax TeX fonts](%1). Download and install those fonts to improve your MathJax experience.",f]]},removeAfter:12*1000,fadeoutSteps:10,fadeoutTime:1.5*1000});if(MathJax.Hub.Browser.isIE9&&document.documentMode>=9){delete h.messageStyle.filter}var c={div:null,fade:0};var e=function(m){if(c.div){return}var j=MathJax.OutputJax["HTML-CSS"],n=document.body;if(b.Browser.isMSIE){if(h.messageStyle.position==="fixed"){MathJax.Message.Init();n=document.getElementById("MathJax_MSIE_Frame")||n;if(n!==document.body){h.messageStyle.position="absolute"}}}else{delete h.messageStyle.filter}h.messageStyle.maxWidth=(document.body.clientWidth-75)+"px";var k=0;while(k1?z/h:1);C=Math.floor(Math.max(this.config.minScaleAdjust/100,C)*this.config.scale);if(C/100!==g.scale){o.push([v.style,C])}g.scale=C/100;g.fontScale=C+"%";g.ex=z;g.mex=h}if("scrollWidth" in g&&(r||g.scrollWidth!==k.firstChild.scrollWidth)){g.scrollWidth=k.firstChild.scrollWidth;t.push([k.parentNode.style,g.scrollWidth/g.ex/g.scale])}if(k.MathJaxMtds){for(var u=0,p=k.MathJaxMtds.length;u0){this.HoverFadeTimer(q,q.hover.inc);return}s.parentNode.removeChild(s);if(r){r.parentNode.removeChild(r)}if(q.hover.remove){clearTimeout(q.hover.remove)}delete q.hover},HoverFadeTimer:function(q,s,r){q.hover.inc=s;if(!q.hover.timer){q.hover.timer=setTimeout(g(["HoverFade",this,q]),(r||o.fadeDelay))}},HoverMenu:function(q){if(!q){q=window.event}return b[this.jax].ContextMenu(q,this.math,true)},ClearHover:function(q){if(q.hover.remove){clearTimeout(q.hover.remove)}if(q.hover.timer){clearTimeout(q.hover.timer)}f.ClearHoverTimer();delete q.hover},Px:function(q){if(Math.abs(q)<0.006){return"0px"}return q.toFixed(2).replace(/\.?0+$/,"")+"px"},getImages:function(){if(k.discoverable){var q=new Image();q.src=o.button.src}}};var a=c.Touch={last:0,delay:500,start:function(r){var q=new Date().getTime();var s=(q-a.last=0){h=a.cloneNode(h,true)}var i=a.cloneNode(h);for(var g=0,f=h.childNodes.length;g1){a.applyTransform(o,p[0],g)}a.appendToken(o,"mo",f);if(p.length>0){var q=p[(p.length===1)?0:1];a.applyTransform(o,q,g)}if(k){a.appendToken(o,"mo",")")}n.appendChild(o)}},infix:function(f,g){return function(r,k,o,t,i,p,h){var s=a.createElement("mrow");var n=h>g;if(n){a.appendToken(s,"mo","(")}for(var q=0,m=t.length;q0){a.appendToken(s,"mo",f)}a.applyTransform(s,t[q],g)}if(n){a.appendToken(s,"mo",")")}r.appendChild(s)}},iteration:function(f,g){return function(q,y,C,l,h,u,m){var t=a.createElement("mrow");var x=a.createElement("mo");a.setTextContent(x,f);var o=a.createElement("munderover");o.appendChild(x);var k=a.createElement("mrow");var A,w,v,B,n,s,z,r;for(A=0,v=u.length;A0){a.appendToken(y,"mo",",")}n=a.getChildren(t);if(n.length){a.applyTransform(y,n[0],0)}}var x=a.createElement("mrow");var A=false;for(v=0,p=s.length;v0){a.appendToken(n,"mo",",")}a.applyTransform(n,s[p],0)}if(o.length){a.appendToken(n,"mo","|");for(p=0,k=o.length;p",1),lt:a.transforms.infix("<",1),geq:a.transforms.infix("\u2265",1),leq:a.transforms.infix("\u2264",1),equivalent:a.transforms.infix("\u2261",1),approx:a.transforms.infix("\u2248",1),subset:a.transforms.infix("\u2286",2),prsubset:a.transforms.infix("\u2282",2),cartesianproduct:a.transforms.infix("\u00D7",2),cartesian_product:a.transforms.infix("\u00D7",2),vectorproduct:a.transforms.infix("\u00D7",2),scalarproduct:a.transforms.infix(".",2),outerproduct:a.transforms.infix("\u2297",2),sum:a.transforms.iteration("\u2211","="),product:a.transforms.iteration("\u220F","="),forall:a.transforms.bind("\u2200",".",","),exists:a.transforms.bind("\u2203",".",","),lambda:a.transforms.bind("\u03BB",".",","),limit:a.transforms.iteration("lim","\u2192"),sdev:a.transforms.fn("\u03c3"),determinant:a.transforms.fn("det"),max:a.transforms.minmax("max"),min:a.transforms.minmax("min"),real:a.transforms.fn("\u211b"),imaginary:a.transforms.fn("\u2111"),set:a.transforms.set("{","}"),list:a.transforms.set("(",")"),exp:function(h,k,g,j,i,m,f){var l=a.createElement("msup");a.appendToken(l,"mi","e");a.applyTransform(l,j[0],0);h.appendChild(l)},union:function(h,k,g,j,i,l,f){if(i.length){a.transforms.iteration("\u22C3","=")(h,k,g,j,i,l,f)}else{a.transforms.infix("\u222A",2)(h,k,g,j,i,l,f)}},intersect:function(q,i,n,s,g,o,f){if(g.length){a.transforms.iteration("\u22C2","=")(q,i,n,s,g,o,f)}else{var r=a.createElement("mrow");var m=f>2;if(m){a.appendToken(r,"mo","(")}for(var p=0,k=s.length;p0){a.appendToken(r,"mo","\u2229");if(s[p].nodeName==="apply"){var h=a.getChildren(s[p])[0];t=h.nodeName==="union"}}if(t){a.appendToken(r,"mo","(")}a.applyTransform(r,s[p],2);if(t){a.appendToken(r,"mo",")")}}if(m){a.appendToken(r,"mo",")")}q.appendChild(r)}},floor:function(h,l,g,k,j,m,f){var i=a.createElement("mrow");a.appendToken(i,"mo","\u230a");a.applyTransform(i,k[0],0);a.appendToken(i,"mo","\u230b");h.appendChild(i)},conjugate:function(h,l,g,k,j,m,f){var i=a.createElement("mover");a.applyTransform(i,k[0],0);a.appendToken(i,"mo","\u00af");h.appendChild(i)},abs:function(h,l,g,k,j,m,f){var i=a.createElement("mrow");a.appendToken(i,"mo","|");a.applyTransform(i,k[0],0);a.appendToken(i,"mo","|");h.appendChild(i)},and:function(h,k,g,j,i,l,f){if(i.length||l.length){a.transforms.iteration("\u22c0","=")(h,k,g,j,i,l,4)}else{a.transforms.infix("\u2227",2)(h,k,g,j,i,l,f)}},or:function(h,k,g,j,i,l,f){if(i.length||l.length){a.transforms.iteration("\u22c1","=")(h,k,g,j,i,l,4)}else{a.transforms.infix("\u2228",2)(h,k,g,j,i,l,f)}},xor:function(h,k,g,j,i,l,f){if(i.length||l.length){a.transforms.iteration("xor","=")(h,k,g,j,i,l,4)}else{a.transforms.infix("xor",2)(h,k,g,j,i,l,f)}},card:function(h,l,g,k,j,m,f){var i=a.createElement("mrow");a.appendToken(i,"mo","|");a.applyTransform(i,k[0],0);a.appendToken(i,"mo","|");h.appendChild(i)},mean:function(h,l,g,k,j,m,f){if(k.length===1){var i=a.createElement("mover");a.applyTransform(i,k[0],0);a.appendToken(i,"mo","\u00af");h.appendChild(i)}else{h.appendChild(a.createmfenced(k,"\u27e8","\u27e9"))}},moment:function(s,k,o,w,g,p,f){var n,v,h,r,q,m;for(r=0,m=p.length;r1){y.appendChild(a.createmfenced(w,"(",")"))}else{a.applyTransform(y,w[0],0)}if(n){var x=a.createElement("msup");x.appendChild(y);h=a.getChildren(n);for(q=0,m=h.length;q3;if(k){a.appendToken(q,"mo","(")}for(var o=0,i=r.length;o0){a.appendToken(q,"mo",(r[o].nodeName==="cn")?"\u00D7":"\u2062")}a.applyTransform(q,r[o],3)}if(k){a.appendToken(q,"mo",")")}p.appendChild(q)},plus:function(s,k,p,u,g,q,f){var t=a.createElement("mrow");var o=f>2;if(o){a.appendToken(t,"mo","(")}for(var r=0,m=u.length;r0){var i;if(a.settings.collapsePlusMinus){if(v.nodeName==="cn"&&!(h.length)&&(i=Number(a.getTextContent(v)))<0){a.appendToken(t,"mo","\u2212");a.appendToken(t,"mn",-i)}else{if(v.nodeName==="apply"&&h.length===2&&h[0].nodeName==="minus"){a.appendToken(t,"mo","\u2212");a.applyTransform(t,h[1],2)}else{if(v.nodeName==="apply"&&h.length>2&&h[0].nodeName==="times"&&h[1].nodeName==="cn"&&(i=Number(a.getTextContent(h[1])))<0){a.appendToken(t,"mo","\u2212");h[1].textContent=-i;a.applyTransform(t,v,2)}else{a.appendToken(t,"mo","+");a.applyTransform(t,v,2)}}}}else{a.appendToken(t,"mo","+");a.applyTransform(t,v,2)}}else{a.applyTransform(t,v,2)}}if(o){a.appendToken(t,"mo",")")}s.appendChild(t)},transpose:function(h,k,g,j,i,m,f){var l=a.createElement("msup");a.applyTransform(l,j[0],f);a.appendToken(l,"mi","T");h.appendChild(l)},power:function(h,k,g,j,i,m,f){var l=a.createElement("msup");a.applyTransform(l,j[0],3);a.applyTransform(l,j[1],f);h.appendChild(l)},selector:function(p,h,k,s,g,n,f){var r=a.createElement("msub");var q=s?s[0]:a.createElement("mrow");a.applyTransform(r,q,0);var m=a.createElement("mrow");for(var o=1,j=s.length;o1){a.applyTransform(i,k[1],0)}}a.appendToken(i,"mo","\u230B");h.appendChild(i)},factorial:function(h,l,g,k,j,m,f){var i=a.createElement("mrow");a.applyTransform(i,k[0],4);a.appendToken(i,"mo","!");h.appendChild(i)},root:function(p,j,m,q,h,n,f){var g;if(m.nodeName==="root"&&(n.length===0||(n[0].nodeName==="degree"&&a.getTextContent(n[0])==="2"))){g=a.createElement("msqrt");for(var o=0,k=q.length;o1){var i=a.createElement("msup");a.applyTransform(i,j,0);a.appendToken(i,"mn",l);M.appendChild(i)}else{a.applyTransform(M,j,0)}}for(K=0,F=z.length;K0){if(x){a.appendToken(s,"mo","+")}a.appendToken(s,"mn",m)}}if(g.length){L=g[0]}for(K=0,F=f.length;K ltr ) ( ] [ } { ) ( ] [ } { \ )(}{><∋∈ top right 0 decimalpoint decimalpoint . decimalpoint * 0.1em 0.15em 0.2em 0.15em 0 ) ( / : = top ) ';var b;if(window.XSLTProcessor){if(!d.ParseXML){d.ParseXML=d.createParser()}d.mml3XSLT=new XSLTProcessor();d.mml3XSLT.importStylesheet(d.ParseXML(e))}else{if(MathJax.Hub.Browser.isMSIE){if(MathJax.Hub.Browser.versionAtLeast("9.0")||(document.documentMode||0)>=9){b=new ActiveXObject("Msxml2.FreeThreadedDOMDocument");b.loadXML(e);var a=new ActiveXObject("Msxml2.XSLTemplate");a.stylesheet=b;d.mml3XSLT={mml3:a.createProcessor(),transformToDocument:function(h){this.mml3.input=h;this.mml3.transform();return this.mml3.output}}}else{b=d.createMSParser();b.async=false;b.loadXML(e);d.mml3XSLT={mml3:b,transformToDocument:function(h){return h.documentElement.transformNode(this.mml3)}}}}else{d.mml3XSLT=null}}MathJax.Ajax.Styles({".MathJax .mi, .MathJax .mo, .MathJax .mn, .MathJax .mtext":{direction:"ltr",display:"inline-block"},".MathJax .ms, .MathJax .mspace, .MathJax .mglyph":{direction:"ltr",display:"inline-block"}});MathJax.Hub.Startup.signal.Post("MathML mml3.js Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/MathML/mml3.js"); diff --git a/revisions_report_files/mathjax-27/extensions/MathMenu.js b/revisions_report_files/mathjax-27/extensions/MathMenu.js new file mode 100644 index 0000000..1896c3b --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/MathMenu.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/MathMenu.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +(function(f,o,q,e,r){var p="2.7.6";var d=MathJax.Callback.Signal("menu");MathJax.Extension.MathMenu={version:p,signal:d};var t=function(u){return MathJax.Localization._.apply(MathJax.Localization,[["MathMenu",u]].concat([].slice.call(arguments,1)))};var i=MathJax.Object.isArray;var a=f.Browser.isPC,l=f.Browser.isMSIE,m=((document.documentMode||0)>8);var j=(a?null:"5px");var s=f.CombineConfig("MathMenu",{delay:150,showRenderer:true,showMathPlayer:true,showFontMenu:false,showContext:false,showDiscoverable:false,showLocale:true,showLocaleURL:false,semanticsAnnotations:{TeX:["TeX","LaTeX","application/x-tex"],StarMath:["StarMath 5.0"],Maple:["Maple"],ContentMathML:["MathML-Content","application/mathml-content+xml"],OpenMath:["OpenMath"]},windowSettings:{status:"no",toolbar:"no",locationbar:"no",menubar:"no",directories:"no",personalbar:"no",resizable:"yes",scrollbars:"yes",width:400,height:300,left:Math.round((screen.width-400)/2),top:Math.round((screen.height-300)/3)},styles:{"#MathJax_About":{position:"fixed",left:"50%",width:"auto","text-align":"center",border:"3px outset",padding:"1em 2em","background-color":"#DDDDDD",color:"black",cursor:"default","font-family":"message-box","font-size":"120%","font-style":"normal","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":"15px","-webkit-border-radius":"15px","-moz-border-radius":"15px","-khtml-border-radius":"15px","box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},"#MathJax_About.MathJax_MousePost":{outline:"none"},".MathJax_Menu":{position:"absolute","background-color":"white",color:"black",width:"auto",padding:(a?"2px":"5px 0px"),border:"1px solid #CCCCCC",margin:0,cursor:"default",font:"menu","text-align":"left","text-indent":0,"text-transform":"none","line-height":"normal","letter-spacing":"normal","word-spacing":"normal","word-wrap":"normal","white-space":"nowrap","float":"none","z-index":201,"border-radius":j,"-webkit-border-radius":j,"-moz-border-radius":j,"-khtml-border-radius":j,"box-shadow":"0px 10px 20px #808080","-webkit-box-shadow":"0px 10px 20px #808080","-moz-box-shadow":"0px 10px 20px #808080","-khtml-box-shadow":"0px 10px 20px #808080",filter:"progid:DXImageTransform.Microsoft.dropshadow(OffX=2, OffY=2, Color='gray', Positive='true')"},".MathJax_MenuItem":{padding:(a?"2px 2em":"1px 2em"),background:"transparent"},".MathJax_MenuArrow":{position:"absolute",right:".5em","padding-top":".25em",color:"#666666","font-family":(l?"'Arial unicode MS'":null),"font-size":".75em"},".MathJax_MenuActive .MathJax_MenuArrow":{color:"white"},".MathJax_MenuArrow.RTL":{left:".5em",right:"auto"},".MathJax_MenuCheck":{position:"absolute",left:".7em","font-family":(l?"'Arial unicode MS'":null)},".MathJax_MenuCheck.RTL":{right:".7em",left:"auto"},".MathJax_MenuRadioCheck":{position:"absolute",left:(a?"1em":".7em")},".MathJax_MenuRadioCheck.RTL":{right:(a?"1em":".7em"),left:"auto"},".MathJax_MenuLabel":{padding:(a?"2px 2em 4px 1.33em":"1px 2em 3px 1.33em"),"font-style":"italic"},".MathJax_MenuRule":{"border-top":(a?"1px solid #CCCCCC":"1px solid #DDDDDD"),margin:(a?"4px 1px 0px":"4px 3px")},".MathJax_MenuDisabled":{color:"GrayText"},".MathJax_MenuActive":{"background-color":(a?"Highlight":"#606872"),color:(a?"HighlightText":"white")},".MathJax_MenuDisabled:focus, .MathJax_MenuLabel:focus":{"background-color":"#E8E8E8"},".MathJax_ContextMenu:focus":{outline:"none"},".MathJax_ContextMenu .MathJax_MenuItem:focus":{outline:"none"},"#MathJax_AboutClose":{top:".2em",right:".2em"},".MathJax_Menu .MathJax_MenuClose":{top:"-10px",left:"-10px"},".MathJax_MenuClose":{position:"absolute",cursor:"pointer",display:"inline-block",border:"2px solid #AAA","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","font-family":"'Courier New',Courier","font-size":"24px",color:"#F0F0F0"},".MathJax_MenuClose span":{display:"block","background-color":"#AAA",border:"1.5px solid","border-radius":"18px","-webkit-border-radius":"18px","-moz-border-radius":"18px","-khtml-border-radius":"18px","line-height":0,padding:"8px 0 6px"},".MathJax_MenuClose:hover":{color:"white!important",border:"2px solid #CCC!important"},".MathJax_MenuClose:hover span":{"background-color":"#CCC!important"},".MathJax_MenuClose:hover:focus":{outline:"none"}}});var n,k,b;f.Register.StartupHook("MathEvents Ready",function(){n=MathJax.Extension.MathEvents.Event.False;k=MathJax.Extension.MathEvents.Hover;b=MathJax.Extension.MathEvents.Event.KEY});var h=MathJax.Object.Subclass({Keydown:function(u,v){switch(u.keyCode){case b.ESCAPE:this.Remove(u,v);break;case b.RIGHT:this.Right(u,v);break;case b.LEFT:this.Left(u,v);break;case b.UP:this.Up(u,v);break;case b.DOWN:this.Down(u,v);break;case b.RETURN:case b.SPACE:this.Space(u,v);break;default:return;break}return n(u)},Escape:function(u,v){},Right:function(u,v){},Left:function(u,v){},Up:function(u,v){},Down:function(u,v){},Space:function(u,v){}},{});var g=MathJax.Menu=h.Subclass({version:p,items:[],posted:false,title:null,margin:5,Init:function(u){this.items=[].slice.call(arguments,0)},With:function(u){if(u){f.Insert(this,u)}return this},Post:function(M,E,B){if(!M){M=window.event||{}}var I=document.getElementById("MathJax_MenuFrame");if(!I){I=g.Background(this);delete c.lastItem;delete c.lastMenu;delete g.skipUp;d.Post(["post",g.jax]);g.isRTL=(MathJax.Localization.fontDirection()==="rtl")}var v=o.Element("div",{onmouseup:g.Mouseup,ondblclick:n,ondragstart:n,onselectstart:n,oncontextmenu:n,menuItem:this,className:"MathJax_Menu",onkeydown:g.Keydown,role:"menu"});if(M.type==="contextmenu"||M.type==="mouseover"){v.className+=" MathJax_ContextMenu"}if(!B){MathJax.Localization.setCSS(v)}for(var N=0,K=this.items.length;NA-this.margin){H=A-v.offsetWidth-this.margin}if(g.isMobile){H=Math.max(5,H-Math.floor(v.offsetWidth/2));F-=20}g.skipUp=M.isContextMenu}else{var z="left",J=E.offsetWidth;H=(g.isMobile?30:J-2);F=0;while(E&&E!