SymPy

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 3-clause BSD. The lead developers are Ondřej Čertík and Aaron Meurer. It was started in 2005 by Ondřej Čertík.

Features

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:

Core capabilities

• 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

Polynomials

• Basic arithmetic: division, gcd, etc.
• Factorization
• Square-free factorization
• Gröbner bases
• Partial fraction decomposition
• Resultants

Calculus

• Limits
• Differentiation
• Integration: Implemented Risch–Norman heuristic
• Taylor series (Laurent series)

Solving equations

• Systems of linear equations
• Systems of algebraic equations that are solvable by radicals
• Differential equations
• Difference equations

Discrete math

• Binomial coefficients
• Summations
• Products
• Number theory: generating Prime numbers, primality testing, integer factorization, etc.
• Logic expressions

Matrices

• Basic arithmetic
• Eigenvalues and their eigenvectors when the characteristic polynomial is solvable by radicals
• Determinants
• Inversion
• Solving

Geometry

• Points, lines, rays, ellipses, circles, polygons, etc.
• Intersections
• Tangency
• Similarity

Plotting

Note, plotting requires the external Matplotlib or Pyglet module.

• Coordinate models
• Plotting Geometric Entities
• 2D and 3D
• Interactive interface
• Colors
• Animations

Physics

• Units
• Classical mechanics
• Continuum mechanics
• Quantum mechanics
• Gaussian optics
• Linear control

Statistics

• Normal distributions
• Uniform distributions
• Probability

Combinatorics

• Permutations
• Combinations
• Partitions
• Subsets
• Permutation group: Polyhedral, Rubik, Symmetric, etc.
• Prufer sequence and Gray codes

Printing

• Pretty-printing: ASCII/Unicode pretty-printing, LaTeX
• Code generation: C, Fortran, Python