SymPy – Python library for symbolic mathematics

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.

Website: www.sympy.org
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

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