==I){H+=E.offsetLeft;F+=E.offsetTop;E=E.parentNode}if(!g.isMobile){if((g.isRTL&&H-J-v.offsetWidth>this.margin)||(!g.isRTL&&H+v.offsetWidth>A-this.margin)){z="right";H=Math.max(this.margin,H-J-v.offsetWidth+6)}}if(!a){v.style["borderRadiusTop"+z]=0;v.style["WebkitBorderRadiusTop"+z]=0;v.style["MozBorderRadiusTop"+z]=0;v.style["KhtmlBorderRadiusTop"+z]=0}}v.style.left=H+"px";v.style.top=F+"px";if(document.selection&&document.selection.empty){document.selection.empty()}var G=window.pageXOffset||document.documentElement.scrollLeft;var D=window.pageYOffset||document.documentElement.scrollTop;g.Focus(v);if(M.type==="keydown"){g.skipMouseoverFromKey=true;setTimeout(function(){delete g.skipMouseoverFromKey},s.delay)}window.scrollTo(G,D);return n(M)},Remove:function(u,v){d.Post(["unpost",g.jax]);var w=document.getElementById("MathJax_MenuFrame");if(w){w.parentNode.removeChild(w);if(this.msieFixedPositionBug){detachEvent("onresize",g.Resize)}}if(g.jax.hover){delete g.jax.hover.nofade;k.UnHover(g.jax)}g.Unfocus(v);if(u.type==="mousedown"){g.CurrentNode().blur()}return n(u)},Find:function(u){return this.FindN(1,u,[].slice.call(arguments,1))},FindId:function(u){return this.FindN(0,u,[].slice.call(arguments,1))},FindN:function(y,v,x){for(var w=0,u=this.items.length;w0){u.oldTabIndex=u.tabIndex}u.tabIndex=-1}},SetTabIndex:function(){var v=g.AllNodes();for(var w=0,u;u=v[w];w++){if(u.oldTabIndex!==undefined){u.tabIndex=u.oldTabIndex;delete u.oldTabIndex}else{u.tabIndex=f.getTabOrder(u)}}},Mod:function(u,v){return((u%v)+v)%v},IndexOf:(Array.prototype.indexOf?function(u,v,w){return u.indexOf(v,w)}:function(u,x,y){for(var w=(y||0),v=u.length;w=0&&c.GetMenuNode(w).menuItem!==v[u].menuItem){v[u].menuItem.posted=false;v[u].parentNode.removeChild(v[u]);u--}},Touchstart:function(u,v){return this.TouchEvent(u,v,"Mousedown")},Touchend:function(u,v){return this.TouchEvent(u,v,"Mouseup")},TouchEvent:function(v,w,u){if(this!==c.lastItem){if(c.lastMenu){g.Event(v,c.lastMenu,"Mouseout")}g.Event(v,w,"Mouseover",true);c.lastItem=this;c.lastMenu=w}if(this.nativeTouch){return null}g.Event(v,w,u);return false},Remove:function(u,v){v=v.parentNode.menuItem;return v.Remove(u,v)},With:function(u){if(u){f.Insert(this,u)}return this},isRTL:function(){return g.isRTL},rtlClass:function(){return(this.isRTL()?" RTL":"")}},{GetMenuNode:function(u){return u.parentNode}});g.ENTRY=g.ITEM.Subclass({role:"menuitem",Attributes:function(u){u=f.Insert({onmouseover:g.Mouseover,onmouseout:g.Mouseout,onmousedown:g.Mousedown,onkeydown:g.Keydown,"aria-disabled":!!this.disabled},u);u=this.SUPER(arguments).Attributes.call(this,u);if(this.disabled){u.className+=" MathJax_MenuDisabled"}return u},MoveVertical:function(u,E,w){var x=c.GetMenuNode(E);var D=[];for(var z=0,C=x.menuItem.items,y;y=C[z];z++){if(!y.hidden){D.push(y)}}var B=g.IndexOf(D,this);if(B===-1){return}var A=D.length;var v=x.childNodes;do{B=g.Mod(w(B),A)}while(D[B].hidden||!v[B].role||v[B].role==="separator");this.Deactivate(E);D[B].Activate(u,v[B])},Up:function(v,u){this.MoveVertical(v,u,function(w){return w-1})},Down:function(v,u){this.MoveVertical(v,u,function(w){return w+1})},Right:function(v,u){this.MoveHorizontal(v,u,g.Right,!this.isRTL())},Left:function(v,u){this.MoveHorizontal(v,u,g.Left,this.isRTL())},MoveHorizontal:function(A,z,u,B){var x=c.GetMenuNode(z);if(x.menuItem===g.menu&&A.shiftKey){u(A,z)}if(B){return}if(x.menuItem!==g.menu){this.Deactivate(z)}var v=x.previousSibling.childNodes;var y=v.length;while(y--){var w=v[y];if(w.menuItem.submenu&&w.menuItem.submenu===x.menuItem){g.Focus(w);break}}this.RemoveSubmenus(z)},Space:function(u,v){this.Mouseup(u,v)},Activate:function(u,v){this.Deactivate(v);if(!this.disabled){v.className+=" MathJax_MenuActive"}this.DeactivateSubmenus(v);g.Focus(v)},Deactivate:function(u){u.className=u.className.replace(/ MathJax_MenuActive/,"")}});g.ITEM.COMMAND=g.ENTRY.Subclass({action:function(){},Init:function(u,w,v){if(!i(u)){u=[u,u]}this.name=u;this.action=w;this.With(v)},Label:function(u,v){return[this.Name()]},Mouseup:function(u,v){if(!this.disabled){this.Remove(u,v);d.Post(["command",this]);this.action.call(this,u)}return n(u)}});g.ITEM.SUBMENU=g.ENTRY.Subclass({submenu:null,marker:"\u25BA",markerRTL:"\u25C4",Attributes:function(u){u=f.Insert({"aria-haspopup":"true"},u);u=this.SUPER(arguments).Attributes.call(this,u);return u},Init:function(u,w){if(!i(u)){u=[u,u]}this.name=u;var v=1;if(!(w instanceof g.ITEM)){this.With(w),v++}this.submenu=g.apply(g,[].slice.call(arguments,v))},Label:function(u,v){this.submenu.posted=false;return[this.Name()+" ",["span",{className:"MathJax_MenuArrow"+this.rtlClass()},[this.isRTL()?this.markerRTL:this.marker]]]},Timer:function(u,v){this.ClearTimer();u={type:u.type,clientX:u.clientX,clientY:u.clientY};this.timer=setTimeout(e(["Mouseup",this,u,v]),s.delay)},ClearTimer:function(){if(this.timer){clearTimeout(this.timer)}},Touchend:function(v,x){var w=this.submenu.posted;var u=this.SUPER(arguments).Touchend.apply(this,arguments);if(w){this.Deactivate(x);delete c.lastItem;delete c.lastMenu}return u},Mouseout:function(u,v){if(!this.submenu.posted){this.Deactivate(v)}this.ClearTimer()},Mouseover:function(u,v){this.Activate(u,v)},Mouseup:function(u,v){if(!this.disabled){if(!this.submenu.posted){this.ClearTimer();this.submenu.Post(u,v,this.ltr);g.Focus(v)}else{this.DeactivateSubmenus(v)}}return n(u)},Activate:function(u,v){if(!this.disabled){this.Deactivate(v);v.className+=" MathJax_MenuActive"}if(!this.submenu.posted){this.DeactivateSubmenus(v);if(!g.isMobile){this.Timer(u,v)}}g.Focus(v)},MoveVertical:function(w,v,u){this.ClearTimer();this.SUPER(arguments).MoveVertical.apply(this,arguments)},MoveHorizontal:function(w,y,v,x){if(!x){this.SUPER(arguments).MoveHorizontal.apply(this,arguments);return}if(this.disabled){return}if(!this.submenu.posted){this.Activate(w,y);return}var u=c.GetMenuNode(y).nextSibling.childNodes;if(u.length>0){this.submenu.items[0].Activate(w,u[0])}}});g.ITEM.RADIO=g.ENTRY.Subclass({variable:null,marker:(a?"\u25CF":"\u2713"),role:"menuitemradio",Attributes:function(v){var u=s.settings[this.variable]===this.value?"true":"false";v=f.Insert({"aria-checked":u},v);v=this.SUPER(arguments).Attributes.call(this,v);return v},Init:function(v,u,w){if(!i(v)){v=[v,v]}this.name=v;this.variable=u;this.With(w);if(this.value==null){this.value=this.name[0]}},Label:function(v,w){var u={className:"MathJax_MenuRadioCheck"+this.rtlClass()};if(s.settings[this.variable]!==this.value){u={style:{display:"none"}}}return[["span",u,[this.marker]]," "+this.Name()]},Mouseup:function(x,y){if(!this.disabled){var z=y.parentNode.childNodes;for(var v=0,u=z.length;v/g,">");var y=t("EqSource","MathJax Equation Source");if(g.isMobile){u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("
");u.document.write("");u.document.close()}else{u.document.open();u.document.write(""+y+"");u.document.write("
"+z+"
");u.document.write("");u.document.close();var v=u.document.body.firstChild;setTimeout(function(){var B=(u.outerHeight-u.innerHeight)||30,A=(u.outerWidth-u.innerWidth)||30,w,E;A=Math.max(140,Math.min(Math.floor(0.5*screen.width),v.offsetWidth+A+25));B=Math.max(40,Math.min(Math.floor(0.5*screen.height),v.offsetHeight+B+25));if(g.prototype.msieHeightBug){B+=35}u.resizeTo(A,B);var D;try{D=x.screenX}catch(C){}if(x&&D!=null){w=Math.max(0,Math.min(x.screenX-Math.floor(A/2),screen.width-A-20));E=Math.max(0,Math.min(x.screenY-Math.floor(B/2),screen.height-B-20));u.moveTo(w,E)}},50)}};g.Scale=function(){var z=["CommonHTML","HTML-CSS","SVG","NativeMML","PreviewHTML"],u=z.length,y=100,w,v;for(w=0;w7;g.Augment({margin:20,msieBackgroundBug:((document.documentMode||0)<9),msieFixedPositionBug:(v||!w),msieAboutBug:v,msieHeightBug:((document.documentMode||0)<9)});if(m){delete s.styles["#MathJax_About"].filter;delete s.styles[".MathJax_Menu"].filter}},Firefox:function(u){g.skipMouseover=u.isMobile&&u.versionAtLeast("6.0");g.skipMousedown=u.isMobile}});g.isMobile=f.Browser.isMobile;g.noContextMenu=f.Browser.noContextMenu;g.CreateLocaleMenu=function(){if(!g.menu){return}var z=g.menu.Find("Language").submenu,w=z.items;var v=[],B=MathJax.Localization.strings;for(var A in B){if(B.hasOwnProperty(A)){v.push(A)}}v=v.sort();z.items=[];for(var x=0,u=v.length;xt){z.style.height=t+"px";z.style.width=(x.zW+this.scrollSize)+"px"}if(z.offsetWidth>l){z.style.width=l+"px";z.style.height=(x.zH+this.scrollSize)+"px"}}if(this.operaPositionBug){z.style.width=Math.min(l,x.zW)+"px"}if(z.offsetWidth>m&&z.offsetWidth-m=9);h.msiePositionBug=!m;h.msieSizeBug=l.versionAtLeast("7.0")&&(!document.documentMode||n===7||n===8);h.msieZIndexBug=(n<=7);h.msieInlineBlockAlignBug=(n<=7);h.msieTrapEventBug=!window.addEventListener;if(document.compatMode==="BackCompat"){h.scrollSize=52}if(m){delete i.styles["#MathJax_Zoom"].filter}},Opera:function(l){h.operaPositionBug=true;h.operaRefreshBug=true}});h.topImg=(h.msieInlineBlockAlignBug?d.Element("img",{style:{width:0,height:0,position:"relative"},src:"about:blank"}):d.Element("span",{style:{width:0,height:0,display:"inline-block"}}));if(h.operaPositionBug||h.msieTopBug){h.topImg.style.border="1px solid"}MathJax.Callback.Queue(["StartupHook",MathJax.Hub.Register,"Begin Styles",{}],["Styles",f,i.styles],["Post",a.Startup.signal,"MathZoom Ready"],["loadComplete",f,"[MathJax]/extensions/MathZoom.js"])})(MathJax.Hub,MathJax.HTML,MathJax.Ajax,MathJax.OutputJax["HTML-CSS"],MathJax.OutputJax.NativeMML); diff --git a/revisions_report_files/mathjax-27/extensions/Safe.js b/revisions_report_files/mathjax-27/extensions/Safe.js new file mode 100644 index 0000000..f277792 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/Safe.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/Safe.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +(function(d,c){var f="2.7.6";var a=MathJax.Hub.CombineConfig("Safe",{allow:{URLs:"safe",classes:"safe",cssIDs:"safe",styles:"safe",fontsize:"all",require:"safe"},sizeMin:0.7,sizeMax:1.44,lengthMax:3,safeProtocols:{http:true,https:true,file:true,javascript:false},safeStyles:{color:true,backgroundColor:true,border:true,cursor:true,margin:true,padding:true,textShadow:true,fontFamily:true,fontSize:true,fontStyle:true,fontWeight:true,opacity:true,outline:true},safeRequire:{action:true,amscd:true,amsmath:true,amssymbols:true,autobold:false,"autoload-all":false,bbox:true,begingroup:true,boldsymbol:true,cancel:true,color:true,enclose:true,extpfeil:true,HTML:true,mathchoice:true,mhchem:true,newcommand:true,noErrors:false,noUndefined:false,unicode:true,verb:true},styleParts:{border:true,padding:true,margin:true,outline:true},styleLengths:{borderTop:"borderTopWidth",borderRight:"borderRightWidth",borderBottom:"borderBottomWidth",borderLeft:"borderLeftWidth",paddingTop:true,paddingRight:true,paddingBottom:true,paddingLeft:true,marginTop:true,marginRight:true,marginBottom:true,marginLeft:true,outlineTop:true,outlineRight:true,outlineBottom:true,outlineLeft:true,fontSize:[0.7,1.44]}});var e=a.allow;if(e.fontsize!=="all"){a.safeStyles.fontSize=false}var b=MathJax.Extension.Safe={version:f,config:a,div1:document.createElement("div"),div2:document.createElement("div"),filter:{href:"filterURL",src:"filterURL",altimg:"filterURL","class":"filterClass",style:"filterStyles",id:"filterID",fontsize:"filterFontSize",mathsize:"filterFontSize",scriptminsize:"filterFontSize",scriptsizemultiplier:"filterSizeMultiplier",scriptlevel:"filterScriptLevel"},filterURL:function(g){var h=(g.match(/^\s*([a-z]+):/i)||[null,""])[1].toLowerCase();if(e.URLs==="none"||(e.URLs!=="all"&&!a.safeProtocols[h])){g=null}return g},filterClass:function(g){if(e.classes==="none"||(e.classes!=="all"&&!g.match(/^MJX-[-a-zA-Z0-9_.]+$/))){g=null}return g},filterID:function(g){if(e.cssIDs==="none"||(e.cssIDs!=="all"&&!g.match(/^MJX-[-a-zA-Z0-9_.]+$/))){g=null}return g},filterStyles:function(l){if(e.styles==="all"){return l}if(e.styles==="none"){return null}try{var k=this.div1.style,j=this.div2.style,m;k.cssText=l;j.cssText="";for(var g in a.safeStyles){if(a.safeStyles.hasOwnProperty(g)){if(a.styleParts[g]){for(var h=0;h<4;h++){var o=g+["Top","Right","Bottom","Left"][h];m=this.filterStyle(o,k);if(m){j[o]=m}}}else{m=this.filterStyle(g,k);if(m){j[g]=m}}}}l=j.cssText}catch(n){l=null}return l},filterStyle:function(g,h){var i=h[g];if(typeof i!=="string"||i===""){return null}if(i.match(/^\s*expression/)){return null}if(i.match(/javascript:/)){return null}var j=g.replace(/Top|Right|Left|Bottom/,"");if(!a.safeStyles[g]&&!a.safeStyles[j]){return null}if(!a.styleLengths[g]){return i}return(this.filterStyleLength(g,i,h)?i:null)},filterStyleLength:function(g,i,h){if(typeof a.styleLengths[g]==="string"){i=h[a.styleLengths[g]]}i=this.length2em(i);if(i==null){return false}var j=[-a.lengthMax,a.lengthMax];if(MathJax.Object.isArray(a.styleLengths[g])){j=a.styleLengths[g]}return(i>=j[0]&&i<=j[1])},unit2em:{em:1,ex:0.5,ch:0.5,rem:1,px:1/16,mm:96/25.4/16,cm:96/2.54/16,"in":96/16,pt:96/72/16,pc:96/6/16},length2em:function(h){var g=h.match(/(.+)(em|ex|ch|rem|px|mm|cm|in|pt|pc)/);if(!g){return null}return parseFloat(g[1])*this.unit2em[g[2]]},filterSize:function(g){if(e.fontsize==="none"){return null}if(e.fontsize!=="all"){g=Math.min(Math.max(g,a.sizeMin),a.sizeMax)}return g},filterFontSize:function(g){return(e.fontsize==="all"?g:null)},filterSizeMultiplier:function(g){if(e.fontsize==="none"){g=null}else{if(e.fontsize!=="all"){g=Math.min(1,Math.max(0.6,g)).toString()}}return g},filterScriptLevel:function(g){if(e.fontsize==="none"){g=null}else{if(e.fontsize!=="all"){g=Math.max(0,g).toString()}}return g},filterRequire:function(g){if(e.require==="none"||(e.require!=="all"&&!a.safeRequire[g.toLowerCase()])){g=null}return g}};d.Register.StartupHook("TeX HTML Ready",function(){var g=MathJax.InputJax.TeX;g.Parse.Augment({HREF_attribute:function(j){var i=b.filterURL(this.GetArgument(j)),h=this.GetArgumentMML(j);if(i){h.With({href:i})}this.Push(h)},CLASS_attribute:function(i){var j=b.filterClass(this.GetArgument(i)),h=this.GetArgumentMML(i);if(j){if(h["class"]!