SymPy – Python library for symbolic mathematics

Last Updated on September 6, 2023

SymPy is an open source 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.

Features include:

  • Core functionality:
    • Basic arithmetic: Support for operators such as +, -, *, /, ** (power).
    • Simplification Trigonometry, Polynomials.
    • Expansion: of a polynomial .
    • Functions: trigonometric, hyperbolic, exponential, roots, logarithms, absolute value, spherical harmonics, factorials and gamma functions, zeta functions, polynomials, special functions, …
    • Substitution:.
    • Numbers: arbitrary precision integers, rationals, and floats.
    • Non-commutative symbols.
    • Pattern matching.
  • Polynomials.
  • Calculus:
    • Limits: limit(x*log(x), x, 0) -> 0
    • Differentiation
    • Integration: It uses extended Risch-Norman heuristic.
    • Taylor (Laurent) series
  • Solving polynomial, algebraic, differential, difference, systems of, and diophantine equations.
  • Combinatorics – permutations, combinations, partitions, subsets, permutation groups, and Prufer and Gray codes.
  • Discrete mathematics – binomial coefficients, summations, products, number theory, and logic expressions.
  • Matrices – basic arithmetic, eigenvalues / eigenvectors, determinants, inversion, solving, and abstract expressions.
  • Geometric algebra.
  • Geometry – points, lines, rays, segments, ellipses, circles, polygons. Intersection, tangency, and similarity are also supported.
  • Plotting – coordinate modes, plotting geometric entities, 2D and 3D, interactive interface, colours, and mathplotlib support.
  • Physics – units, mechanics, quantum, Gaussian optics, and Pauli algebra.
  • Statistics:
    • Random variable types:
      • Normal distributions.
      • Uniform distributions.
      • Bernoulli distributions.
      • Binomial distributions.
      • Hypergeometric distributions.
    • Probability.
    • Expected value and variance.
    • Probability density.
  • Cryptography:
    • Shift cipher.
    • Affine cipher.
    • Bifid ciphers.
    • Vigenere’s cipher.
    • Substitution ciphers.
    • Hill’s cipher.
    • RSA.
    • Kid RSA.
    • Linear feedback shift registers.
    • ElGamal encryption.
  • Parsing:
    • Conversion from Python objects to SymPy objects.
    • Optional implicit multiplication and function application parsing.
    • Limited Mathematica and Maxima parsing.
    • Custom parsing transformations.
  • Printing, with pretty printing, code generation (C, Fortran, Python), and Theano interaction.

Support: Documentation, Mailing List, Gitter, GitHub Code Repository
Developer: SymPy Development Team
License: New BSD License

SymPy is written in Python. Learn Python with our recommended free books and free tutorials.

Return to Python Maths Tools | Return to Computer Algebra Systems

Popular series
Free and Open Source SoftwareThe largest compilation of the best free and open source software in the universe. Each article is supplied with a legendary ratings chart helping you to make informed decisions.
ReviewsHundreds of in-depth reviews offering our unbiased and expert opinion on software. We offer helpful and impartial information.
Alternatives to Proprietary SoftwareReplace proprietary software with open source alternatives: Google, Microsoft, Apple, Adobe, IBM, Autodesk, Oracle, Atlassian, Corel, Cisco, Intuit, and SAS.
GamesAwesome Free Linux Games Tools showcases a series of tools that making gaming on Linux a more pleasurable experience. This is a new series.
Artificial intelligence iconMachine Learning explores practical applications of machine learning and deep learning from a Linux perspective. This is a new series.
Guide to LinuxNew to Linux? Read our Linux for Starters series. We start right at the basics and teach you everything you need to know to get started with Linux.
Alternatives to popular CLI tools showcases essential tools that are modern replacements for core Linux utilities.
System ToolsEssential Linux system tools focuses on small, indispensable utilities, useful for system administrators as well as regular users.
ProductivityLinux utilities to maximise your productivity. Small, indispensable tools, useful for anyone running a Linux machine.
AudioSurveys popular streaming services from a Linux perspective: Amazon Music Unlimited, Myuzi, Spotify, Deezer, Tidal.
Saving Money with LinuxSaving Money with Linux looks at how you can reduce your energy bills running Linux.
Home ComputersHome computers became commonplace in the 1980s. Emulate home computers including the Commodore 64, Amiga, Atari ST, ZX81, Amstrad CPC, and ZX Spectrum.
Now and ThenNow and Then examines how promising open source software fared over the years. It can be a bumpy ride.
Linux at HomeLinux at Home looks at a range of home activities where Linux can play its part, making the most of our time at home, keeping active and engaged.
Linux CandyLinux Candy reveals the lighter side of Linux. Have some fun and escape from the daily drudgery.
DockerGetting Started with Docker helps you master Docker, a set of platform as a service products that delivers software in packages called containers.
Android AppsBest Free Android Apps. We showcase free Android apps that are definitely worth downloading. There's a strict eligibility criteria for inclusion in this series.
Programming BooksThese best free books accelerate your learning of every programming language. Learn a new language today!
Programming TutorialsThese free tutorials offer the perfect tonic to our free programming books series.
Linux Around The WorldLinux Around The World showcases usergroups that are relevant to Linux enthusiasts. Great ways to meet up with fellow enthusiasts.
Stars and StripesStars and Stripes is an occasional series looking at the impact of Linux in the USA.
Notify of

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Inline Feedbacks
View all comments