SymPy

SymPy is an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live or SymPy Gamma. SymPy is simple to install and to inspect because it is written entirely in Python with few dependencies. This ease of access combined with a simple and extensible code base in a well known language make SymPy a computer algebra system with a relatively low barrier to entry. SymPy includes features ranging from basic symbolic arithmetic to calculus, algebra, discrete mathematics, and quantum physics. It is capable of formatting the result of the computations as LaTeX code. SymPy is free software and is licensed under the New BSD license. The lead developers are Ondřej Čertík and Aaron Meurer. It was started in 2005 by Ondřej Čertík. The SymPy library is split into a core with many optional modules. Currently, the core of SymPy has around 260,000 lines of code (it also includes a comprehensive set of self-tests: over 100,000 lines in 350 files as of version 0.7.5), and its capabilities include: Basic arithmetic: *, /, +, -, ** Simplification Expansion Functions: trigonometric, hyperbolic, exponential, roots, logarithms, absolute value, spherical harmonics, factorials and gamma functions, zeta functions, polynomials, hypergeometric, special functions, etc. Substitution Arbitrary precision integers, rationals and floats Noncommutative symbols Pattern matching Basic arithmetic: division, gcd, etc. Factorization Square-free factorization Gröbner bases Partial fraction decomposition Resultants Limits Differentiation Integration: Implemented Risch–Norman heuristic Taylor series (Laurent series) Systems of linear equations Systems of algebraic equations that are solvable by radicals Differential equations Difference equations Binomial coefficients Summations Products Number theory: generating Prime numbers, primality testing, integer factorization, etc.