=null){j=h["class"]+" "+j}h.With({"class":j})}this.Push(h)},STYLE_attribute:function(i){var j=b.filterStyles(this.GetArgument(i)),h=this.GetArgumentMML(i);if(j){if(h.style!=null){if(j.charAt(j.length-1)!==";"){j+=";"}j=h.style+" "+j}h.With({style:j})}this.Push(h)},ID_attribute:function(j){var i=b.filterID(this.GetArgument(j)),h=this.GetArgumentMML(j);if(i){h.With({id:i})}this.Push(h)}})});d.Register.StartupHook("TeX Jax Ready",function(){var i=MathJax.InputJax.TeX,h=i.Parse,g=b.filter;h.Augment({Require:function(j){var k=this.GetArgument(j).replace(/.*\//,"").replace(/[^a-z0-9_.-]/ig,"");k=b.filterRequire(k);if(k){this.Extension(null,k)}},MmlFilterAttribute:function(j,k){if(g[j]){k=b[g[j]](k)}return k},SetSize:function(j,k){k=b.filterSize(k);if(k){this.stack.env.size=k;this.Push(i.Stack.Item.style().With({styles:{mathsize:k+"em"}}))}}})});d.Register.StartupHook("TeX bbox Ready",function(){var g=MathJax.InputJax.TeX;g.Parse.Augment({BBoxStyle:function(h){return b.filterStyles(h)},BBoxPadding:function(i){var h=b.filterStyles("padding: "+i);return(h?i:0)}})});d.Register.StartupHook("MathML Jax Ready",function(){var h=MathJax.InputJax.MathML.Parse,g=b.filter;h.Augment({filterAttribute:function(i,j){if(g[i]){j=b[g[i]](j)}return j}})});d.Startup.signal.Post("Safe Extension Ready");c.loadComplete("[MathJax]/extensions/Safe.js")})(MathJax.Hub,MathJax.Ajax); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/AMScd.js b/revisions_report_files/mathjax-27/extensions/TeX/AMScd.js new file mode 100644 index 0000000..165f53a --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/AMScd.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/AMScd.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/AMScd"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.CD",{colspace:"5pt",rowspace:"5pt",harrowsize:"2.75em",varrowsize:"1.75em",hideHorizontalLabels:false})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,e=MathJax.InputJax.TeX,d=e.Stack.Item,c=e.Definitions,a=MathJax.Extension["TeX/AMScd"].config;c.environment.CD="CD_env";c.special["@"]="CD_arrow";c.macros.minCDarrowwidth="CD_minwidth";c.macros.minCDarrowheight="CD_minheight";e.Parse.Augment({CD_env:function(f){this.Push(f);return d.array().With({arraydef:{columnalign:"center",columnspacing:a.colspace,rowspacing:a.rowspace,displaystyle:true},minw:this.stack.env.CD_minw||a.harrowsize,minh:this.stack.env.CD_minh||a.varrowsize})},CD_arrow:function(g){var l=this.string.charAt(this.i);if(!l.match(/[>":"\u2192","<":"\u2190",V:"\u2193",A:"\u2191"}[l];var p=this.GetUpTo(g+l,l),m=this.GetUpTo(g+l,l);if(l===">"||l==="<"){h=b.mo(r).With(f);if(!p){p="\\kern "+o.minw}if(p||m){var j={width:"+11mu",lspace:"6mu"};h=b.munderover(this.mmlToken(h));if(p){p=e.Parse(p,this.stack.env).mml();h.SetData(h.over,b.mpadded(p).With(j).With({voffset:".1em"}))}if(m){m=e.Parse(m,this.stack.env).mml();h.SetData(h.under,b.mpadded(m).With(j))}if(a.hideHorizontalLabels){h=b.mpadded(h).With({depth:0,height:".67em"})}}}else{h=r=this.mmlToken(b.mo(r).With(k));if(p||m){h=b.mrow();if(p){h.Append(e.Parse("\\scriptstyle\\llap{"+p+"}",this.stack.env).mml())}h.Append(r.With({texClass:b.TEXCLASS.ORD}));if(m){h.Append(e.Parse("\\scriptstyle\\rlap{"+m+"}",this.stack.env).mml())}}}}}}if(h){this.Push(h)}this.CD_cell(g)},CD_cell:function(f){var g=this.stack.Top();if((g.table||[]).length%2===0&&(g.row||[]).length===0){this.Push(b.mpadded().With({height:"8.5pt",depth:"2pt"}))}this.Push(d.cell().With({isEntry:true,name:f}))},CD_minwidth:function(f){this.stack.env.CD_minw=this.GetDimen(f)},CD_minheight:function(f){this.stack.env.CD_minh=this.GetDimen(f)}})});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/AMScd.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/AMSmath.js b/revisions_report_files/mathjax-27/extensions/TeX/AMSmath.js new file mode 100644 index 0000000..9997fb8 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/AMSmath.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/AMSmath.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/AMSmath"]={version:"2.7.6",number:0,startNumber:0,IDs:{},eqIDs:{},labels:{},eqlabels:{},refs:[]};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.ElementJax.mml,h=MathJax.InputJax.TeX,g=MathJax.Extension["TeX/AMSmath"];var d=h.Definitions,f=h.Stack.Item,a=h.config.equationNumbers;var c=function(k){var n=[];for(var l=0,j=k.length;l0){p+="rl";o.push("0em 0em");q--}o=o.join(" ");if(i){return this.AMSarray(l,j,i,p,o)}var m=this.AMSarray(l,j,i,p,o);return this.setArrayAlign(m,k)},EquationBegin:function(i,j){this.checkEqnEnv();this.stack.global.forcetag=(j&&a.autoNumber!=="none");return i},EquationStar:function(i,j){this.stack.global.tagged=true;return j},checkEqnEnv:function(){if(this.stack.global.eqnenv){h.Error(["ErroneousNestingEq","Erroneous nesting of equation structures"])}this.stack.global.eqnenv=true},MultiIntegral:function(j,m){var l=this.GetNext();if(l==="\\"){var k=this.i;l=this.GetArgument(j);this.i=k;if(l==="\\limits"){if(j==="\\idotsint"){m="\\!\\!\\mathop{\\,\\,"+m+"}"}else{m="\\!\\!\\!\\mathop{\\,\\,\\,"+m+"}"}}}this.string=m+" "+this.string.slice(this.i);this.i=0},xArrow:function(k,o,n,i){var m={width:"+"+(n+i)+"mu",lspace:n+"mu"};var p=this.GetBrackets(k),q=this.ParseArg(k);var s=b.mo(b.chars(String.fromCharCode(o))).With({stretchy:true,texClass:b.TEXCLASS.REL});var j=b.munderover(s);j.SetData(j.over,b.mpadded(q).With(m).With({voffset:".15em"}));if(p){p=h.Parse(p,this.stack.env).mml();j.SetData(j.under,b.mpadded(p).With(m).With({voffset:"-.24em"}))}this.Push(j.With({subsupOK:true}))},GetDelimiterArg:function(i){var j=this.trimSpaces(this.GetArgument(i));if(j==""){return null}if(j in d.delimiter){return j}h.Error(["MissingOrUnrecognizedDelim","Missing or unrecognized delimiter for %1",i])},GetStar:function(){var i=(this.GetNext()==="*");if(i){this.i++}return i}});f.Augment({autoTag:function(){var j=this.global;if(!j.notag){g.number++;j.tagID=a.formatNumber(g.number.toString());var i=h.Parse("\\text{"+a.formatTag(j.tagID)+"}",{}).mml();j.tag=b.mtd(i).With({id:a.formatID(j.tagID)})}},getTag:function(){var m=this.global,k=m.tag;m.tagged=true;if(m.label){if(a.useLabelIds){k.id=a.formatID(m.label)}g.eqlabels[m.label]={tag:m.tagID,id:k.id}}if(document.getElementById(k.id)||g.IDs[k.id]||g.eqIDs[k.id]){var l=0,j;do{l++;j=k.id+"_"+l}while(document.getElementById(j)||g.IDs[j]||g.eqIDs[j]);k.id=j;if(m.label){g.eqlabels[m.label].id=j}}g.eqIDs[k.id]=1;this.clearTag();return k},clearTag:function(){var i=this.global;delete i.tag;delete i.tagID;delete i.label},fixInitialMO:function(l){for(var k=0,j=l.length;k0){this.stack[i].Undef(e,f);i--}if(!MathJax.Object.isArray(h)){h=[h]}if(this.isEqn){h.global=true}}this.stack[i].Def(e,h,f)},Push:function(e){this.stack.push(e);this.top=this.stack.length},Pop:function(){var e;if(this.top>1){e=this.stack[--this.top];if(this.isEqn){this.stack.pop()}}else{if(this.isEqn){this.Clear()}}return e},Find:function(e,g){for(var f=this.top-1;f>=0;f--){var h=this.stack[f].Find(e,g);if(h){return h}}return null},Merge:function(e){e.stack[0].MergeGlobals(this);this.stack[this.top-1].Merge(e.stack[0]);var f=[this.top,this.stack.length-this.top].concat(e.stack.slice(1));this.stack.splice.apply(this.stack,f);this.top=this.stack.length},Reset:function(){this.top=this.stack.length},Clear:function(e){this.stack=[this.stack[0].Clear()];this.top=this.stack.length}},{nsFrame:a});b.Add({macros:{begingroup:"BeginGroup",endgroup:"EndGroup",global:"Global",gdef:["Macro","\\global\\def"]}},null,true);d.Parse.Augment({BeginGroup:function(e){d.eqnStack.Push(a())},EndGroup:function(e){if(d.eqnStack.top>1){d.eqnStack.Pop()}else{if(d.rootStack.top===1){d.Error(["ExtraEndMissingBegin","Extra %1 or missing \\begingroup",e])}else{d.eqnStack.Clear();d.rootStack.Pop()}}},csFindMacro:function(e){return(d.eqnStack.Find(e,"macros")||d.rootStack.Find(e,"macros"))},envFindName:function(e){return(d.eqnStack.Find(e,"environments")||d.rootStack.Find(e,"environments"))},setDef:function(e,f){f.isUser=true;d.eqnStack.Def(e,f,"macros",this.stack.env.isGlobal);delete this.stack.env.isGlobal},setEnv:function(e,f){f.isUser=true;d.eqnStack.Def(e,f,"environments")},Global:function(e){var f=this.i;var g=this.GetCSname(e);this.i=f;if(g!=="let"&&g!=="def"&&g!=="newcommand"&&g!=="DeclareMathOperator"&&g!=="Newextarrow"){d.Error(["GlobalNotFollowedBy","%1 not followed by \\let, \\def, or \\newcommand",e])}this.stack.env.isGlobal=true}});d.rootStack=c();d.eqnStack=c(true);d.prefilterHooks.Add(function(){d.rootStack.Reset();d.eqnStack.Clear(true)});d.postfilterHooks.Add(function(){d.rootStack.Merge(d.eqnStack)});MathJax.Hub.Startup.signal.Post("TeX begingroup Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/begingroup.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/boldsymbol.js b/revisions_report_files/mathjax-27/extensions/TeX/boldsymbol.js new file mode 100644 index 0000000..63f2545 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/boldsymbol.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/boldsymbol.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/boldsymbol"]={version:"2.7.6"};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var a=MathJax.ElementJax.mml;var d=MathJax.InputJax.TeX;var b=d.Definitions;var c={};c[a.VARIANT.NORMAL]=a.VARIANT.BOLD;c[a.VARIANT.ITALIC]=a.VARIANT.BOLDITALIC;c[a.VARIANT.FRAKTUR]=a.VARIANT.BOLDFRAKTUR;c[a.VARIANT.SCRIPT]=a.VARIANT.BOLDSCRIPT;c[a.VARIANT.SANSSERIF]=a.VARIANT.BOLDSANSSERIF;c["-tex-caligraphic"]="-tex-caligraphic-bold";c["-tex-oldstyle"]="-tex-oldstyle-bold";b.Add({macros:{boldsymbol:"Boldsymbol"}},null,true);d.Parse.Augment({mmlToken:function(f){if(this.stack.env.boldsymbol){var e=f.Get("mathvariant");if(e==null){f.mathvariant=a.VARIANT.BOLD}else{f.mathvariant=(c[e]||e)}}return f},Boldsymbol:function(h){var e=this.stack.env.boldsymbol,f=this.stack.env.font;this.stack.env.boldsymbol=true;this.stack.env.font=null;var g=this.ParseArg(h);this.stack.env.font=f;this.stack.env.boldsymbol=e;this.Push(g)}});MathJax.Hub.Startup.signal.Post("TeX boldsymbol Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/boldsymbol.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/cancel.js b/revisions_report_files/mathjax-27/extensions/TeX/cancel.js new file mode 100644 index 0000000..ee2d5bc --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/cancel.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/cancel.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/cancel"]={version:"2.7.6",ALLOWED:{color:1,mathcolor:1,background:1,mathbackground:1,padding:1,thickness:1}};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX,a=MathJax.ElementJax.mml,b=MathJax.Extension["TeX/cancel"];b.setAttributes=function(h,e){if(e!==""){e=e.replace(/ /g,"").split(/,/);for(var g=0,d=e.length;g1){this.TEX.Error(["ModelArg2","Color values for the %1 model must be between %2 and %3","rgb",0,1])}d=Math.floor(d*255).toString(16);if(d.length<2){d="0"+d}a+=d}return a},get_RGB:function(b){b=b.replace(/^\s+/,"").replace(/\s+$/,"").split(/\s*,\s*/);var a="#";if(b.length!==3){this.TEX.Error(["ModelArg1","Color values for the %1 model require 3 numbers","RGB"])}for(var c=0;c<3;c++){if(!b[c].match(/^\d+$/)){this.TEX.Error(["InvalidNumber","Invalid number"])}var d=parseInt(b[c]);if(d>255){this.TEX.Error(["ModelArg2","Color values for the %1 model must be between %2 and %3","RGB",0,255])}d=d.toString(16);if(d.length<2){d="0"+d}a+=d}return a},get_gray:function(a){if(!a.match(/^\s*(\d+(\.\d*)?|\.\d+)\s*$/)){this.TEX.Error(["InvalidDecimalNumber","Invalid decimal number"])}var b=parseFloat(a);if(b<0||b>1){this.TEX.Error(["ModelArg2","Color values for the %1 model must be between %2 and %3","gray",0,1])}b=Math.floor(b*255).toString(16);if(b.length<2){b="0"+b}return"#"+b+b+b},get_named:function(a){if(this.colors.hasOwnProperty(a)){return this.colors[a]}return a},padding:function(){var c="+"+this.config.padding;var a=this.config.padding.replace(/^.*?([a-z]*)$/,"$1");var b="+"+(2*parseFloat(c))+a;return{width:b,height:c,depth:c,lspace:this.config.padding}}};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var d=MathJax.InputJax.TeX,a=MathJax.ElementJax.mml;var c=d.Stack.Item;var b=MathJax.Extension["TeX/color"];b.TEX=d;d.Definitions.Add({macros:{color:"Color",textcolor:"TextColor",definecolor:"DefineColor",colorbox:"ColorBox",fcolorbox:"fColorBox"}},null,true);d.Parse.Augment({Color:function(h){var g=this.GetBrackets(h),e=this.GetArgument(h);e=b.getColor(g,e);var f=c.style().With({styles:{mathcolor:e}});this.stack.env.color=e;this.Push(f)},TextColor:function(h){var g=this.GetBrackets(h),f=this.GetArgument(h);f=b.getColor(g,f);var e=this.stack.env.color;this.stack.env.color=f;var i=this.ParseArg(h);if(e){this.stack.env.color}else{delete this.stack.env.color}this.Push(a.mstyle(i).With({mathcolor:f}))},DefineColor:function(g){var f=this.GetArgument(g),e=this.GetArgument(g),h=this.GetArgument(g);b.colors[f]=b.getColor(e,h)},ColorBox:function(g){var f=this.GetArgument(g),e=this.InternalMath(this.GetArgument(g));this.Push(a.mpadded.apply(a,e).With({mathbackground:b.getColor("named",f)}).With(b.padding()))},fColorBox:function(g){var h=this.GetArgument(g),f=this.GetArgument(g),e=this.InternalMath(this.GetArgument(g));this.Push(a.mpadded.apply(a,e).With({mathbackground:b.getColor("named",f),style:"border: "+b.config.border+" solid "+b.getColor("named",h)}).With(b.padding()))}});MathJax.Hub.Startup.signal.Post("TeX color Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/color.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/enclose.js b/revisions_report_files/mathjax-27/extensions/TeX/enclose.js new file mode 100644 index 0000000..233da36 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/enclose.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/enclose.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/enclose"]={version:"2.7.6",ALLOWED:{arrow:1,color:1,mathcolor:1,background:1,mathbackground:1,padding:1,thickness:1}};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX,a=MathJax.ElementJax.mml,b=MathJax.Extension["TeX/enclose"].ALLOWED;c.Definitions.Add({macros:{enclose:"Enclose"}},null,true);c.Parse.Augment({Enclose:function(g){var k=this.GetArgument(g),e=this.GetBrackets(g),j=this.ParseArg(g);var l={notation:k.replace(/,/g," ")};if(e){e=e.replace(/ /g,"").split(/,/);for(var h=0,d=e.length;h0){f=Math.min(3,e.scriptlevel+1)}else{f=(e.displaystyle?0:1)}var g=this.inherit;while(g&&g.type!