SymPy is a Python library for symbolic mathematics. It aims to become a full-featured computer algebra system (CAS) while keeping the code as simple as possible in order to be comprehensible and easily extensible. SymPy is written entirely in Python. Its core features include basic arithmetic, simplification trigonometry, polynomials, expansion, functions, substitution, numbers, noncommutative symbols, and pattern matching.
Projects in a variety of fields rely upon SymPy, including Mathics (a free, online CAS featuring Mathematica compatible syntax and functions), Cadabra (a CAS designed specifically for the resolution of problems encountered in field theory), IKFast (a robot kinematics compiler provided by OpenRAVE), SageMath (a free, open-source mathematics software system), PyDy (for multibody dynamics with Python), galgebra (a Python package for geometric algebra), SymPy Gamma (an open source analog of Wolfram | Alpha), GNU Octave Symbolic Package (an implementation of a symbolic toolbox for Octave using SymPy), SfePy (a Python package for solving PDEs in 1D, 2D, and 3D by the Finite Element method), Quameon (Quantum Monte Carlo in Python), Lcapy (an experimental Python package for teaching linear circuit analysis), and yt (a package for analyzing and visualizing volumetric data).