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.
- 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, …
- Numbers: arbitrary precision integers, rationals, and floats.
- Non-commutative symbols.
- Pattern matching.
- Limits: limit(x*log(x), x, 0) -> 0
- 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.
- Random variable types:
- Normal distributions.
- Uniform distributions.
- Bernoulli distributions.
- Binomial distributions.
- Hypergeometric distributions.
- Expected value and variance.
- Probability density.
- Random variable types:
- Shift cipher.
- Affine cipher.
- Bifid ciphers.
- Vigenere’s cipher.
- Substitution ciphers.
- Hill’s cipher.
- Kid RSA.
- Linear feedback shift registers.
- ElGamal encryption.
- 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.
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