=="math"){g=g.inherit}if(g){this.selection=f}this.choosing=false;return f},selected:function(){return this.data[this.choice()]},setTeXclass:function(e){return this.selected().setTeXclass(e)},isSpacelike:function(){return this.selected().isSpacelike()},isEmbellished:function(){return this.selected().isEmbellished()},Core:function(){return this.selected()},CoreMO:function(){return this.selected().CoreMO()},toHTML:function(e){e=this.HTMLcreateSpan(e);e.bbox=this.Core().toHTML(e).bbox;if(e.firstChild&&e.firstChild.style.marginLeft){e.style.marginLeft=e.firstChild.style.marginLeft;e.firstChild.style.marginLeft=""}return e},toSVG:function(){var e=this.Core().toSVG();this.SVGsaveData(e);return e},toCommonHTML:function(e){e=this.CHTMLcreateNode(e);this.CHTMLhandleStyle(e);this.CHTMLhandleColor(e);this.CHTMLaddChild(e,this.choice(),{});return e},toPreviewHTML:function(e){e=this.PHTMLcreateSpan(e);this.PHTMLhandleStyle(e);this.PHTMLhandleColor(e);this.PHTMLaddChild(e,this.choice(),{});return e}});MathJax.Hub.Startup.signal.Post("TeX mathchoice Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/mathchoice.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/mediawiki-texvc.js b/revisions_report_files/mathjax-27/extensions/TeX/mediawiki-texvc.js new file mode 100644 index 0000000..bad2797 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/mediawiki-texvc.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/mediawiki-texvc.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/mediawiki-texvc"]={version:"2.7.6"};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){MathJax.InputJax.TeX.Definitions.Add({macros:{AA:["Macro","\u00c5"],alef:["Macro","\\aleph"],alefsym:["Macro","\\aleph"],Alpha:["Macro","\\mathrm{A}"],and:["Macro","\\land"],ang:["Macro","\\angle"],Bbb:["Macro","\\mathbb"],Beta:["Macro","\\mathrm{B}"],bold:["Macro","\\mathbf"],bull:["Macro","\\bullet"],C:["Macro","\\mathbb{C}"],Chi:["Macro","\\mathrm{X}"],clubs:["Macro","\\clubsuit"],cnums:["Macro","\\mathbb{C}"],Complex:["Macro","\\mathbb{C}"],coppa:["Macro","\u03D9"],Coppa:["Macro","\u03D8"],Dagger:["Macro","\\ddagger"],Digamma:["Macro","\u03DC"],darr:["Macro","\\downarrow"],dArr:["Macro","\\Downarrow"],Darr:["Macro","\\Downarrow"],dashint:["Macro","\\unicodeInt{x2A0D}"],ddashint:["Macro","\\unicodeInt{x2A0E}"],diamonds:["Macro","\\diamondsuit"],empty:["Macro","\\emptyset"],Epsilon:["Macro","\\mathrm{E}"],Eta:["Macro","\\mathrm{H}"],euro:["Macro","\u20AC"],exist:["Macro","\\exists"],geneuro:["Macro","\u20AC"],geneuronarrow:["Macro","\u20AC"],geneurowide:["Macro","\u20AC"],H:["Macro","\\mathbb{H}"],hAar:["Macro","\\Leftrightarrow"],harr:["Macro","\\leftrightarrow"],Harr:["Macro","\\Leftrightarrow"],hearts:["Macro","\\heartsuit"],image:["Macro","\\Im"],infin:["Macro","\\infty"],Iota:["Macro","\\mathrm{I}"],isin:["Macro","\\in"],Kappa:["Macro","\\mathrm{K}"],koppa:["Macro","\u03DF"],Koppa:["Macro","\u03DE"],lang:["Macro","\\langle"],larr:["Macro","\\leftarrow"],Larr:["Macro","\\Leftarrow"],lArr:["Macro","\\Leftarrow"],lrarr:["Macro","\\leftrightarrow"],Lrarr:["Macro","\\Leftrightarrow"],lrArr:["Macro","\\Leftrightarrow"],Mu:["Macro","\\mathrm{M}"],N:["Macro","\\mathbb{N}"],natnums:["Macro","\\mathbb{N}"],Nu:["Macro","\\mathrm{N}"],O:["Macro","\\emptyset"],oint:["Macro","\\unicodeInt{x222E}"],oiint:["Macro","\\unicodeInt{x222F}"],oiiint:["Macro","\\unicodeInt{x2230}"],ointctrclockwise:["Macro","\\unicodeInt{x2233}"],officialeuro:["Macro","\u20AC"],Omicron:["Macro","\\mathrm{O}"],or:["Macro","\\lor"],P:["Macro","\u00B6"],pagecolor:["Macro","",1],part:["Macro","\\partial"],plusmn:["Macro","\\pm"],Q:["Macro","\\mathbb{Q}"],R:["Macro","\\mathbb{R}"],rang:["Macro","\\rangle"],rarr:["Macro","\\rightarrow"],Rarr:["Macro","\\Rightarrow"],rArr:["Macro","\\Rightarrow"],real:["Macro","\\Re"],reals:["Macro","\\mathbb{R}"],Reals:["Macro","\\mathbb{R}"],Rho:["Macro","\\mathrm{P}"],sdot:["Macro","\\cdot"],sampi:["Macro","\u03E1"],Sampi:["Macro","\u03E0"],sect:["Macro","\\S"],spades:["Macro","\\spadesuit"],stigma:["Macro","\u03DB"],Stigma:["Macro","\u03DA"],sub:["Macro","\\subset"],sube:["Macro","\\subseteq"],supe:["Macro","\\supseteq"],Tau:["Macro","\\mathrm{T}"],textvisiblespace:["Macro","\u2423"],thetasym:["Macro","\\vartheta"],uarr:["Macro","\\uparrow"],uArr:["Macro","\\Uparrow"],Uarr:["Macro","\\Uparrow"],unicodeInt:["Macro","\\mathop{\\vcenter{\\mathchoice{\\huge\\unicode{#1}\\,}{\\unicode{#1}}{\\unicode{#1}}{\\unicode{#1}}}\\,}\\nolimits",1],varcoppa:["Macro","\u03D9"],varstigma:["Macro","\u03DB"],varointclockwise:["Macro","\\unicodeInt{x2232}"],vline:["Macro","\\smash{\\large\\lvert}",0],weierp:["Macro","\\wp"],Z:["Macro","\\mathbb{Z}"],Zeta:["Macro","\\mathrm{Z}"]}})});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/mediawiki-texvc.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/mhchem.js b/revisions_report_files/mathjax-27/extensions/TeX/mhchem.js new file mode 100644 index 0000000..7901f0e --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/mhchem.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/mhchem.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +if(MathJax.Extension["TeX/mhchem"]){MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/mhchem.js")}else{MathJax.Extension["TeX/mhchem"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.mhchem",{legacy:true})};if(!MathJax.Extension["TeX/mhchem"].config.legacy){if(!MathJax.Ajax.config.path.mhchem){MathJax.Ajax.config.path.mhchem=MathJax.Hub.config.root+"/extensions/TeX/mhchem3"}MathJax.Callback.Queue(["Require",MathJax.Ajax,"[mhchem]/mhchem.js"],["loadComplete",MathJax.Ajax,"[MathJax]/extensions/TeX/mhchem.js"])}else{MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.InputJax.TeX;var a=MathJax.Object.Subclass({string:"",i:0,tex:"",TEX:"",atom:false,sup:"",sub:"",presup:"",presub:"",Init:function(c){this.string=c},ParseTable:{"-":"Minus","+":"Plus","(":"Open",")":"Close","[":"Open","]":"Close","<":"Less","^":"Superscript",_:"Subscript","*":"Dot",".":"Dot","=":"Equal","#":"Pound","$":"Math","\\":"Macro"," ":"Space"},Arrows:{"->":"rightarrow","<-":"leftarrow","<->":"leftrightarrow","<=>":"rightleftharpoons","<=>>":"Rightleftharpoons","<<=>":"Leftrightharpoons","^":"uparrow",v:"downarrow"},Bonds:{"-":"-","=":"=","#":"\\equiv","~":"\\tripledash","~-":"\\begin{CEstack}{}\\tripledash\\\\-\\end{CEstack}","~=":"\\raise2mu{\\begin{CEstack}{}\\tripledash\\\\-\\\\-\\end{CEstack}}","~--":"\\raise2mu{\\begin{CEstack}{}\\tripledash\\\\-\\\\-\\end{CEstack}}","-~-":"\\raise2mu{\\begin{CEstack}{}-\\\\\\tripledash\\\\-\\end{CEstack}}","...":"{\\cdot}{\\cdot}{\\cdot}","....":"{\\cdot}{\\cdot}{\\cdot}{\\cdot}","->":"\\rightarrow","<-":"\\leftarrow","??":"\\text{??}"},Parse:function(){this.tex="";this.atom=false;while(this.i"){this.i+=2;this.AddArrow("->");return}else{this.tex+="{-}"}}this.i++},ParsePlus:function(d){if(this.atom){this.sup+=d}else{this.FinishAtom();this.tex+=d}this.i++},ParseDot:function(d){this.FinishAtom();this.tex+="\\cdot ";this.i++},ParseEqual:function(d){this.FinishAtom();this.tex+="{=}";this.i++},ParsePound:function(d){this.FinishAtom();this.tex+="{\\equiv}";this.i++},ParseOpen:function(e){this.FinishAtom();var d=this.Match(/^\([v^]\)/);if(d){this.tex+="{\\"+this.Arrows[d.charAt(1)]+"}"}else{this.tex+="{"+e;this.i++}},ParseClose:function(d){this.FinishAtom();this.atom=true;this.tex+=d+"}";this.i++},ParseLess:function(e){this.FinishAtom();var d=this.Match(/^(<->?|<=>>?|<<=>)/);if(!d){this.tex+=e;this.i++}else{this.AddArrow(d)}},ParseSuperscript:function(f){f=this.string.charAt(++this.i);if(f==="{"){this.i++;var d=this.Find("}");if(d==="-."){this.sup+="{-}{\\cdot}"}else{if(d){this.sup+=a(d).Parse().replace(/^\{-\}/,"-")}}}else{if(f===" "||f===""){this.tex+="{\\"+this.Arrows["^"]+"}";this.i++}else{var e=this.Match(/^(\d+|-\.)/);if(e){this.sup+=e}}}},ParseSubscript:function(e){if(this.string.charAt(++this.i)=="{"){this.i++;this.sub+=a(this.Find("}")).Parse().replace(/^\{-\}/,"-")}else{var d=this.Match(/^\d+/);if(d){this.sub+=d}}},ParseMath:function(d){this.FinishAtom();this.i++;this.tex+=this.Find(d)},ParseMacro:function(f){this.FinishAtom();this.i++;var d=this.Match(/^([a-z]+|.)/i)||" ";if(d==="sbond"){this.tex+="{-}"}else{if(d==="dbond"){this.tex+="{=}"}else{if(d==="tbond"){this.tex+="{\\equiv}"}else{if(d==="bond"){var e=(this.Match(/^\{.*?\}/)||"");e=e.substr(1,e.length-2);this.tex+="{"+(this.Bonds[e]||"\\text{??}")+"}"}else{if(d==="{"){this.tex+="{\\{"}else{if(d==="}"){this.tex+="\\}}";this.atom=true}else{this.tex+=f+d}}}}}}},ParseSpace:function(d){this.FinishAtom();this.i++},ParseOther:function(d){this.FinishAtom();this.tex+=d;this.i++},AddArrow:function(e){var g=this.Match(/^[CT]\[/);if(g){this.i--;g=g.charAt(0)}var d=this.GetBracket(g),f=this.GetBracket(g);e=this.Arrows[e];if(d||f){if(f){e+="["+f+"]"}e+="{"+d+"}";e="\\mathrel{\\x"+e+"}"}else{e="\\long"+e+" "}this.tex+=e},FinishAtom:function(c){if(this.sup||this.sub||this.presup||this.presub){if(!c&&!this.atom){if(this.tex===""&&!this.sup&&!this.sub){return}if(!this.presup&&!this.presub&&(this.tex===""||this.tex==="{"||(this.tex==="}"&&this.TEX.substr(-1)==="{"))){this.presup=this.sup,this.presub=this.sub;this.sub=this.sup="";this.TEX+=this.tex;this.tex="";return}}if(this.sub&&!this.sup){this.sup="\\Space{0pt}{0pt}{.2em}"}if((this.presup||this.presub)&&this.tex!=="{"){if(!this.presup&&!this.sup){this.presup="\\Space{0pt}{0pt}{.2em}"}this.tex="\\CEprescripts{"+(this.presub||"\\CEnone")+"}{"+(this.presup||"\\CEnone")+"}{"+(this.tex!=="}"?this.tex:"")+"}{"+(this.sub||"\\CEnone")+"}{"+(this.sup||"\\CEnone")+"}"+(this.tex==="}"?"}":"");this.presub=this.presup=""}else{if(this.sup){this.tex+="^{"+this.sup+"}"}if(this.sub){this.tex+="_{"+this.sub+"}"}}this.sup=this.sub=""}this.TEX+=this.tex;this.tex="";this.atom=false},GetBracket:function(e){if(this.string.charAt(this.i)!=="["){return""}this.i++;var d=this.Find("]");if(e==="C"){d="\\ce{"+d+"}"}else{if(e==="T"){if(!d.match(/^\{.*\}$/)){d="{"+d+"}"}d="\\text"+d}}return d},Match:function(d){var c=d.exec(this.string.substr(this.i));if(c){c=c[0];this.i+=c.length}return c},Find:function(h){var d=this.string.length,e=this.i,g=0;while(this.i0))return c;if(f.k||(t=_.$),!f.A)break t}}if(i<=0)throw["MhchemBugU","mhchem bug U. Please report."]}}, +v:function(t,n){if(n)if(Array.isArray(n))for(var e=0;e]/,"#":/^[#\u2261]/,"+":/^\+/,"-$":/^-(?=[\s_},;\]/]|$|\([a-z]+\))/,"-9":/^-(?=[0-9])/,"@g":/^-(?=(?:[spd]|sp)(?:$|[\s,;\)\]\}]))/,"-":/^-/,"``":/^(?:\\pm|\$\\pm\$|\+-|\+\/-)/,"~N":/^(?:\+|(?:[\-=<>]|<<|>>|\\approx|\$\\approx\$)(?=\s|$|-?[0-9]))/,"~`":/^(?:v|\(v\)|\^|\(\^\))(?=$|[\s,;\)\]\}])/, +"@s":function(t){return e._.M(t,"\\bond{","","","}")},"->":/^(?:<->|<-->|->|<-|<=>>|<<=>|<=>|[\u2192\u27F6\u21CC])/,"@n":/^[CMT](?=\[)/, +"@p":function(t){return e._.M(t,"[","","","]")},"`c":/^(&|@r|\\hline)\s*/,"@q":/^(?:\\[,\ ;:])/, +"@H":function(t){return e._.M(t,"",/^\\[a-zA-Z]+\{/,"}","","","{","}","",!0)}, +"@G":function(t){return e._.M(t,"",/^\\[a-zA-Z]+\{/,"}","")},"@u":/^\\ca(?:\s+|(?![a-zA-Z]))/,"@F":/^(?:\\[a-zA-Z]+\s*|\\[_&{}%])/,"~O":/^(?:[0-9]{1,2}[spdfgh]|[0-9]{0,2}sp)(?=$|[^a-zA-Z])/,"~P":/^[\/~|]/, +"@z":function(t){return e._.M(t,"\\frac{","","","}","{","","","}")}, +"@B":function(t){return e._.M(t,"\\overset{","","","}","{","","","}")}, +"@D":function(t){return e._.M(t,"\\underset{","","","}","{","","","}")}, +"@C":function(t){return e._.M(t,"\\underbrace{","","","}_","{","","","}")}, +"@x":function(t){return e._.M(t,"\\color{","","","}")}, +"@y":function(t){return e._.M(t,"\\color{","","","}","{","","","}")}, +"@w":function(t){return e._.M(t,"\\color","\\","",/^(?=\{)/,"{","","","}")}, +"@v":function(t){return e._.M(t,"\\ce{","","","}")},"~W":/^(?:[+-][IVX]+|\\pm\s*0|\$\\pm\$\s*0)$/,"%Y":/^(?:[+-]?\s?[IVX]+|\\pm\s*0|\$\\pm\$\s*0)$/,"%a":/^[IVX]+/,"@k":/^[+\-]?(?:[0-9]+|\$[a-z]\$|[a-z])\/[0-9]+(?:\$[a-z]\$|[a-z])?$/, +"~@":function(t){var n;if(n=t.match(/^(?:(?:(?:\([+\-]?[0-9]+\/[0-9]+\)|[+\-]?(?:[0-9]+|\$[a-z]\$|[a-z])\/[0-9]+|[+\-]?[0-9]+[.,][0-9]+|[+\-]?\.[0-9]+|[+\-]?[0-9]+)(?:[a-z](?=\s*[A-Z]))?)|[+\-]?[a-z](?=\s*[A-Z])|\+(?!\s))/))return{s:n[0],$:t.substr(n[0].length)};var a=e._.M(t,"","$","$","");return a&&(n=a.s.match(/^\$(?:\(?[+\-]?(?:[0-9]*[a-z]?[+\-])?[0-9]*[a-z](?:[+\-][0-9]*[a-z]?)?\)?|\+|-)\$$/))?{s:n[0],$:t.substr(n[0].length)}:null}, +"~~":function(t){return this["~@"](t)},"@c":/^(?:[A-Z][a-z]{0,2}|i)(?=,)/, +"~B":function(t){if(t.match(/^\([a-z]+\)$/))return null;var n=t.match(/^(?:[a-z]|(?:[0-9\ \+\-\,\.\(\)]+[a-z])+[0-9\ \+\-\,\.\(\)]*|(?:[a-z][0-9\ \+\-\,\.\(\)]+)+[a-z]?)$/);return n?{s:n[0],$:t.substr(n[0].length)}:null},"%w":/^(?:pH|pOH|pC|pK|iPr|iBu)(?=$|[^a-zA-Z])/,"/":/^\s*(\/)\s*/,"//":/^\s*(\/\/)\s*/,"*":/^\s*[*.]\s*/}, +M:function(t,n,e,a,o,r,i,c,u,p){var s=function(t,n){if("string"==typeof n)return 0!==t.indexOf(n)?null:n;var e=t.match(n);return e?e[0]:null},_=s(t,n);if(null===_)return null;if(t=t.substr(_.length),null===(_=s(t,e)))return null;var f=function(t,n,e){for(var a=0;n":{"0|1|2|3":{h:"r=",g:"r"},"a|as":{h:["~Q","r="],g:"r"},"*":{h:["~Q","r="],g:"r"}}, +"+":{o:{h:"~q",g:"d"},"d|D":{h:"d=",g:"d"},q:{h:"d=",g:"qd"},"qd|qD":{h:"d=",g:"qd"},dq:{h:["~Q","d="],g:"d"},3:{h:["%g","~Q","~N"],g:"0"}}, +"~@":{"0|2":{h:"a=",g:"a"}}, +"``":{"0|1|2|a|as":{h:["%g","~Q",{l:"~N",S:"\\pm"}],g:"0"}}, +"~N":{"0|1|2|a|as":{h:["%g","~Q","~N"],g:"0"}}, +"-$":{"o|q":{h:["~d","~Q"],g:"qd"},d:{h:"d=",g:"d"},D:{h:["~Q",{l:"~c",S:"-"}],g:"3"},q:{h:"d=",g:"qd"},qd:{h:"d=",g:"qd"},"qD|dq":{h:["~Q",{l:"~c",S:"-"}],g:"3"}}, +"-9":{"3|o":{h:["~Q",{l:"~G",S:"~F"}],g:"3"}}, +"@g":{o:{h:["~Q",{l:"~G",S:"~F"}],g:"2"},d:{h:["~Q",{l:"~G",S:"~F"}],g:"2"}}, +"-":{"0|1|2":{h:[{l:"~Q",S:1},"~b",{l:"~c",S:"-"}],g:"3"},3:{h:{l:"~c",S:"-"}}, +a:{h:["~Q",{l:"~G",S:"~F"}],g:"2"},as:{h:[{l:"~Q",S:2},{l:"~c",S:"-"}],g:"3"},b:{h:"b="},o:{h:{l:"`d",S:!1},g:"2"},q:{h:{l:"`d",S:!1},g:"2"},"d|qd|dq":{h:{l:"`d",S:!0},g:"2"},"D|qD|p":{h:["~Q",{l:"~c",S:"-"}],g:"3"}}, +"~~":{"1|3":{h:"a=",g:"a"}}, +"~J":{"0|1|2|3|a|as|b|p|bp|o":{h:"o=",g:"o"},"q|dq":{h:["~Q","o="],g:"o"},"d|D|qd|qD":{h:"~K",g:"o"}}, +"~r":{o:{h:"q=",g:"q"},"d|D":{h:"q=",g:"dq"},q:{h:["~Q","o="],g:"o"},a:{h:"o=",g:"o"}}, +"%i":{"b|p|bp":{}}, +"%j":{a:{g:"as"},0:{h:"%g"},"1|2":{h:"%h"},"r|rt|rd|%f|%e":{h:"~Q",g:"0"},"*":{h:["~Q","%h"],g:"1"}}, +"`c":{"1|2":{h:["~Q",{l:"~H",S:"`c"}]}, +"*":{h:["~Q",{l:"~H",S:"`c"}],g:"0"}}, +"@p":{"r|rt":{h:"%~",g:"rd"},"rd|%f":{h:"%c",g:"%e"}}, +"@j":{"o|d|D|dq|qd|qD":{h:["~Q",{l:"~c",S:"..."