Maths

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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