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 (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

Polynomials

Calculus

Solving equations

Discrete math

Matrices

Geometry

Plotting

Note, plotting requires the external Matplotlib or Pyglet module.

Physics

Statistics

Combinatorics

Printing

Related projects

Dependencies

Since version 1.0, SymPy has the mpmath package as a dependency. There are several optional dependencies that can enhance its capabilities:

Usage examples

Pretty-printing

Sympy allows outputs to be formatted into a more appealing format through the function. Alternatively, the method will enable pretty-printing, so need not be called. Pretty-printing will use unicode symbols when available in the current environment, otherwise it will fall back to ASCII characters.

Expansion

Arbitrary-precision example

Differentiation

Plotting

Limits

Differential equations

Integration

Series

Logical reasoning

Example 1

Example 2