}],g:"3"},"*":{h:[{l:"~Q",S:1},{l:"~G",S:"~w"}],g:"1"}}, +". |* ":{"*":{h:["~Q",{l:"~G",S:"@Y"}],g:"1"}}, +"%k":{"*":{h:["~Q","%m"],g:"1"}}, +"@L":{"a|as|o":{h:["o=","~Q","~X"],g:"2"},"0|1|2|3":{h:["o=","~Q","~X"],g:"2"},"*":{h:["~Q","o=","~Q","~X"],g:"2"}}, +"@d":{"0|1|2|3|b|p|bp|o":{h:["o=","~Y"],g:"o"},"a|as|d|D|q|qd|qD|dq":{h:["~Q","o=","~Y"],g:"o"}}, +", ":{"*":{h:["~Q","~n"],g:"0"}}, +"^_":{"*":{}}, +"@Q|@M":{"0|1|2|as":{h:"b=",g:"b"},p:{h:"b=",g:"bp"},"3|o":{h:"~q",g:"D"},q:{h:"d=",g:"qD"},"d|D|qd|qD|dq":{h:["~Q","d="],g:"D"}}, +"^a|@P|@O|^\\x|'":{"0|1|2|as":{h:"b=",g:"b"},p:{h:"b=",g:"bp"},"3|o":{h:"~q",g:"d"},q:{h:"d=",g:"qd"},"d|qd|D|qD":{h:"d="},dq:{h:["~Q","d="],g:"d"}}, +"`~":{"d|D|q|qd|qD|dq":{h:["~Q","q="],g:"q"}}, +"@V|@R|_9|@U|@T|@S":{"0|1|2|as":{h:"p=",g:"p"},b:{h:"p=",g:"bp"},"3|o":{h:"q=",g:"q"},"d|D":{h:"q=",g:"dq"},"q|qd|qD|dq":{h:["~Q","q="],g:"q"}}, +"%A":{"0|1|2|3|a|as|o|q|d|D|qd|qD|dq":{h:[{l:"~Q",S:2},"~c"],g:"3"}}, +"#":{"0|1|2|3|a|as|o":{h:[{l:"~Q",S:2},{l:"~c",S:"#"}],g:"3"}}, +"{}":{"*":{h:{l:"~Q",S:1},g:"1"}}, +"%y":{"0|1|2|3|a|as|b|p|bp":{h:"o=",g:"o"},"o|d|D|q|qd|qD|dq":{h:["~Q","o="],g:"o"}}, +"@`":{a:{h:"a="},"0|1|2|3|as|b|p|bp|o":{h:"o=",g:"o"},"as|o":{h:"o="},"q|d|D|qd|qD|dq":{h:["~Q","o="],g:"o"}}, +"@s":{"*":{h:[{l:"~Q",S:2},"~c"],g:"3"}}, +"@z":{"*":{h:[{l:"~Q",S:1},"~E"],g:"3"}}, +"@B":{"*":{h:[{l:"~Q",S:2},"~U"],g:"3"}}, +"@D":{"*":{h:[{l:"~Q",S:2},"%v"],g:"3"}}, +"@C":{"*":{h:[{l:"~Q",S:2},"%t"],g:"3"}}, +"@y|@w":{"*":{h:[{l:"~Q",S:2},"~h"],g:"3"}}, +"@x":{"*":{h:[{l:"~Q",S:2},"~j"]}}, +"@v":{"*":{h:[{l:"~Q",S:2},"ce"],g:"3"}}, +"@q":{"*":{h:[{l:"~Q",S:1},"~p"],g:"1"}}, +"@H|@G|@F":{"0|1|2|3|a|as|b|p|bp|o|c0":{h:["o=","~Q"],g:"3"},"*":{h:["~Q","o=","~Q"],g:"3"}}, +"~P":{"*":{h:[{l:"~Q",S:1},"~p"],g:"3"}}, +"~y":{a:{h:"@W",g:"o",k:!0},as:{h:["~Q","%h"],g:"1",k:!0},"r|rt|rd|%f|%e":{h:["~Q"],g:"0",k:!0},"*":{h:["~Q","~p"],g:"3"}}}),m:{ +"~K":function(t,n){var a;if((t.d||"").match(/^[0-9]+$/)){var o=t.d;t.d=void 0,a=this["~Q"](t),t.b=o}else a=this["~Q"](t);return e.m["o="](t,n),a}, +"~q":function(t,n){t.d=n,t.dType="kv"}, +"~d":function(t,n){if(t["@~"]){var a=[];return e.v(a,this["~Q"](t)),e.v(a,e.m["~c"](t,n,"-")),a}t.d=n}, +"`d":function(t,n,a){var o=e._.s("~O",t.o||""),r=e._.s("~L",t.o||""),i=e._.s("~M",t.o||""),c=e._.s("@a",t.o||""),u="-"===n&&(o&&""===o.$||r||i||c);!u||t.a||t.b||t.p||t.d||t.q||o||!i||(t.o="$"+t.o+"$");var p=[];return u?(e.v(p,this["~Q"](t)),p.push({l:"~F"})):(o=e._.s("~r",t.d||""),a&&o&&""===o.$?(e.v(p,e.m["d="](t,n)),e.v(p,this["~Q"](t))):(e.v(p,this["~Q"](t)),e.v(p,e.m["~c"](t,n,"-")))),p}, +"@W":function(t){t.o=t.a,t.a=void 0}, +"%h":function(t){t.sb=!0}, +"%g":function(t){t.sb=!1}, +"~b":function(t){t["@~"]=!0}, +"~a":function(t){t["@~"]=!1}, +"~X":function(t){t["@@"]++}, +"~Y":function(t){t["@@"]--}, +"%m":function(t,n){return{l:"%m",p1:e.go(n,"o")}}, +"~n":function(t,n){var e=n.replace(/\s*$/,"");return e!==n&&0===t["@@"]?{l:"~k",p1:e}:{l:"~l",p1:e}}, +"~Q":function(t,n,a){var o,r,i;t.r?(r="M"===t.rdt?e.go(t.rd,"%o"):"T"===t.rdt?[{l:"%p",p1:t.rd||""}]:e.go(t.rd),i="M"===t.rqt?e.go(t.rq,"%o"):"T"===t.rqt?[{l:"%p",p1:t.rq||""}]:e.go(t.rq),o={l:"~%",r:t.r,rd:r,rq:i}):(o=[],(t.a||t.b||t.p||t.o||t.q||t.d||a)&&(t.sb&&o.push({l:"~A"}),t.o||t.q||t.d||t.b||t.p||2===a?t.o||t.q||t.d||!t.b&&!t.p?t.o&&"kv"===t.dType&&e._.s("%Y",t.d||"")?t.dType="~V":t.o&&"kv"===t.dType&&!t.q&&(t.dType=void 0):(t.o=t.a,t.d=t.b,t.q=t.p,t.a=t.b=t.p=void 0):(t.o=t.a,t.a=void 0),o.push({l:"~e",a:e.go(t.a,"a"),b:e.go(t.b,"bd"),p:e.go(t.p,"pq"),o:e.go(t.o,"o"),q:e.go(t.q,"pq"),d:e.go(t.d,"~V"===t.dType?"~V":"bd"),dType:t.dType})));for(var c in t)"@@"!==c&&"@~"!==c&&delete t[c];return o}, +"`@":function(t,n){var a=["{"];return e.v(a,e.go(n,"~V")),a.push("}"),a}, +"~E":function(t,n){return{l:"~D",p1:e.go(n[0]),p2:e.go(n[1])}}, +"~U":function(t,n){return{l:"~T",p1:e.go(n[0]),p2:e.go(n[1])}}, +"%v":function(t,n){return{l:"%u",p1:e.go(n[0]),p2:e.go(n[1])}}, +"%t":function(t,n){return{l:"%s",p1:e.go(n[0]),p2:e.go(n[1])}}, +"~h":function(t,n){return{l:"~g",G:n[0],X:e.go(n[1])}}, +"r=":function(t,n){t.r=n}, +"%%":function(t,n){t.rdt=n}, +"%~":function(t,n){t.rd=n}, +"%d":function(t,n){t.rqt=n}, +"%c":function(t,n){t.rq=n}, +"~N":function(t,n,e){return{l:"~N",B:e||n}}}}, +a:{u:e.C({"~z":{"*":{}}, +"@k":{0:{h:"@l"}}, +"~x":{0:{g:"1",k:!0}}, +"@%":{"*":{h:"%n",g:"1"}}, +",":{"*":{h:{l:"~G",S:"~o"}}}, +"~y":{"*":{h:"~p"}}}),m:{}}, +o:{u:e.C({"~z":{"*":{}}, +"@k":{0:{h:"@l"}}, +"~x":{0:{g:"1",k:!0}}, +"~J":{"*":{h:"rm"}}, +"@u":{"*":{h:{l:"~G",S:"~f"}}}, +"@H|@G|@F":{"*":{h:"~p"}}, +"@b|@%":{"*":{h:"%o"}}, +"%x":{"*":{h:"%z"}}, +"~y":{"*":{h:"~p"}}}),m:{}}, +"%p":{u:e.C({"~z":{"*":{h:"~Q"}}, +"%y":{"*":{h:"%q"}}, +"@b|@%":{"*":{h:"%o"}}, +"@A":{"*":{h:["~Q","rm"]}}, +"@q|@H|@G|@F":{"*":{h:["~Q","~p"]}}, +"~x":{"*":{h:"%q"}}}),m:{ +"~Q":function(t){if(t.F){var n={l:"%p",p1:t.F};for(var e in t)delete t[e];return n}}}}, +pq:{u:e.C({"~z":{"*":{}}, +"%k":{"*":{h:"%m"}}, +i$:{0:{g:"!f",k:!0}}, +"@c":{0:{h:"rm",g:"0"}}, +"~B":{0:{g:"f",k:!0}}, +"@k":{0:{h:"@l"}}, +"~x":{0:{g:"!f",k:!0}}, +"@b|@%":{"*":{h:"%o"}}, +"%x":{"*":{h:"%p"}}, +"@X":{f:{h:"%o"}}, +"~J":{"*":{h:"rm"}}, +"@i":{"*":{h:"@m"}}, +",":{"*":{h:{l:"~H",S:"~m"}}}, +"@y|@w":{"*":{h:"~h"}}, +"@x":{"*":{h:"~j"}}, +"@v":{"*":{h:"ce"}}, +"@q|@H|@G|@F":{"*":{h:"~p"}}, +"~y":{"*":{h:"~p"}}}),m:{ +"%m":function(t,n){return{l:"%H",p1:e.go(n,"o")}}, +"~h":function(t,n){return{l:"~g",G:n[0],X:e.go(n[1],"pq")}}}}, +bd:{u:e.C({"~z":{"*":{}}, +x$:{0:{g:"!f",k:!0}}, +"~B":{0:{g:"f",k:!0}}, +"~x":{0:{g:"!f",k:!0}}, +"@h":{"*":{h:"@m"}}, +".":{"*":{h:{l:"~G",S:"~v"}}}, +"@X":{f:{h:"%o"}}, +x:{"*":{h:{l:"~G",S:"@o"}}}, +"~J":{"*":{h:"rm"}}, +"'":{"*":{h:{l:"~G",S:"%@"}}}, +"@b|@%":{"*":{h:"%o"}}, +"%x":{"*":{h:"%p"}}, +"@y|@w":{"*":{h:"~h"}}, +"@x":{"*":{h:"~j"}}, +"@v":{"*":{h:"ce"}}, +"@q|@H|@G|@F":{"*":{h:"~p"}}, +"~y":{"*":{h:"~p"}}}),m:{ +"~h":function(t,n){return{l:"~g",G:n[0],X:e.go(n[1],"bd")}}}}, +"~V":{u:e.C({"~z":{"*":{}}, +"%a":{"*":{h:"%b"}}, +"@b|@%":{"*":{h:"%o"}}, +"~x":{"*":{h:"~p"}}}),m:{ +"%b":function(t,n){return{l:"%a",p1:n||""}}}}, +"%o":{u:e.C({"~z":{"*":{h:"~Q"}}, +"@v":{"*":{h:["~Q","ce"]}}, +"%y|@q|@H|@G|@F":{"*":{h:"o="}}, +"~x":{"*":{h:"o="}}}),m:{ +"~Q":function(t){if(t.o){var n={l:"%o",p1:t.o};for(var e in t)delete t[e];return n}}}}, +"%n":{u:e.C({"~z":{"*":{h:"~Q"}}, +"@v":{"*":{h:["~Q","ce"]}}, +"%y|@q|@H|@G|@F":{"*":{h:"o="}}, +"-|+":{"*":{h:"%r"}}, +"~x":{"*":{h:"o="}}}),m:{ +"%r":function(t,n){t.o=(t.o||"")+"{"+n+"}"}, +"~Q":function(t){if(t.o){var n={l:"%o",p1:t.o};for(var e in t)delete t[e];return n}}}}, +"@m":{u:e.C({"~z":{"*":{}}, +",":{"*":{h:"~n"}}, +"~x":{"*":{h:"~p"}}}),m:{ +"~n":function(){return{l:"~o"}}}}, +pu:{u:e.C({"~z":{"*":{h:"~Q"}}, +"`e":{"*":{h:["~Q","%j"]}}, +"@L|@d":{"0|a":{h:"~p"}}, +"`a":{0:{h:"`b",g:"a"}}, +"%Q":{0:{h:"%W",g:"a"}}, +"%j":{"0|a":{}}, +"``":{"0|a":{h:{l:"~N",S:"\\pm"},g:"0"}}, +"~N":{"0|a":{h:"~p",g:"0"}}, +"//":{d:{h:"o=",g:"/"}}, +"/":{d:{h:"o=",g:"/"}}, +"%y|~x":{"0|d":{h:"d=",g:"d"},a:{h:["%j","d="],g:"d"},"/|q":{h:"q=",g:"q"}}}),m:{ +"%W":function(t,n){var a=[];return"+-"===n[0]||"+/-"===n[0]?a.push("\\pm "):n[0]&&a.push(n[0]),n[1]&&(e.v(a,e.go(n[1],"%U")),n[2]&&(n[2].match(/[,.]/)?e.v(a,e.go(n[2],"%U")):a.push(n[2])),n[3]=n[4]||n[3],n[3]&&(n[3]=n[3].trim(),"e"===n[3]||"*"===n[3].substr(0,1)?a.push({l:"%K"}):a.push({l:"%M"}))),n[3]&&a.push("10^{"+n[5]+"}"),a}, +"`b":function(t,n){var a=[];return"+-"===n[0]||"+/-"===n[0]?a.push("\\pm "):n[0]&&a.push(n[0]),e.v(a,e.go(n[1],"%U")),a.push("^{"+n[2]+"}"),a}, +"~N":function(t,n,e){return{l:"~N",B:e||n}}, +"%j":function(){return{l:"%N"}}, +"~Q":function(t){var n,a=e._.s("%x",t.d||"");a&&""===a.$&&(t.d=a.s);var o=e._.s("%x",t.q||"");if(o&&""===o.$&&(t.q=o.s),t.d&&(t.d=t.d.replace(/\u00B0C|\^oC|\^{o}C/g,"{}^{\\circ}C"),t.d=t.d.replace(/\u00B0F|\^oF|\^{o}F/g,"{}^{\\circ}F")),t.q){t.q=t.q.replace(/\u00B0C|\^oC|\^{o}C/g,"{}^{\\circ}C"),t.q=t.q.replace(/\u00B0F|\^oF|\^{o}F/g,"{}^{\\circ}F");var r={d:e.go(t.d,"pu"),q:e.go(t.q,"pu")};"//"===t.o?n={l:"%P",p1:r.d,p2:r.q}:(n=r.d,r.d.length>1||r.q.length>1?n.push({l:"%S"}):n.push({l:"/"}),e.v(n,r.q))}else n=e.go(t.d,"%O");for(var i in t)delete t[i];return n}}}, +"%O":{u:e.C({"~z":{"*":{h:"~Q"}}, +"*":{"*":{h:["~Q","%K"],g:"0"}}, +"@F":{"*":{h:"%`"}}, +"%j":{"*":{h:["~Q","%j"],g:"0"}}, +"@Q|%R":{1:{h:"%R"}}, +"@i":{0:{h:"%`",g:"0"},1:{h:"%R",g:"0"}}, +"%y|~x":{"*":{h:"%`",g:"1"}}}),m:{ +"%K":function(){return{l:"%L"}}, +"%R":function(t,n){t.rm+="^{"+n+"}"}, +"%j":function(){return{l:"`%"}}, +"~Q":function(t){var n=[];if(t.rm){var a=e._.s("%x",t.rm||"");n=a&&""===a.$?e.go(a.s,"pu"):{l:"rm",p1:t.rm}}for(var o in t)delete t[o];return n}}}, +"%U":{u:e.C({"~z":{0:{h:"~R"},o:{h:"~S"}}, +",":{0:{h:["~R","~n"],g:"o"}}, +".":{0:{h:["~R","~p"],g:"o"}}, +"~x":{"*":{h:"%q"}}}),m:{ +"~n":function(){return{l:"~o"}}, +"~R":function(t){var n=[];if(t.F=t.F||"",t.F.length>4){var e=t.F.length%3;0===e&&(e=3);for(var a=t.F.length-3;a>0;a-=3)n.push(t.F.substr(a,3)),n.push({l:"%T"});n.push(t.F.substr(0,e)),n.reverse()}else n.push(t.F);for(var o in t)delete t[o];return n}, +"~S":function(t){var n=[];if(t.F=t.F||"",t.F.length>4){for(var e=t.F.length-3,a=0;a"===t.r||"<=>>"===t.r||"<<=>"===t.r||"<--\x3e"===t.r?(u="\\long"+u,i&&(u="\\overset{"+i+"}{"+u+"}"),c&&(u="\\underset{\\lower7mu{"+c+"}}{"+u+"}"),u=" {}\\mathrel{"+u+"}{} "):(c&&(u+="[{"+c+"}]"),u=" {}\\mathrel{\\x"+(u+="{"+i+"}")+"}{} "):u=" {}\\mathrel{\\long"+u+"}{} ",n=u;break;case"~N":n=a.J(t.B);break;case"`c":n=t.p1+" ";break;case"%j":n=" ";break;case"~A":case"%N":n="~";break;case"`%":n="\\mkern3mu ";break;case"%T":n="\\mkern2mu ";break;case"~o":n="{,}";break;case"~k":n="{"+t.p1+"}\\mkern6mu ";break;case"~l":n="{"+t.p1+"}\\mkern3mu ";break;case"~m":n="{"+t.p1+"}\\mkern1mu ";break;case"~F":n="\\text{-}";break;case"@Y":n="\\,{\\cdot}\\,";break;case"~v":n="\\mkern1mu \\bullet\\mkern1mu ";break;case"@o":n="{\\times}";break;case"%@":n="\\prime ";break;case"%K":n="\\cdot ";break;case"%L":n="\\mkern1mu{\\cdot}\\mkern1mu ";break;case"%M":n="\\times ";break;case"~f":n="{\\sim}";break;case"^":n="uparrow";break;case"v":n="downarrow";break;case"~w":n="\\ldots ";break;case"/":n="/";break;case"%S":n="\\,/\\,";break;default:throw["MhchemBugT","mhchem bug T. Please report."]}return n}, +H:function(t){switch(t){case"->":case"\u2192":case"\u27f6":return"rightarrow";case"<-":return"leftarrow";case"<->":return"leftrightarrow";case"<--\x3e":return"leftrightarrows";case"<=>":case"\u21cc":return"rightleftharpoons";case"<=>>":return"Rightleftharpoons";case"<<=>":return"Leftrightharpoons";default:throw["MhchemBugT","mhchem bug T. Please report."]}}, +j:function(t){switch(t){case"-":case"1":return"{-}";case"=":case"2":return"{=}";case"#":case"3":return"{\\equiv}";case"~":return"{\\tripledash}";case"~-":return"{\\rlap{\\lower.1em{-}}\\raise.1em{\\tripledash}}";case"~=":case"~--":return"{\\rlap{\\lower.2em{-}}\\rlap{\\raise.2em{\\tripledash}}-}";case"-~-":return"{\\rlap{\\lower.2em{-}}\\rlap{\\raise.2em{-}}\\tripledash}";case"...":return"{{\\cdot}{\\cdot}{\\cdot}}";case"....":return"{{\\cdot}{\\cdot}{\\cdot}{\\cdot}}";case"->":return"{\\rightarrow}";case"<-":return"{\\leftarrow}";case"<":return"{<}";case">":return"{>}";default:throw["MhchemBugT","mhchem bug T. Please report."]}}, +J:function(t){switch(t){case"+":return" {}+{} ";case"-":return" {}-{} ";case"=":return" {}={} ";case"<":return" {}<{} ";case">":return" {}>{} ";case"<<":return" {}\\ll{} ";case">>":return" {}\\gg{} ";case"\\pm":return" {}\\pm{} ";case"\\approx":case"$\\approx$":return" {}\\approx{} ";case"v":case"(v)":return" \\downarrow{} ";case"^":case"(^)":return" \\uparrow{} ";default:throw["MhchemBugT","mhchem bug T. Please report."]}}};MathJax.Extension["TeX/mhchem"].CE=n,t.Definitions.Add({macros:{ce:"CE",pu:"PU",xleftrightarrow:["Extension","AMSmath"],xrightleftharpoons:["Extension","AMSmath"],xRightleftharpoons:["Extension","AMSmath"],xLeftrightharpoons:["Extension","AMSmath"],longrightleftharpoons:["Macro","\\stackrel{\\textstyle{-}\\!\\!{\\rightharpoonup}}{\\smash{{\\leftharpoondown}\\!\\!{-}}}"],longRightleftharpoons:["Macro","\\stackrel{\\textstyle{-}\\!\\!{\\rightharpoonup}}{\\smash{\\leftharpoondown}}"],longLeftrightharpoons:["Macro","\\stackrel{\\textstyle\\vphantom{{-}}{\\rightharpoonup}}{\\smash{{\\leftharpoondown}\\!\\!{-}}}"],longleftrightarrows:["Macro","\\stackrel{\\longrightarrow}{\\smash{\\longleftarrow}\\Rule{0px}{.25em}{0px}}"],tripledash:["Macro","\\vphantom{-}\\raise2mu{\\kern2mu\\tiny\\text{-}\\kern1mu\\text{-}\\kern1mu\\text{-}\\kern2mu}"]}}, +null,!0),MathJax.Extension["TeX/AMSmath"]||t.Definitions.Add({macros:{xrightarrow:["Extension","AMSmath"],xleftarrow:["Extension","AMSmath"]}}, +null,!0),MathJax.Hub.Register.StartupHook("TeX AMSmath Ready",function(){t.Definitions.Add({macros:{xleftrightarrow:["xArrow",8596,6,6],xrightleftharpoons:["xArrow",8652,5,7],xRightleftharpoons:["xArrow",8652,5,7],xLeftrightharpoons:["xArrow",8652,5,7]}}, +null,!0)}),t.Parse.Augment({ +CE:function(t){var e=this.GetArgument(t),a=n(e).Parse();this.string=a+this.string.substr(this.i),this.i=0}, +PU:function(t){var e=this.GetArgument(t),a=n(e).Parse("pu");this.string=a+this.string.substr(this.i),this.i=0}}),MathJax.Hub.Startup.signal.Post("TeX mhchem Ready")}),MathJax.Ajax.loadComplete("[mhchem]/mhchem.js"); + diff --git a/revisions_report_files/mathjax-27/extensions/TeX/newcommand.js b/revisions_report_files/mathjax-27/extensions/TeX/newcommand.js new file mode 100644 index 0000000..be7bdee --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/newcommand.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/newcommand.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/newcommand"]={version:"2.7.6"};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.InputJax.TeX;var a=b.Definitions;a.Add({macros:{newcommand:"NewCommand",renewcommand:"NewCommand",newenvironment:"NewEnvironment",renewenvironment:"NewEnvironment",def:"MacroDef",let:"Let"}},null,true);b.Parse.Augment({NewCommand:function(c){var e=this.trimSpaces(this.GetArgument(c)),g=this.GetBrackets(c),d=this.GetBrackets(c),f=this.GetArgument(c);if(e.charAt(0)==="\\"){e=e.substr(1)}if(!e.match(/^(.|[a-z]+)$/i)){b.Error(["IllegalControlSequenceName","Illegal control sequence name for %1",c])}if(g){g=this.trimSpaces(g);if(!g.match(/^[0-9]+$/)){b.Error(["IllegalParamNumber","Illegal number of parameters specified in %1",c])}}this.setDef(e,["Macro",f,g,d])},NewEnvironment:function(d){var f=this.trimSpaces(this.GetArgument(d)),h=this.GetBrackets(d),e=this.GetBrackets(d),g=this.GetArgument(d),c=this.GetArgument(d);if(h){h=this.trimSpaces(h);if(!h.match(/^[0-9]+$/)){b.Error(["IllegalParamNumber","Illegal number of parameters specified in %1",d])}}this.setEnv(f,["BeginEnv",[null,"EndEnv"],g,c,h,e])},MacroDef:function(c){var d=this.GetCSname(c),f=this.GetTemplate(c,"\\"+d),e=this.GetArgument(c);if(!