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 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, 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
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
Statistics
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
Related projects
- SageMath: an open source alternative to Mathematica, Maple, MATLAB, and Magma
- SymEngine: a rewriting of SymPy's core in C++, in order to increase its performance. Work is currently in progress to make SymEngine the underlying engine of Sage too.
- mpmath: a Python library for arbitrary-precision floating-point arithmetic
- SympyCore: another Python computer algebra system
- SfePy: Software for solving systems of coupled partial differential equations by the finite element method in 1D, 2D and 3D.
- GAlgebra: Geometric algebra module.
- Quameon: Quantum Monte Carlo in Python.
- Lcapy: Experimental Python package for teaching linear circuit analysis.
- LaTeX Expression project: Easy LaTeX typesetting of algebraic expressions in symbolic form with automatic substitution and result computation.
- Symbolic statistical modeling: Adding statistical operations to complex physical models.
- Diofant: a fork of SymPy, started by Sergey B Kirpichev
Dependencies
Since version 1.0, SymPy has the mpmath package as a dependency.There are several optional dependencies that can enhance its capabilities:
- : If is installed, SymPy's polynomial module will automatically use it for faster ground types. This can provide a several times boost in performance of certain operations.
- matplotlib: If matplotlib is installed, SymPy can use it for plotting.
- Pyglet: Alternative plotting package.