SymPy is a symbolic mathematics library for working with mathematical expressions in exact form. Unlike numerical libraries that primarily calculate approximate floating-point results, SymPy can manipulate mathematical objects symbolically and preserve relationships between variables.
The library provides computer algebra capabilities covering elementary algebra, calculus, number theory, linear algebra and more specialised mathematical disciplines. Expressions are represented as structured mathematical objects that can be transformed, simplified, analysed and combined.
SymPy is useful in education, mathematical research, engineering and scientific computing. It can solve equations, derive formulas, manipulate symbolic matrices and generate expressions suitable for numerical evaluation.
Its modular design also allows developers to use symbolic mathematics within other applications, including mathematical modelling tools, scientific workflows and code-generation systems.
This is free and open source software.
Key Features
- Symbolic expression manipulation including expansion, factorisation, substitution and simplification.
- Exact arithmetic with integers, rational numbers and symbolic constants.
- Assumptions system for recording and reasoning about mathematical properties of expressions.
- Symbolic differentiation, integration, limits and series expansions.
- Algebraic equation solving, systems of equations and inequality solving.
- Ordinary differential equations, recurrence relations and selected partial differential equation methods.
- Polynomial operations including factorisation, division, roots and Gröbner bases.
- Symbolic matrices with determinants, inverses, eigenvalues, eigenvectors and matrix decompositions.
- Number theory operations involving primes, divisibility, modular arithmetic and Diophantine equations.
- Combinatorics tools for permutations, partitions, groups and discrete mathematical structures.
- Symbolic probability distributions, random variables and statistical operations.
- Geometry tools for points, lines, circles, polygons and intersections.
- Physics modules covering mechanics, quantum mechanics, vectors, tensors and units.
- Expression parsing, pattern matching and custom mathematical functions.
- Two-dimensional and three-dimensional plotting of mathematical expressions.
- LaTeX, mathematical pretty-printing and code generation for numerical programs.
Website: www.sympy.org
Support:
Developer: SymPy Development Team
License: BSD 3-Clause ‘New’ or ‘Revised’ License
SymPy is written in Python. Learn Python with our recommended free books and free tutorials.
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