SymPy

SymPy is a Python library for symbolic mathematics, providing a full-featured computer algebra system (CAS) that performs exact mathematical computations rather than numerical approximations. Founded in 2005 by Ondrej Certik and now maintained by the SymPy Development Team with over 12,800 stars as of 2026, SymPy aims to become a full-featured CAS comparable to Mathematica, Maple, and Maxima while remaining entirely free, open-source (BSD licensed), and dependency-free (pure Python with no required C extensions). Core capabilities include: symbolic expression manipulation (simplification with simplify, expand, factor, collect, apart for partial fractions), calculus operations (differentiation with diff, integration with integrate including definite and indefinite integrals, limits with limit, series expansion with series and summation with summation), equation solving (symbolic solutions for algebraic, transcendental, differential, and systems of equations with solve and solveset), linear algebra (matrix operations, eigenvalues, eigenvectors, matrix decompositions: LU, QR, Cholesky, Jordan, Smith), polynomial mathematics (factoring, GCD, resultants, Groebner bases), discrete mathematics (number theory, combinatorics, logic expressions), geometry (2D geometric objects), plotting (via matplotlib backend), code generation (C, C++, Fortran, JavaScript, Julia, Rust, Mathematica), and LaTeX rendering of mathematical expressions. SymPy integrates with Jupyter notebooks for interactive computation and powers the math engine behind SageMath and Google Colab. The library supports Python 3.9+ and can be used alongside NumPy and SciPy for mixed symbolic-numeric workflows.