[PROJECT STOPPED] Combinatorics, Simulation Package
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Further development on this project has stopped!!

Combinatorics, Simulation Package

Simulacra, a combinatorics, probability and simulation PHP package

An effort was made for state-of-the-art algorithms to be used in most situations Inspired by various C/Python/Java packages for Scientific Computations and custom research and experimentation Links/Papers are provided were applicable and sources are accessible

see also:

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  • Xpresion a simple and flexible eXpression parser engine (with custom functions and variables support) for PHP, Python, Node/JS, ActionScript
  • Regex Analyzer/Composer Regular Expression Analyzer and Composer for Node/JS, PHP, Python, ActionScript
  • PublishSubscribe a simple and flexible publish-subscribe pattern implementation for Node/JS, PHP, Python, ActionScript

This package can be used to:

  1. generate Discrete Random Sequences based on various (non-uniform) discrete probability distributions
  2. generate Random Variables/Vectors having continous probability distributions (uniform, normal, exponential, log-normal, chi-square)
  3. generate Permutations/Combinations/Partitions/Power Sets of a set (array) of elements
  4. compute Convex Hulls of set of points
  5. do computations with Complex Number arithmetic
  6. do computations with General Univariate Polynomials (derivative/integration/evaluation/addition/scalar multiplication/pointwise multiplication/shift multiplication/multiplication/division)
  7. do Linear Algebra computations, compute Singular Value Decomposition (SVD Algorithm)
  8. compute Factorials/Gamma Functions/Combinations/Partition Functions/Multinomial Coefficients/Fibonacci Numbers/Catalan Numbers/Bell Numbers/GCD/Integer Factorization
  9. compute Fast Fourier Transforms (FFT Algorithm)
  10. solve Linear Programming problems (Simplex Algorithm) (TODO)
  11. solve systems of General Multivariate Polynomial Equations, compute Grobner Bases (Buchberger algorithm) (TODO)

Pascal triangle

###Some References