(f instanceof Array)){this.setDef(d,["Macro",e,f])}else{this.setDef(d,["MacroWithTemplate",e].concat(f))}},Let:function(d){var e=this.GetCSname(d),f;var g=this.GetNext();if(g==="="){this.i++;g=this.GetNext()}if(g==="\\"){d=this.GetCSname(d);f=this.csFindMacro(d);if(!f){if(a.mathchar0mi.hasOwnProperty(d)){f=["csMathchar0mi",a.mathchar0mi[d]]}else{if(a.mathchar0mo.hasOwnProperty(d)){f=["csMathchar0mo",a.mathchar0mo[d]]}else{if(a.mathchar7.hasOwnProperty(d)){f=["csMathchar7",a.mathchar7[d]]}else{if(a.delimiter.hasOwnProperty("\\"+d)){f=["csDelimiter",a.delimiter["\\"+d]]}else{return}}}}}}else{f=["Macro",g];this.i++}this.setDef(e,f)},GetCSname:function(e){var f=this.GetNext();if(f!=="\\"){b.Error(["MissingCS","%1 must be followed by a control sequence",e])}var d=this.trimSpaces(this.GetArgument(e));return d.substr(1)},GetTemplate:function(f,e){var j,g=[],h=0;j=this.GetNext();var d=this.i;while(this.i0){return[h,g]}else{return h}}}this.i++}b.Error(["MissingReplacementString","Missing replacement string for definition of %1",f])},MacroWithTemplate:function(d,g,h,f){if(h){var c=[];this.GetNext();if(f[0]&&!this.MatchParam(f[0])){b.Error(["MismatchUseDef","Use of %1 doesn't match its definition",d])}for(var e=0;eb.config.MAXMACROS){b.Error(["MaxMacroSub1","MathJax maximum macro substitution count exceeded; is there a recursive macro call?"])}},BeginEnv:function(g,k,c,j,h){if(j){var e=[];if(h!=null){var d=this.GetBrackets("\\begin{"+name+"}");e.push(d==null?h:d)}for(var f=e.length;f1){var n=(q.h+q.d)/2,j=h.TeX.x_height/2;p.parentNode.style.verticalAlign=h.Em(q.d+(j-n));q.h=j+n;q.d=n-j}p.bbox={h:q.h,d:q.d,w:k,lw:0,rw:k};return p}})});b.Register.StartupHook("SVG Jax Config",function(){b.Config({SVG:{styles:{".MathJax_SVG .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("SVG Jax Ready",function(){var g=MathJax.ElementJax.mml;var f=g.math.prototype.toSVG,h=g.merror.prototype.toSVG;g.math.Augment({toSVG:function(i,j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){i=k.data[0].toSVG(i)}else{i=f.apply(this,arguments)}return i}});g.merror.Augment({toSVG:function(n){if(!this.isError||this.Parent().type!=="math"){return h.apply(this,arguments)}n=e.addElement(n,"span",{className:"noError",isMathJax:true});if(this.multiLine){n.style.display="inline-block"}var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,j=o.length;l1){var k=n.offsetHeight/2;n.style.verticalAlign=(-k+(k/j))+"px"}return n}})});b.Register.StartupHook("NativeMML Jax Ready",function(){var h=MathJax.ElementJax.mml;var g=MathJax.Extension["TeX/noErrors"].config;var f=h.math.prototype.toNativeMML,i=h.merror.prototype.toNativeMML;h.math.Augment({toNativeMML:function(j){var k=this.data[0];if(k&&k.data[0]&&k.data[0].isError){j=k.data[0].toNativeMML(j)}else{j=f.apply(this,arguments)}return j}});h.merror.Augment({toNativeMML:function(n){if(!this.isError){return i.apply(this,arguments)}n=n.appendChild(document.createElement("span"));var o=this.data[0].data[0].data.join("").split(/\n/);for(var l=0,k=o.length;l1){n.style.verticalAlign="middle"}}for(var p in g.style){if(g.style.hasOwnProperty(p)){var j=p.replace(/-./g,function(m){return m.charAt(1).toUpperCase()});n.style[j]=g.style[p]}}return n}})});b.Register.StartupHook("PreviewHTML Jax Config",function(){b.Config({PreviewHTML:{styles:{".MathJax_PHTML .noError":b.Insert({"vertical-align":(b.Browser.isMSIE&&a.multiLine?"-2px":"")},a.style)}}})});b.Register.StartupHook("PreviewHTML Jax Ready",function(){var f=MathJax.ElementJax.mml;var h=MathJax.HTML;var g=f.merror.prototype.toPreviewHTML;f.merror.Augment({toPreviewHTML:function(l){if(!this.isError){return g.apply(this,arguments)}l=this.PHTMLcreateSpan(l);l.className="noError";if(this.multiLine){l.style.display="inline-block"}var n=this.data[0].data[0].data.join("").split(/\n/);for(var k=0,j=n.length;k1){var l=1.2*j/2;o.h=l+0.25;o.d=l-0.25;n.style.verticalAlign=g.Em(0.45-l)}else{o.h=1;o.d=0.2+2/g.em}return n}})});b.Startup.signal.Post("TeX noErrors Ready")})(MathJax.Hub,MathJax.HTML);MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noErrors.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/noUndefined.js b/revisions_report_files/mathjax-27/extensions/TeX/noUndefined.js new file mode 100644 index 0000000..f4100a7 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/noUndefined.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/noUndefined.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/noUndefined"]={version:"2.7.6",config:MathJax.Hub.CombineConfig("TeX.noUndefined",{disabled:false,attributes:{mathcolor:"red"}})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var b=MathJax.Extension["TeX/noUndefined"].config;var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX.Parse.prototype.csUndefined;MathJax.InputJax.TeX.Parse.Augment({csUndefined:function(d){if(b.disabled){return c.apply(this,arguments)}MathJax.Hub.signal.Post(["TeX Jax - undefined control sequence",d]);this.Push(a.mtext(d).With(b.attributes))}});MathJax.Hub.Startup.signal.Post("TeX noUndefined Ready")});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/noUndefined.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/unicode.js b/revisions_report_files/mathjax-27/extensions/TeX/unicode.js new file mode 100644 index 0000000..9f82f47 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/unicode.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/unicode.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/unicode"]={version:"2.7.6",unicode:{},config:MathJax.Hub.CombineConfig("TeX.unicode",{fonts:"STIXGeneral,'Arial Unicode MS'"})};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var c=MathJax.InputJax.TeX;var a=MathJax.ElementJax.mml;var b=MathJax.Extension["TeX/unicode"].unicode;c.Definitions.Add({macros:{unicode:"Unicode"}},null,true);c.Parse.Augment({Unicode:function(e){var i=this.GetBrackets(e),d;if(i){if(i.replace(/ /g,"").match(/^(\d+(\.\d*)?|\.\d+),(\d+(\.\d*)?|\.\d+)$/)){i=i.replace(/ /g,"").split(/,/);d=this.GetBrackets(e)}else{d=i;i=null}}var j=this.trimSpaces(this.GetArgument(e)).replace(/^0x/,"x");if(!j.match(/^(x[0-9A-Fa-f]+|[0-9]+)$/)){c.Error(["BadUnicode","Argument to \\unicode must be a number"])}var h=parseInt(j.match(/^x/)?"0"+j:j);if(!b[h]){b[h]=[800,200,d,h]}else{if(!d){d=b[h][2]}}if(i){b[h][0]=Math.floor(i[0]*1000);b[h][1]=Math.floor(i[1]*1000)}var f=this.stack.env.font,g={};if(d){b[h][2]=g.fontfamily=d.replace(/"/g,"'");if(f){if(f.match(/bold/)){g.fontweight="bold"}if(f.match(/italic|-mathit/)){g.fontstyle="italic"}}}else{if(f){g.mathvariant=f}}g.unicode=[].concat(b[h]);this.Push(a.mtext(a.entity("#"+j)).With(g))}});MathJax.Hub.Startup.signal.Post("TeX unicode Ready")});MathJax.Hub.Register.StartupHook("HTML-CSS Jax Ready",function(){var a=MathJax.ElementJax.mml;var c=MathJax.Extension["TeX/unicode"].config.fonts;var b=a.mbase.prototype.HTMLgetVariant;a.mbase.Augment({HTMLgetVariant:function(){var d=b.apply(this,arguments);if(d.unicode){delete d.unicode;delete d.FONTS}if(!this.unicode){return d}d.unicode=true;if(!d.defaultFont){d=MathJax.Hub.Insert({},d);d.defaultFont={family:c}}var e=this.unicode[2];if(e){e+=","+c}else{e=c}d.defaultFont[this.unicode[3]]=[this.unicode[0],this.unicode[1],500,0,500,{isUnknown:true,isUnicode:true,font:e}];return d}})});MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){var a=MathJax.ElementJax.mml;var c=MathJax.Extension["TeX/unicode"].config.fonts;var b=a.mbase.prototype.SVGgetVariant;a.mbase.Augment({SVGgetVariant:function(){var d=b.call(this);if(d.unicode){delete d.unicode;delete d.FONTS}if(!this.unicode){return d}d.unicode=true;if(!d.forceFamily){d=MathJax.Hub.Insert({},d)}d.defaultFamily=c;d.noRemap=true;d.h=this.unicode[0];d.d=this.unicode[1];return d}})});MathJax.Ajax.loadComplete("[MathJax]/extensions/TeX/unicode.js"); diff --git a/revisions_report_files/mathjax-27/extensions/TeX/verb.js b/revisions_report_files/mathjax-27/extensions/TeX/verb.js new file mode 100644 index 0000000..7916c6d --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/TeX/verb.js @@ -0,0 +1,19 @@ +/* + * /MathJax/extensions/TeX/verb.js + * + * Copyright (c) 2009-2018 The MathJax Consortium + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +MathJax.Extension["TeX/verb"]={version:"2.7.6"};MathJax.Hub.Register.StartupHook("TeX Jax Ready",function(){var a=MathJax.ElementJax.mml;var c=MathJax.InputJax.TeX;var b=c.Definitions;b.Add({macros:{verb:"Verb"}},null,true);c.Parse.Augment({Verb:function(d){var g=this.GetNext();var f=++this.i;if(g==""){c.Error(["MissingArgFor","Missing argument for %1",d])}while(this.i=0;f--){var g=this.dependents[f];g.Disable&&g.Disable(!1,e)}d&&a.Queue(["Rerender",a])},Dependent:function(a){this.dependents.push(a)},Startup:function(){var b=MathJax.Extension.collapsible;b&&b.Dependent(this),a.postInputHooks.Add(["Filter",e],150),a.Queue(function(){return e.CollapseWideMath()}),window.addEventListener?window.addEventListener("resize",e.resizeHandler,!1):window.attachEvent?window.attachEvent("onresize",e.resizeHandler):window.onresize=e.resizeHandler},Filter:function(a,b,c){a.enriched&&!this.config.disabled&&("block"===a.root.Get("display")||c.parentNode.childNodes.length<=3)&&(a.root.SRE={action:this.Actions(a.root)})},Actions:function(a){var b=[];return this.getActions(a,0,b),this.sortActions(b)},getActions:function(a,b,c){if(!a.isToken&&a.data){b++;for(var d=0,e=a.data.length;db?1:0},CollapseWideMath:function(b){if(!this.config.disabled){this.GetContainerWidths(b);var c=a.getAllJax(b),d={collapse:[],jax:c,m:c.length,i:0,changed:!1};return this.collapseState(d)}},collapseState:function(b){for(var c=b.collapse;b.ie.M)){var f=this.getActionWidths(d,b);if(f)return f;this.collapseActions(e,b),b.changed&&c.push(d.SourceElement())}b.i++}if(0!==c.length)return 1===c.length&&(c=c[0]),a.Rerender(c)},collapseActions:function(a,b){for(var c=a.width,d=c,e=1e6,f=a.action.length-1;f>=0;f--){var g=a.action[f],h=g.selection;c>a.cwidth?(g.selection=1,d=g.SREwidth,e=c):g.selection=2,c=g.SREwidth,a.DOMupdate?document.getElementById(g.id).setAttribute("selection",g.selection):g.selection!==h&&(b.changed=!0)}a.m=d,a.M=e},getActionWidths:function(a,b){if(!a.root.SRE.actionWidths){MathJax.OutputJax[a.outputJax].getMetrics(a);try{this.computeActionWidths(a)}catch(a){if(!a.restart)throw a;return MathJax.Callback.After(["collapseState",this,b],a.restart)}b.changed=!0}return null},computeActionWidths:function(a){var b,c=a.root.SRE,d=c.action,e={};for(c.width=a.sreGetRootWidth(e),b=d.length-1;b>=0;b--)d[b].selection=2;for(b=d.length-1;b>=0;b--){var f=d[b];null==f.SREwidth&&(f.selection=1,f.SREwidth=a.sreGetActionWidth(e,f))}c.actionWidths=!0},GetContainerWidths:function(b){var c,d,e,f,g,h=a.getAllJax(b),i=MathJax.HTML.Element("span",{style:{display:"block"}}),j=[];for(c=0,d=h.length;c=0;f--){var g=this.dependents[f];g.Disable&&g.Disable(!1,e)}b&&a.Queue(["Reprocess",a])},Dependent:function(a){this.dependents.push(a)},Startup:function(){b=MathJax.ElementJax.mml;var c=MathJax.Extension["semantic-enrich"];c&&c.Dependent(this),a.postInputHooks.Add(["Filter",g],100)},Filter:function(a,b,c){a.enriched&&!this.config.disabled&&(a.root=a.root.Collapse(),a.root.inputID=c.id)},Marker:function(a){return b.mtext("\u25c2"+a+"\u25b8").With({mathcolor:"blue",attr:{},attrNames:[]})},MakeAction:function(a,c){var d=b.maction(a).With({id:this.getActionID(),actiontype:"toggle",complexity:a.getComplexity(),collapsible:!0,attrNames:["id","actiontype","selection",e],attr:{},selection:2});if(d.attr[e]=d.complexity,"math"===c.type){var f=b.mrow().With({complexity:c.complexity,attrNames:[],attr:{}});f.Append.apply(f,c.data);for(var g,h=c.attrNames.length-1;g=c.attrNames[h];h--)"data-semantic-"===g.substr(0,14)&&(f.attr[g]=c.attr[g],f.attrNames.push(g),delete c.attr[g],c.attrNames.splice(h,1));f.complexity=c.complexity,d.Append(f),c.data=[],c.Append(d),c.complexity=d.complexity,d=c}else d.Append(c);return d},actionID:1,getActionID:function(){return"MJX-Collapse-"+this.actionID++},Collapse:function(a){a.getComplexity();var b=(a.attr||{})["data-semantic-type"];if(b)if(this["Collapse_"+b])a=this["Collapse_"+b](a);else if(this.COLLAPSE[b]&&this.MARKER[b]){var c=a.attr["data-semantic-role"],d=this.COLLAPSE[b];if("number"!=typeof d&&(d=d[c]||d.value),a.complexity>d){var e=this.MARKER[b];"string"!=typeof e&&(e=e[c]||e.value),a=this.MakeAction(this.Marker(e),a)}}return a},UncollapseChild:function(a,b,c){if(null==c&&(c=1),this.SplitAttribute(a,"children").length===c){var d=1===a.data.length&&a.data[0].inferred?a.data[0]:a;if(d&&d.data[b]&&d.data[b].collapsible)return d.SetData(b,d.data[b].data[1]),a.complexity=d.complexity=null,a.getComplexity(),1}return 0},FindChildText:function(a,b){var c=this.FindChild(a,b);return c?(c.CoreMO()||c).data.join(""):"?"},FindChild:function(a,b){if(a){if(a.attr&&a.attr["data-semantic-id"]===b)return a;if(!a.isToken)for(var c=0,d=a.data.length;cthis.COLLAPSE.fenced&&"leftright"===a.attr["data-semantic-role"]){var b=a.data[0].data.join("")+a.data[a.data.length-1].data.join("");a=this.MakeAction(this.Marker(b),a)}return a},Collapse_appl:function(a){if(this.UncollapseChild(a,2,2)){var b=this.MARKER.appl;b=b[a.attr["data-semantic-role"]]||b.value,a=this.MakeAction(this.Marker(b),a)}return a},Collapse_sqrt:function(a){return this.UncollapseChild(a,0),a.complexity>this.COLLAPSE.sqrt&&(a=this.MakeAction(this.Marker(this.MARKER.sqrt),a)),a},Collapse_root:function(a){return this.UncollapseChild(a,0),a.complexity>this.COLLAPSE.sqrt&&(a=this.MakeAction(this.Marker(this.MARKER.sqrt),a)),a},Collapse_enclose:function(a){if(1===this.SplitAttribute(a,"children").length){var b=1===a.data.length&&a.data[0].inferred?a.data[0]:a;if(b.data[0]&&b.data[0].collapsible){var c=b.data[0];b.SetData(0,c.data[1]),c.SetData(1,a),a=c}}return a},Collapse_bigop:function(a){if(a.complexity>this.COLLAPSE.bigop||"mo"!==a.data[0].type){var b=this.SplitAttribute(a,"content").pop(),c=g.FindChildText(a,b);a=this.MakeAction(this.Marker(c),a)}return a},Collapse_integral:function(a){if(a.complexity>this.COLLAPSE.integral||"mo"!==a.data[0].type){var b=this.SplitAttribute(a,"content")[0],c=g.FindChildText(a,b);a=this.MakeAction(this.Marker(c),a)}return a},Collapse_relseq:function(a){if(a.complexity>this.COLLAPSE.relseq){var b=this.SplitAttribute(a,"content"),c=g.FindChildText(a,b[0]);b.length>1&&(c+="\u22ef"),a=this.MakeAction(this.Marker(c),a)}return a},Collapse_multirel:function(a){if(a.complexity>this.COLLAPSE.multirel){var b=this.SplitAttribute(a,"content"),c=g.FindChildText(a,b[0])+"\u22ef";a=this.MakeAction(this.Marker(c),a)}return a},Collapse_superscript:function(a){return this.UncollapseChild(a,0,2),a.complexity>this.COLLAPSE.superscript&&(a=this.MakeAction(this.Marker(this.MARKER.superscript),a)),a},Collapse_subscript:function(a){return this.UncollapseChild(a,0,2),a.complexity>this.COLLAPSE.subscript&&(a=this.MakeAction(this.Marker(this.MARKER.subscript),a)),a},Collapse_subsup:function(a){return this.UncollapseChild(a,0,3),a.complexity>this.COLLAPSE.subsup&&(a=this.MakeAction(this.Marker(this.MARKER.subsup),a)),a}};a.Register.StartupHook("End Extensions",function(){null==c.collapsible?c.collapsible=!g.config.disabled:g.config.disabled=!c.collapsible,a.Register.StartupHook("MathMenu Ready",function(){d=MathJax.Menu.cookie;var a,b=function(a){g[c.collapsible?"Enable":"Disable"](!0,!0),MathJax.Menu.saveCookie()},e=MathJax.Menu.ITEM,f=MathJax.Menu.menu,h=e.CHECKBOX(["CollapsibleMath","Collapsible Math"],"collapsible",{action:b}),i=(f.FindId("Accessibility")||{}).submenu;i?