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.
Key Features
- 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.
- Random variable types:
- 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.
Related Software
| Python Mathematics Tools | |
|---|---|
| scikit-learn | Machine learning library for Python |
| NumPy | Core package for scientific computing with Python |
| SciPy | Ecosystem for mathematics, science, and engineering. |
| statsmodels | Statistical modeling and econometrics |
| SymPy | Library for symbolic mathematics |
| SageMath | Computer algebra system |
| patsy | Package for describing statistical models and to build design matrices |
| mpmath | Library for arbitrary-precision floating-point arithmetic |
Read our verdict in the software roundup.
| Computer Algebra Systems | |
|---|---|
| Scilab | Numerical computational package |
| Maxima | System for the manipulation of symbolic and numerical expressions |
| Octave | Powerful programming language with built-in plotting and visualization tools |
| SageMath | Open source alternative to Magma, Maple, Mathematica and Matlab |
| SymPy | Python library for symbolic mathematics |
| SINGULAR | Computer Algebra System for polynomial computations |
| Macaulay2 | Software system for research in algebraic geometry |
| Cadabra | Symbolic computer algebra system for field theory problems |
| PARI/GP | Widely used algebra system designed for fast computations in number theory |
| GAP | System for computational discrete algebra |
| FriCAS | Fork of Axiom |
| CoCoA | System for doing computations in commutative algebra |
| Mathics | General-purpose CAS with Mathematica-compatible syntax and functions |
| FORM | Symbolic Manipulation System |
| Nelson | Numerical computational language |
| wxMaxima | GUI for the sublime Maxima CAS |
| Xcas | Cross-platform mathematical environment |
| REDUCE | General-purpose computer algebra system for symbolic computation |
| Axiom | General purpose Computer Algebra system |
| Symja | Computer algebra system and symbolic mathematics library |
| CGSuite | For research in combinatorial game theory |
Read our verdict in the software roundup.
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