(a=i.IndexOfId("CollapsibleMath"),null!==a?i.items[a]=h:i.items.push(e.RULE(),h)):(a=f.IndexOfId("About"),f.items.splice(a,0,h,e.RULE()))},15)},15)}(MathJax.Hub),MathJax.Ajax.Require("[a11y]/semantic-enrich.js"),MathJax.Hub.Register.StartupHook("Semantic Enrich Ready",function(){var a=MathJax.ElementJax.mml,b=MathJax.Extension.collapsible,c=b.COMPLEXITY,d=b.COMPLEXATTR;b.Startup(),a.mbase.Augment({Collapse:function(){return b.Collapse(this)},getComplexity:function(){if(null==this.complexity){var a=0;if(this.isToken)a=c.TEXT*this.data.join("").length+c.TOKEN;else{for(var b=0,e=this.data.length;b1&&(a+=e*c.CHILD)}!this.attrNames||"complexity"in this||this.attrNames.push(d),this.attr&&(this.attr[d]=a),this.complexity=a}return this.complexity},reportComplexity:function(){!this.attr||!this.attrNames||d in this.attr||(this.attrNames.push(d),this.attr[d]=this.complexity)}}),a.mfrac.Augment({getComplexity:function(){return null==this.complexity&&(this.SUPER(arguments).getComplexity.call(this),this.complexity*=c.SCRIPT,this.complexity+=c.FRACTION,this.attr[d]=this.complexity),this.complexity}}),a.msqrt.Augment({getComplexity:function(){return null==this.complexity&&(this.SUPER(arguments).getComplexity.call(this),this.complexity+=c.SQRT,this.attr[d]=this.complexity),this.complexity}}),a.mroot.Augment({getComplexity:function(){return null==this.complexity&&(this.SUPER(arguments).getComplexity.call(this),this.complexity-=(1-c.SCRIPT)*this.data[1].getComplexity(),this.complexity+=c.SQRT,this.attr[d]=this.complexity),this.complexity}}),a.msubsup.Augment({getComplexity:function(){if(null==this.complexity){var a=0;this.data[this.sub]&&(a=this.data[this.sub].getComplexity()+c.CHILD),this.data[this.sup]&&(a=Math.max(this.data[this.sup].getComplexity(),a)),a*=c.SCRIPT,this.data[this.sub]&&(a+=c.CHILD),this.data[this.sup]&&(a+=c.CHILD),this.data[this.base]&&(a+=this.data[this.base].getComplexity()+c.CHILD),this.complexity=a+c.SUBSUP,this.reportComplexity()}return this.complexity}}),a.munderover.Augment({getComplexity:function(){if(null==this.complexity){var a=0;this.data[this.sub]&&(a=this.data[this.sub].getComplexity()+c.CHILD),this.data[this.sup]&&(a=Math.max(this.data[this.sup].getComplexity(),a)),a*=c.SCRIPT,this.data[this.base]&&(a=Math.max(this.data[this.base].getComplexity(),a)),this.data[this.sub]&&(a+=c.CHILD),this.data[this.sup]&&(a+=c.CHILD),this.data[this.base]&&(a+=c.CHILD),this.complexity=a+c.UNDEROVER,this.reportComplexity()}return this.complexity}}),a.mphantom.Augment({getComplexity:function(){return this.complexity=c.PHANTOM,this.reportComplexity(),this.complexity}}),a.ms.Augment({getComplexity:function(){return this.SUPER(arguments).getComplexity.call(this),this.complexity+=this.Get("lquote").length*c.TEXT,this.complexity+=this.Get("rquote").length*c.TEXT,this.attr[d]=this.complexity,this.complexity}}),a.menclose.Augment({getComplexity:function(){return null==this.complexity&&(this.SUPER(arguments).getComplexity.call(this),this.complexity+=c.ACTION,this.attr[d]=this.complexity),this.complexity}}),a.maction.Augment({getComplexity:function(){return this.complexity=(this.collapsible?this.data[0]:this.selected()).getComplexity(),this.reportComplexity(),this.complexity}}),a.semantics.Augment({getComplexity:function(){return null==this.complexity&&(this.complexity=this.data[0]?this.data[0].getComplexity():0,this.reportComplexity()),this.complexity}}),a["annotation-xml"].Augment({getComplexity:function(){return this.complexity=c.XML,this.reportComplexity(),this.complexity}}),a.annotation.Augment({getComplexity:function(){return this.complexity=c.XML,this.reportComplexity(),this.complexity}}),a.mglyph.Augment({getComplexity:function(){return this.complexity=c.GLYPH,this.reportComplexity(),this.complexity}}),MathJax.Hub.Startup.signal.Post("Collapsible Ready"),MathJax.Ajax.loadComplete("[a11y]/collapsible.js")}); \ No newline at end of file diff --git a/revisions_report_files/mathjax-27/extensions/a11y/explorer.js b/revisions_report_files/mathjax-27/extensions/a11y/explorer.js new file mode 100644 index 0000000..5478cce --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/a11y/explorer.js @@ -0,0 +1 @@ +MathJax.Hub.Register.StartupHook("Sre Ready",function(){var a,b,c=MathJax.Hub.config.menuSettings,d={};MathJax.Hub.Register.StartupHook("MathEvents Ready",function(){a=MathJax.Extension.MathEvents.Event.False,b=MathJax.Extension.MathEvents.Event.KEY});var e=MathJax.Extension.explorer={version:"1.5.0",dependents:[],defaults:{walker:"table",highlight:"none",background:"blue",foreground:"black",speech:!0,generation:"lazy",subtitle:!1,ruleset:"mathspeak-default"},eagerComplexity:80,prefix:"Assistive-",hook:null,locHook:null,oldrules:null,addMenuOption:function(a,b){c[e.prefix+a]=b},addDefaults:function(){for(var a,b=MathJax.Hub.CombineConfig("explorer",e.defaults),d=Object.keys(b),f=0;a=d[f];f++)void 0===c[e.prefix+a]&&e.addMenuOption(a,b[a]);e.setSpeechOption(),h.Reset()},setOption:function(a,b){c[e.prefix+a]!==b&&(e.addMenuOption(a,b),h.Reset())},getOption:function(a){return c[e.prefix+a]},speechOption:function(a){e.oldrules!==a.value&&(e.setSpeechOption(),h.Regenerate())},setSpeechOption:function(){var a=c[e.prefix+"ruleset"],b=a.split("-");sre.System.getInstance().setupEngine({locale:MathJax.Localization.locale,domain:e.Domain(b[0]),style:b[1],rules:e.RuleSet(b[0])}),e.oldrules=a},Domain:function(a){switch(a){case"chromevox":return"default";case"mathspeak":default:return"mathspeak"}},RuleSet:function(a){switch(a){case"chromevox":return["AbstractionRules","SemanticTreeRules"];case"mathspeak":default:return["AbstractionRules","AbstractionSpanish","MathspeakRules","MathspeakSpanish"]}},hook:null,locHook:null,Enable:function(a,b){c.explorer=!0,b&&(d.explorer=!0),MathJax.Extension.collapsible.Enable(!1,b),MathJax.Extension.AssistiveMML&&(MathJax.Extension.AssistiveMML.config.disabled=!0,c.assistiveMML=!1,b&&(d.assistiveMML=!1)),this.DisableMenus(!1),this.hook||(this.hook=MathJax.Hub.Register.MessageHook("New Math",["Register",this.Explorer])),this.locHook||(this.locHook=MathJax.Hub.Register.MessageHook("Locale Reset",["RemoveSpeech",this.Explorer])),a&&MathJax.Hub.Queue(["Reprocess",MathJax.Hub])},Disable:function(a,b){c.explorer=!1,b&&(d.explorer=!1),this.DisableMenus(!0),this.hook&&(MathJax.Hub.UnRegister.MessageHook(this.hook),this.hook=null);for(var e=this.dependents.length-1;e>=0;e--){var f=this.dependents[e];f.Disable&&f.Disable(!1,b)}},DisableMenus:function(a){if(MathJax.Menu){var b=MathJax.Menu.menu.FindId("Accessibility","Explorer");if(b){b=b.submenu;for(var d,f=b.items,g=2;d=f[g];g++)d.disabled=a;a||!b.FindId("SpeechOutput")||c[e.prefix+"speech"]||(b.FindId("Subtitles").disabled=!0)}}},Dependent:function(a){this.dependents.push(a)}},f=MathJax.Object.Subclass({div:null,inner:null,Init:function(){this.div=f.Create("assertive"),this.inner=MathJax.HTML.addElement(this.div,"div")},Add:function(){f.added||(document.body.appendChild(this.div),f.added=!0)},Show:function(a,b){this.div.classList.add("MJX_LiveRegion_Show");var c=a.getBoundingClientRect(),d=c.bottom+10+window.pageYOffset,e=c.left+window.pageXOffset;this.div.style.top=d+"px",this.div.style.left=e+"px";var f=b.colorString();this.inner.style.backgroundColor=f.background,this.inner.style.color=f.foreground},Hide:function(a){this.div.classList.remove("MJX_LiveRegion_Show")},Clear:function(){this.Update(""),this.inner.style.top="",this.inner.style.backgroundColor=""},Update:function(a){e.getOption("speech")&&f.Update(this.inner,a)}},{ANNOUNCE:"Navigatable Math in page. Explore with shift space and arrow keys. Expand or collapse elements hitting enter.",announced:!1,added:!1,styles:{".MJX_LiveRegion":{position:"absolute",top:"0",height:"1px",width:"1px",padding:"1px",overflow:"hidden"},".MJX_LiveRegion_Show":{top:"0",position:"absolute",width:"auto",height:"auto",padding:"0px 0px",opacity:1,"z-index":"202",left:0,right:0,margin:"0 auto","background-color":"white","box-shadow":"0px 10px 20px #888",border:"2px solid #CCCCCC"}},Create:function(a){var b=MathJax.HTML.Element("div",{className:"MJX_LiveRegion"});return b.setAttribute("aria-live",a),b},Update:MathJax.Hub.Browser.isPC?function(a,b){a.textContent="",setTimeout(function(){a.textContent=b},100)}:function(a,b){a.textContent="",a.textContent=b},Announce:function(){if(e.getOption("speech")){f.announced=!0,MathJax.Ajax.Styles(f.styles);var a=f.Create("polite");document.body.appendChild(a),f.Update(a,f.ANNOUNCE),setTimeout(function(){document.body.removeChild(a)},1e3)}}});MathJax.Extension.explorer.LiveRegion=f;var g=MathJax.Ajax.fileURL(MathJax.Ajax.config.path.a11y),h=MathJax.Extension.explorer.Explorer={liveRegion:f(),walker:null,highlighter:null,hoverer:null,flamer:null,speechDiv:null,earconFile:g+"/invalid_keypress"+(-1!==["Firefox","Chrome","Opera"].indexOf(MathJax.Hub.Browser.name)?".ogg":".mp3"),expanded:!1,focusoutEvent:MathJax.Hub.Browser.isFirefox?"blur":"focusout",focusinEvent:"focus",ignoreFocusOut:!1,jaxCache:{},messageID:null,Reset:function(){h.FlameEnriched()},Register:function(a){if(e.hook){var b=document.getElementById(a[1]);if(b&&b.id){var c=MathJax.Hub.getJaxFor(b.id);c&&c.enriched&&(h.StateChange(b.id,c),h.liveRegion.Add(),h.AddEvent(b))}}},StateChange:function(a,b){h.GetHighlighter(.2);var c=h.jaxCache[a];c&&c===b.root||(c&&h.highlighter.resetState(a+"-Frame"),h.jaxCache[a]=b.root)},AddAria:function(a){a.setAttribute("role","application"),a.setAttribute("aria-label","Math")},AddHook:function(a){h.RemoveHook(),h.hook=MathJax.Hub.Register.MessageHook("End Math",function(b){var c=b[1].id+"-Frame",d=document.getElementById(c);a&&c===h.expanded&&(h.ActivateWalker(d,a),d.focus(),h.expanded=!1)})},RemoveHook:function(){h.hook&&(MathJax.Hub.UnRegister.MessageHook(h.hook),h.hook=null)},AddMessage:function(){return MathJax.Message.Set("Generating Speech Output")},RemoveMessage:function(a){a&&MathJax.Message.Clear(a)},AddEvent:function(a){var b=a.id+"-Frame",c=a.previousSibling;if(c){var d=c.id!==b?c.firstElementChild:c;h.AddAria(d),h.AddMouseEvents(d),"MathJax_MathML"===d.className&&(d=d.firstElementChild),d&&(d.onkeydown=h.Keydown,h.Flame(d),d.addEventListener(h.focusinEvent,function(a){e.hook&&(f.announced||f.Announce())}),d.addEventListener(h.focusoutEvent,function(a){if(e.hook)return h.ignoreFocusOut&&(h.ignoreFocusOut=!1,"enter"===h.walker.moved)?void a.target.focus():void(h.walker&&h.DeactivateWalker())}),e.getOption("speech")&&h.AddSpeech(d))}},AddSpeech:function(a){var b=a.id,c=MathJax.Hub.getJaxFor(b),d=c.root.toMathML();if(a.getAttribute("haslabel")||h.AddMathLabel(d,b),!a.getAttribute("hasspeech"))switch(MathJax.Hub.config.explorer.generation){case"eager":h.AddSpeechEager(d,b);break;case"mixed":a.querySelectorAll("[data-semantic-complexity]").length>=e.eagerComplexity&&h.AddSpeechEager(d,b)}},AddSpeechLazy:function(a){var b=new sre.TreeSpeechGenerator;b.setRebuilt(h.walker.rebuilt),b.getSpeech(h.walker.rootNode,h.walker.xml),a.setAttribute("hasspeech","true")},AddSpeechEager:function(a,b){h.MakeSpeechTask(a,b,sre.TreeSpeechGenerator,function(a,b){a.setAttribute("hasspeech","true")},5)},AddMathLabel:function(a,b){h.MakeSpeechTask(a,b,sre.SummarySpeechGenerator,function(a,b){a.setAttribute("haslabel","true"),a.setAttribute("aria-label",b)},5)},MakeSpeechTask:function(a,b,c,d,e){var f=h.AddMessage();setTimeout(function(){var e=new c,g=document.getElementById(b),i=new sre.DummyWalker(g,e,h.highlighter,a),j=i.speech();j&&d(g,j),h.RemoveMessage(f)},e)},Keydown:function(c){if(c.keyCode===b.ESCAPE){if(!h.walker)return;return h.RemoveHook(),h.DeactivateWalker(),void a(c)}if(h.walker&&h.walker.isActive()){void 0!==h.walker.modifier&&(h.walker.modifier=c.shiftKey);var d=h.walker.move(c.keyCode);if(null===d)return;if(d){if("expand"===h.walker.moved){if(h.expanded=h.walker.node.id,MathJax.Hub.Browser.isEdge)return h.ignoreFocusOut=!0,void h.DeactivateWalker();if(MathJax.Hub.Browser.isFirefox||MathJax.Hub.Browser.isMSIE)return void h.DeactivateWalker()}h.liveRegion.Update(h.walker.speech()),h.Highlight()}else h.PlayEarcon();return void a(c)}var f=c.target;if(c.keyCode===b.SPACE){if(c.shiftKey&&e.hook){var g=MathJax.Hub.getJaxFor(f);h.ActivateWalker(f,g),h.AddHook(g)}else MathJax.Extension.MathEvents.Event.ContextMenu(c,f);return void a(c)}},GetHighlighter:function(a){h.highlighter=sre.HighlighterFactory.highlighter({color:e.getOption("background"),alpha:a},{color:e.getOption("foreground"),alpha:1},{renderer:MathJax.Hub.outputJax["jax/mml"][0].id,browser:MathJax.Hub.Browser.name})},AddMouseEvents:function(a){sre.HighlighterFactory.addEvents(a,{mouseover:h.MouseOver,mouseout:h.MouseOut},{renderer:MathJax.Hub.outputJax["jax/mml"][0].id,browser:MathJax.Hub.Browser.name})},MouseOver:function(b){if("none"!==e.getOption("highlight")){if("hover"===e.getOption("highlight")){var c=b.currentTarget;h.GetHighlighter(.1),h.highlighter.highlight([c]),h.hoverer=!0}a(b)}},MouseOut:function(b){return h.hoverer&&(h.highlighter.unhighlight(),h.hoverer=!1),a(b)},Flame:function(a){if("flame"===e.getOption("highlight"))return h.GetHighlighter(.05),h.highlighter.highlightAll(a),void(h.flamer=!0)},UnFlame:function(){h.flamer&&(h.highlighter.unhighlightAll(),h.flamer=null)},FlameEnriched:function(){h.UnFlame();for(var a,b=0,c=MathJax.Hub.getAllJax();a=c[b];b++)h.Flame(a.SourceElement().previousSibling)},Walkers:{syntactic:sre.SyntaxWalker,table:sre.TableWalker,semantic:sre.SemanticWalker,none:sre.DummyWalker},ActivateWalker:function(a,b){var c=e.getOption("speech"),d=e.getOption("walker")?h.Walkers[MathJax.Hub.config.explorer.walker]:h.Walkers.none,f=c?new sre.DirectSpeechGenerator:new sre.DummySpeechGenerator;h.GetHighlighter(.2),h.walker=new d(a,f,h.highlighter,b.root.toMathML()),c&&!a.getAttribute("hasspeech")&&h.AddSpeechLazy(a),h.walker.activate(),c&&(e.getOption("subtitle")&&h.liveRegion.Show(a,h.highlighter),h.liveRegion.Update(h.walker.speech())),h.Highlight(),h.ignoreFocusOut&&setTimeout(function(){h.ignoreFocusOut=!1},500)},DeactivateWalker:function(){h.liveRegion.Clear(),h.liveRegion.Hide(),h.Unhighlight(),h.currentHighlight=null,h.walker.deactivate(),h.walker=null},Highlight:function(){h.Unhighlight(),h.highlighter.highlight(h.walker.getFocus().getNodes())},Unhighlight:function(){h.highlighter.unhighlight()},PlayEarcon:function(){new Audio(h.earconFile).play()},SpeechOutput:function(){h.Reset(),["Subtitles"].forEach(function(a){var b=MathJax.Menu.menu.FindId("Accessibility","Explorer",a);b&&(b.disabled=!b.disabled)}),h.Regenerate()},RemoveSpeech:function(){e.setSpeechOption();for(var a,b=0,c=MathJax.Hub.getAllJax();a=c[b];b++){var d=document.getElementById(a.inputID+"-Frame");d&&(d.removeAttribute("hasspeech"),d.removeAttribute("haslabel"))}},Regenerate:function(){for(var a,b=0,c=MathJax.Hub.getAllJax();a=c[b];b++){var d=document.getElementById(a.inputID+"-Frame");d&&(d.removeAttribute("hasspeech"),h.AddSpeech(d))}},Startup:function(){var a=MathJax.Extension.collapsible;a&&a.Dependent(e),e.addDefaults()}};MathJax.Hub.Register.StartupHook("End Extensions",function(){e[!1===c.explorer?"Disable":"Enable"](),MathJax.Hub.Startup.signal.Post("Explorer Ready"),MathJax.Hub.Register.StartupHook("MathMenu Ready",function(){d=MathJax.Menu.cookie;var a,b=function(a){e[c.explorer?"Enable":"Disable"](!0,!0),MathJax.Menu.saveCookie()},f=MathJax.Menu.ITEM,g=MathJax.Menu.menu,i={action:h.Reset},j={action:e.speechOption},k=f.SUBMENU(["Explorer","Explorer"],f.CHECKBOX(["Active","Active"],"explorer",{action:b}),f.RULE(),f.CHECKBOX(["Walker","Walker"],"Assistive-walker"),f.SUBMENU(["Highlight","Highlight"],f.RADIO(["none","None"],"Assistive-highlight",i),f.RADIO(["hover","Hover"],"Assistive-highlight",i),f.RADIO(["flame","Flame"],"Assistive-highlight",i)),f.SUBMENU(["Background","Background"],f.RADIO(["blue","Blue"],"Assistive-background",i),f.RADIO(["red","Red"],"Assistive-background",i),f.RADIO(["green","Green"],"Assistive-background",i),f.RADIO(["yellow","Yellow"],"Assistive-background",i),f.RADIO(["cyan","Cyan"],"Assistive-background",i),f.RADIO(["magenta","Magenta"],"Assistive-background",i),f.RADIO(["white","White"],"Assistive-background",i),f.RADIO(["black","Black"],"Assistive-background",i)),f.SUBMENU(["Foreground","Foreground"],f.RADIO(["black","Black"],"Assistive-foreground",i),f.RADIO(["white","White"],"Assistive-foreground",i),f.RADIO(["magenta","Magenta"],"Assistive-foreground",i),f.RADIO(["cyan","Cyan"],"Assistive-foreground",i),f.RADIO(["yellow","Yellow"],"Assistive-foreground",i),f.RADIO(["green","Green"],"Assistive-foreground",i),f.RADIO(["red","Red"],"Assistive-foreground",i),f.RADIO(["blue","Blue"],"Assistive-foreground",i)),f.RULE(),f.CHECKBOX(["SpeechOutput","Speech Output"],"Assistive-speech",{action:h.SpeechOutput}),f.CHECKBOX(["Subtitles","Subtitles"],"Assistive-subtitle",{disabled:!c["Assistive-speech"]}),f.RULE(),f.SUBMENU(["Mathspeak","Mathspeak Rules"],f.RADIO(["mathspeak-default","Verbose"],"Assistive-ruleset",j),f.RADIO(["mathspeak-brief","Brief"],"Assistive-ruleset",j),f.RADIO(["mathspeak-sbrief","Superbrief"],"Assistive-ruleset",j)),f.SUBMENU(["Chromevox","ChromeVox Rules"],f.RADIO(["chromevox-default","Verbose"],"Assistive-ruleset",j),f.RADIO(["chromevox-short","Short"],"Assistive-ruleset",j),f.RADIO(["chromevox-alternative","Alternative"],"Assistive-ruleset",j))),l=(g.FindId("Accessibility")||{}).submenu;l?(a=l.IndexOfId("Explorer"),null!==a?l.items[a]=k:(a=l.IndexOfId("CollapsibleMath"),l.items.splice(a+1,0,k))):(a=g.IndexOfId("CollapsibleMath"),g.items.splice(a+1,0,k)),c.explorer||e.DisableMenus(!0)},20)},20)}),MathJax.Hub.Register.StartupHook("SVG Jax Ready",function(){MathJax.Hub.Config({SVG:{addMMLclasses:!0}});var a=MathJax.OutputJax.SVG;if(parseFloat(a.version)<2.7){var b=a.getJaxFromMath;a.Augment({getJaxFromMath:function(a){return a.parentNode.className.match(/MathJax_SVG_Display/)&&(a=a.parentNode),b.call(this,a)}})}}),MathJax.Ajax.config.path.a11y||(MathJax.Ajax.config.path.a11y=MathJax.Hub.config.root+"/extensions/a11y"),MathJax.Ajax.Require("[a11y]/collapsible.js"),MathJax.Hub.Register.StartupHook("Collapsible Ready",function(){MathJax.Extension.explorer.Explorer.Startup(),MathJax.Ajax.loadComplete("[a11y]/explorer.js")}); \ No newline at end of file diff --git a/revisions_report_files/mathjax-27/extensions/a11y/invalid_keypress.mp3 b/revisions_report_files/mathjax-27/extensions/a11y/invalid_keypress.mp3 new file mode 100644 index 0000000000000000000000000000000000000000..cba44de08a288ee4d5aae221b71b740349c0caad GIT binary patch literal 9030 zcmeH~dpK0<8o<|Fn86r~Xxzu0k`_a;$ryLSCZkO$;~FZd(zfApar*oi~ju7F+6w={|dhwK!)F|93aI< zNr0{ZV*zA7E&{v-1PR#7=dgfe0l5N7_*@jwAfQ!1H=h9k;{v7yKzsz5@N*8}=S&0z z!8bI%ov6$8oN|l$7JX}>h0H+yaE)}$(?f>=T}1xw5;P#?kiSxHh7P>X-Od2G08ISZ zAUH+%Tld7_=;0^UUaxhvtKnv0paE3>;2gW*W%9w$@tbI)s zAAPWGX$FE`=AKzgCG7asOGgx7( zZZe!RZ79|v2A(8e0+j)xfmZWAP#(@StYj90rkrUsEF>9Vz}=9{&qBhYK2uXi5{4I0 zapr~!g`=ykBy#q7)?HAU7=ueDoSxY0GvtVpYg>cM?OVTrxHYT^KhQN=2p4i;x{<5H zBmGEA=s{?t2(Q8~Jn6Tk>nMUlckRa@=^S}1wOT7zE!Zy~F{!bXFrj|m4o{d+OJ~6wC0MHd}?jO6pRgu&vOxr%{R@KLd|INvJwe{6!%7Uv zu@vrs7P13Zpr<8u@2VUb1{46<--pqFSWmg;&k=3i0AR!~8 zw24|TWh@e`0|0I5Q8CDg4KGaO?4`95u$_F)O90(G;KGwD?ML_O229lxbC2Fr~T6ZPUn{m=d+{BV2w zfgxLA0$X$?xY*W=J-$?V}9|UqM=+E%}yzp_M~W9W*cFOm?v)>I)2cVy50; zT2Au%YXCr;001y_r?%vt1uOO+hD=TMjXnS4U@QSkjt@$wHRxz0FH4Wrnu4t7=mU}L zbW}g*gO@`KMQr%Ds0RlEo0B(SN^?S5k+?K5KoLY_zrK@6sXDauVu2*^`wrqY;I;ib z@c6~xQ`416_(QN`EHi2-ej}hF=c>6=-hzEej*#S?z&gYVlkvOcHCIfy8Nkhor|ZCj zu1wT%Zqb&)A?Vh;ptJejf0pULQ-VLOvA|FocFIT8Mqy!+zhJ%^67kX%UAvHI`G=uD z{o>#HApiha9?XD#S*SMd>~96-%~swF4TJ&HYbD-R7;qFxPWAhfUBt@mr%W6AN^e)osGt&l=*wnyjbXoHSuL|lb3YAHI|M=5JHhp#V#7eq!ov+_Q1$bLJLhQ71hna2 zhN}K{_`}9i$*OV9xJPl7?Q^w5C;S+BvZhzG>;vpiwyzj@+pv~(Q()*gdTNWv-2mP= z>zkqXx>D7j+V~xO{g)Hk%a9DiNvEVdn`4>44z4!t?_E71_lowMUy%j=(mn?*P%Nto zL+PE4XA517*r4Q=(6dimFbEQV7S>(oAE5p=oQ_|cEMaf!G5p?yWYi$UQxh*R4182> zM~6FwppjJXcxP&_U1Atjs1a|>No-eQ;l#+9Guz}9kHeB$8u01{HMS;Y{)X=fLZ~vf zv}S^8iwoSEK^b;F!U(7*$Uk z<(9-r8Uaq)_vwD%UZ*D|!?D3wb!za%xDvN$0_-IlenCC@2tXe#9!N)ytRvLfB@#Yn zG5X5JNli~*=|FpU8T`Fc2!K)$W*jLpeinGHwnn76`LQ3KYvAf*$MzCt)rb4LDO%mk zt3K!ItBWZ$d4^$VyIQlA?%vjr#*4s{ug1RFo>`7WHJ5Cbq0R78Zar7E8RTU=T387C z3qxQHC(UqugV_ellyQR-u=`*Pc^^oESA&zXx&{{z+Mp8#kUWS_OrA`Cmx13LpV^K+ zHyV9JJ+R%(%J3;Chk4X%(xbR7k9;SVh&^E88iaLuVa zsT!3M^cp}7NCozb{ybY6w)#bAYnkdP+u+L+y(F6e4^eW+BjN$(@;|s zspeSi^}4cp-`g@vqnNf&0&GQZtSr{mmODAC6)A2E^pOd6+34J~#l9rM}-;UQ7 zl8R$>u?)(+k98xY5ZoH1wt`XA=)qgJ*~FU-!bu_ucaxGSE~5>R=H>*iAVs6uEwvXS zNYIO=7j0RaympS!20uktRL;yq&&1e|z5PJSU(&@j&DIaS+;iUP(6K2+Jn5p|DNE`q ztX8q~&5(m8a5mRm{HVoVhk*f35nVC+a?=AjOze?5hhULywM{K@HMmqf)s%z8HHMEc z%h(l>jq$4Z{X^v*kG+&ZCzKg6`bLn22F?+b6*>;ewupoBtrtOU*#@II>nJc1CI-r~ zkAvn21p|vXOOU}11r_PS@-QDSI8xm;36{wI6da`;S|089d=sk|vwJG%0k+Ho!@5A2 zbTZg9mXp(>y!s?A>GM5i!;pn_$obOPISTDkss2^iwi@{;vcM2mA_uve%;1^UtR?ij z><@)!={f=ua|q7LtiiYsdVbh@kGJByVrE|zYv(+PiLsDSbq~T^tY~??G4l9EO^qF4 z%0cMP!=Cb)WT^v$k}H7@n*u|2Tr0nJg}A|{iYQgmD^v5jH8ji9LBST*ALUaprSru> zcevHl|EPbTua*0k`^Z$eOA_%4+hgCEg(aK{Qwua zO5@!K1objYOUnETq>uyXCZ&mh5m#XFB4;l?==IdEs@!`*UX+0BLa2W>S8ovRa%>QGH2AcD7#v0#;_1qGp-3CbQUt zb2m#ZvMgq_ySySNy?UaH96cla_`Suh zuw17plQ52Hd&Kh|%4U}fsc#zUy-qMZQJwEPc8><|gp$$}d?B`OH3XAt6_QVnMOle) zcdMO?Rl7QKL(Vz$I+MQRy^#rNgd5_plh)GHapncYV;YKU&w9Q((FA?&1>nHZbw2^Y zX&j_pDq#mgw3nXlX3QRVtYtlK2Xm)V%WU$OG_TrZ@6U!hL$4B_rQ83yQzKkH_3AI{ zu}?0h{jyU%*3;GAv?4h82<}uE>)gZMcURk=6sGSw`E|EFiY-4ANJbRkyN#G{++mvG zQYqQoH3j1AF6p8Wq|AAH-8bfQZ5tobAl}vVyx*60$40axGd^FpE^QuA!ti?Fpu z8>}6-zZ%rMg`a5rRcTl9Vg~fY%8;n;yO`DlwRfgl*aRMKPs>nOvzULHSKw5Lmvhc- z^w7=6_NX7&4+cM83VWJI51qjIFgp zh_UE>)H{_3FlFNd7x{=RE3(_9ya>lA$3^2^_&|FH)VJB$!ZM9BMRCg0i!56wZ*`@z z0=r(2Iv=hM#re{YTcW4FzJX|3Rgg#X(6(6?-sVf(|-GL-UNNJ zm2!Yh_*hgx)#yYdPYrujVpWOHDoANVV4D(aL&UF(@Q@7HD_cW4nu|PNU2(VnS$7RF$hW-s8~?uX5+||NSP~iZ zjIP-#DsZ>SV2LD^CHA5|nkGU7S70AJtlZpu?I2t*vQ4&atH5ks-g5k%Dc6&(zve^ zQg*G%3S(3|q$HmgqKBifHWkLoTFmy`XVkc2)yDIm8x9ZmKq|WT{;eA1=ONZ{R*<2- zLS*m0&0ldyqthA82#SIpcwhA6jK2fDq((eDGLvD_uOP9jb5W^}4RAaVk~~YPsN{8_ z(0cBr<@Ixp)fP*+O^x;CfdjmgSFFW~hbkF?5IjI%<^IaZVB$ZfR2$;3lYWtHs>6?(37y@h2&b2(x)L(O z(j%|cga!pU)HPOri|k-Ujk2ze@}j>JM7yqvrG}3QhAhh+zYN^ zMOLwuRa*-Ujfaf)4;|rJtU~~T4Z)JGp+MJEpld9sn9){c95OUE8U6Yj9-ce?;6G(2 ztAn!u*uh$p$6AB3!cj*aOi?I!Gc$HmW;rQCJ2TIuj;?%B^(t9zYB%=6%#1vNhsw>80A%+H$)JO5JF?& z?(wVBzshQZvcf3Cp>t$GL7^l68+!ff#r{8o|LX`K@Tj{DpG}@rdWRR#x`G^u3(KL3 zc$FYA*vU#7E(mZ{>7ub(rN8VA7A)8y8e{4}BjwTyOzteUSX65hc~n4QgCOc<-h~nzmEL#nu2xdIH0~4Y=ALA#l1v#7)Ke{ zIsi5$8GYeK|Lf8(1-bw&9_08!fq!o2-G&lbmpg#LZa7rkfP>n=!M@n)+C*`RTs7SI z@gNoe`<`~5%r(5qq%`{ISdn9)(Nv{zy6}kd;&-8#+VvSmBs^9iJJ_JKaQ$U+HyE$n z#$YdL=)Ma|_qGs$7!MdaMUru<@Q9DDp~-0D5eX`l{JtnT3L)sc^J>BL5D?0ZO#Yp0f%aiS_3t%-{0HQgwT6g8micvZ5~A}OcRQ7+%)l0F8in+ z&E&`tl+&bl6m!|tC;-=s2=FP5$>@^;<^rJhkH8M?wO%G_>R^Zu1=R&i*Bp=rOu;ZH zlH&nS^J$ab8uFl0tSy9Nw#GerR0<=dwNegSGbr*g>qlXH9HNhOZ6Hk!F#?DJ2t)vo$ zUXtX-@Pm}Z&Ale2nMgCbwg z>PZFfh{{>a;q)Y=#&R?$D&?O}ER)t9twN=(6N%*kO{U4@vesTjc_io5cyd{Q`_e2~ zQ|I-}=5|`@HZK1ZEw#Ldv@tD<-*6*yelKb1dLDlwd7FPP?d$br=F`TqfZsj4f${<- zHvsT{2?2x^?_1u&`pm7uej&ZX1wh=G2y_zYGtetcXn6?q3TH8?E*`d7DNlVl<~`Q? z4=ROiR;m)6eMKQs&S%&R?25!Omsoodsjt~YeRX4MGU+i26+>;Ip{(QBCK%yjZKOJA zJSnFXPBZJF${e$c)Pb#WK{*^VRZ8-NovQJX~fzF9x4;e@~(7KFZ7#!0?J|1%S z%|{&;F1GC|X)xxg*P|SMc(Iq6W}-z!xT#{2b&Yvs^lB42$edysv;i9Zf%w2Fs+cUE zW#qrZvFBIQ#Jx1r^}MJ$l{4HGML?~t1b{%aTMoKzgF7l@2cEd*EudzGZPA8Z66X}e zI3ScboKR6LUIyY5H<(g32tUOwo4I?O;7Rl(iFnSnY9ga1=aTDt1sCV99p-TJnUF64 z^T89izzu*x8M(4KEh8&uN5L+&Mq6G9H%OQ~z%F=mWedZ?1S*;b{Vm3##Y>o;UQ1bU z8@JuJnQA~J+9E1!2PYD(7iywcf^|N?F4S1N!%wUzI^WO7XLodTY;;_5&fo}cPSW%d zl5(|luLV@y>Tx-~?Y1KT36~VtTNS(5%Py}v{^0SkqQ0NL|A4pX&TpKlLr(JTWz(hH z_pVJeqY^JUAV+jJPTXf29%_TrHBN*BBhOZSk?~Y5n3tA*=HBxySn=2af!9!&bYO=! z{pc|1>cYP*%sq%RG@KR8%i8*5PI)#~>;_)8h1V0W?DJmHnvfCR9G7C(jehB~2e)G7 zi>Pbbb&alT9IsTo91XhbHru@){}P+vS0ssVM=(uoDalmti&INkOfEOGv82a89@L!_ zTnIZ6_f%)e2uj{($&fvrN+w$>#S!vQJGbrc4e1|^f8iiFylVHtD#t$@JHhUpS^MC| zPugOI@aBB`4uajgD_=BU8+n(q{Hw^?ozK^uIC|b|%h>~6zlZX=`fYzRUJHlsaW;r) z@&=XR0Lf?{cIcr3Ky_QLgoZLHwr|MJI~%CmJb_@&9gt>DfSdo(yWs0YLqpqSf$sL-iJ2DLmHIRB^Q<_-N&=ulUWY>bC?t z;EQj5JGDLO5hdtSB!WE0BJ>t`1pYD!W!@l$j|W;V{BNOhQaM3QlQ(D9k3_=b-ja}- z30XS5*qHKYhvC9y%?19mJ^7tuN%lUj_BMBz2f#%~@m!wiR3Q9P4FJ~x#P^`vl%DV> z&x9oEC>vfl{S#;5^{&esI0#D!X@rjk{`pdWofFX2L^$)+%l9LzU0iEExV;2&+hhi@ zhuuJFTRpltK=X!uSP%f6{ZQ%2C#E=? z6{ed&m_>Q{SI8em3)DoyTCeXnElfD8_f3r?7JPda;4gq?)+ZBhrR(l%+-CRbO&y06 z?&Wvq|Bf|O&dU8{kC~5H>f}-Pj(z$u`vS4=%i;b-_%E`R|0S6exE&g4T{3?Sh4bK> z$2(`XbAA{^`dq-`PoJCrKrG(N;dit5JXlp!zggm>%J4bhF-nc$sH-g&9sEwI0qq`{ z?Hos>mt{OypimIVw66Wn&L(aa{qgBbX+OSazv}=#DWZb+M-4sAgXiQ|ar}JGN^epY z;Y3c%G*_|%KiGILnV~=cO!_?5@I)(-bX#0lk>!IW?kWA$^6`hgn!id{pRF9 z1GE2hYPDq%I`Clp?>}&dih5S|oP4)%(r>5%c3xcGc`7OX#I6ti`shN|$x|Dr`lHTQ WCEpm@S)lay>ms`WyLrxY(tiW58)c^e literal 0 HcmV?d00001 diff --git a/revisions_report_files/mathjax-27/extensions/a11y/mathjax-sre.js b/revisions_report_files/mathjax-27/extensions/a11y/mathjax-sre.js new file mode 100644 index 0000000..40a6151 --- /dev/null +++ b/revisions_report_files/mathjax-27/extensions/a11y/mathjax-sre.js @@ -0,0 +1,985 @@ +// Copyright 2014-2018 Volker Sorge +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. +var $jscomp=$jscomp||{};$jscomp.scope={};$jscomp.ASSUME_ES5=!1;$jscomp.ASSUME_NO_NATIVE_MAP=!1;$jscomp.ASSUME_NO_NATIVE_SET=!1;$jscomp.defineProperty=$jscomp.ASSUME_ES5||"function"==typeof Object.defineProperties?Object.defineProperty:function(a,b,c){a!=Array.prototype&&a!=Object.prototype&&(a[b]=c.value)};$jscomp.getGlobal=function(a){return"undefined"!=typeof window&&window===a?a:"undefined"!=typeof global&&null!=global?global:a};$jscomp.global=$jscomp.getGlobal(this);$jscomp.SYMBOL_PREFIX="jscomp_symbol_"; +$jscomp.initSymbol=function(){$jscomp.initSymbol=function(){};$jscomp.global.Symbol||($jscomp.global.Symbol=$jscomp.Symbol)};$jscomp.Symbol=function(){var a=0;return function(b){return $jscomp.SYMBOL_PREFIX+(b||"")+a++}}(); +$jscomp.initSymbolIterator=function(){$jscomp.initSymbol();var a=$jscomp.global.Symbol.iterator;a||(a=$jscomp.global.Symbol.iterator=$jscomp.global.Symbol("iterator"));"function"!=typeof Array.prototype[a]&&$jscomp.defineProperty(Array.prototype,a,{configurable:!0,writable:!0,value:function(){return $jscomp.arrayIterator(this)}});$jscomp.initSymbolIterator=function(){}};$jscomp.arrayIterator=function(a){var b=0;return $jscomp.iteratorPrototype(function(){return b>>0);goog.uidCounter_=0;goog.getHashCode=goog.getUid; +goog.removeHashCode=goog.removeUid;goog.cloneObject=function(a){var b=goog.typeOf(a);if("object"==b||"array"==b){if("function"===typeof a.clone)return a.clone();b="array"==b?[]:{};for(var c in a)b[c]=goog.cloneObject(a[c]);return b}return a};goog.bindNative_=function(a,b,c){return a.call.apply(a.bind,arguments)}; +goog.bindJs_=function(a,b,c){if(!a)throw Error();if(2Number(a[1])?!1:b('(()=>{"use strict";class X{constructor(){if(new.target!=String)throw 1;this.x=42}}let q=Reflect.construct(X,[],String);if(q.x!=42||!(q instanceof String))throw 1;for(const a of[2,3]){if(a==2)continue;function f(z={a}){let a=0;return z.a}{function f(){return 0;}}return f()==3}})()')});a("es6-impl",function(){return!0});a("es7",function(){return b("2 ** 2 == 4")}); +a("es8",function(){return b("async () => 1, true")});a("es9",function(){return b("({...rest} = {}), true")});a("es_next",function(){return!1});return c},goog.Transpiler.prototype.needsTranspile=function(a,b){if("always"==goog.TRANSPILE)return!0;if("never"==goog.TRANSPILE)return!1;this.requiresTranspilation_||(this.requiresTranspilation_=this.createRequiresTranspilation_());if(a in this.requiresTranspilation_)return this.requiresTranspilation_[a]?!0:!goog.inHtmlDocument_()||"es6"!=b||"noModule"in goog.global.document.createElement("script")? +!1:!0;throw Error("Unknown language mode: "+a);},goog.Transpiler.prototype.transpile=function(a,b){return goog.transpile_(a,b)},goog.transpiler_=new goog.Transpiler,goog.protectScriptTag_=function(a){return a.replace(/<\/(SCRIPT)/ig,"\\x3c/$1")},goog.DebugLoader_=function(){this.dependencies_={};this.idToPath_={};this.written_={};this.loadingDeps_=[];this.depsToLoad_=[];this.paused_=!1;this.factory_=new goog.DependencyFactory(goog.transpiler_);this.deferredCallbacks_={};this.deferredQueue_=[]},goog.DebugLoader_.prototype.bootstrap= +function(a,b){function c(){d&&(goog.global.setTimeout(d,0),d=null)}var d=b;if(a.length){b=[];for(var e=0;e\x3c/script>")}else{var d=b.createElement("script");d.defer=goog.Dependency.defer_;d.async=!1;d.type="text/javascript";var e=goog.getScriptNonce();e&&(d.nonce=e);goog.DebugLoader_.IS_OLD_IE_?(a.pause(),d.onreadystatechange=function(){if("loaded"==d.readyState||"complete"==d.readyState)a.loaded(), +a.resume()}):d.onload=function(){d.onload=null;a.loaded()};d.src=this.path;b.head.appendChild(d)}}else goog.logToConsole_("Cannot use default debug loader outside of HTML documents."),"deps.js"==this.relativePath?(goog.logToConsole_("Consider setting CLOSURE_IMPORT_SCRIPT before loading base.js, or seting CLOSURE_NO_DEPS to true."),a.loaded()):a.pause()},goog.Es6ModuleDependency=function(a,b,c,d,e){goog.Dependency.call(this,a,b,c,d,e)},goog.inherits(goog.Es6ModuleDependency,goog.Dependency),goog.Es6ModuleDependency.prototype.load= +function(a){function b(a,b){b?d.write('