SymPy

The SymPy library is split into a core with many optional modules.

Currently, the core of SymPy has around 260,000 lines of code{{cite web|url=https://www.openhub.net/p/sympy|title=Sympy project statistics on Open HUB|accessdate=2014-10-13}} (it also includes a comprehensive set of self-tests: over 100,000 lines in 350 files as of version 0.7.5), and its capabilities include:

{{cite conference

| last1 = Gede

| first1 = Gilbert

| last2 = Peterson

| first2 = Dale L.

| last3 = Nanjangud

| first3 = Angadh

| last4 = Moore

| first4 = Jason K.

| last5 = Hubbard

| first5 = Mont

| year = 2013

| title = Constrained multibody dynamics with Python: From symbolic equation generation to publication

| conference = ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference

| pages = V07BT10A051

| publisher = American Society of Mechanical Engineers

| doi = 10.1115/DETC2013-13470

| url = http://proceedings.asmedigitalcollection.asme.org/proceeding.aspx?articleid=1830918

| isbn = 978-0-7918-5597-3

| url-access= subscription

}}

{{cite journal

| last1 = Rocklin

| first1 = Matthew

| last2 = Terrel

| first2 = Andy

| year = 2012

| title = Symbolic Statistics with SymPy

| journal = Computing in Science & Engineering

| volume = 14

| issue = 3

| pages = 88–93

| doi = 10.1109/MCSE.2012.56

| bibcode = 2012CSE....14c..88R

| s2cid = 18307629

}}

{{cite journal

| last1 = Asif

| first1 = Mushtaq

| last2 = Olaussen

| first2 = Kåre

| year = 2014

| title = Automatic code generator for higher order integrators

| journal = Computer Physics Communications

| volume = 185

| issue = 5

| pages = 1461–1472

| doi = 10.1016/j.cpc.2014.01.012

| arxiv= 1310.2111

| bibcode= 2014CoPhC.185.1461M

| s2cid = 42041635

}}

• Basic arithmetic: *, /, +, -, **
• Simplification
• Expansion
• Functions: trigonometric, hyperbolic, exponential, roots, logarithms, absolute value, spherical harmonics, factorials and gamma functions, zeta functions, polynomials, hypergeometric, special functions, etc.
• Substitution
• Arbitrary precision integers, rationals and floats
• Noncommutative symbols
• Pattern matching

• Basic arithmetic: division, gcd, etc.
• Factorization
• Square-free factorization
• Gröbner bases
• Partial fraction decomposition
• Resultants

• Limits
• Differentiation
• Integration: Implemented Risch–Norman heuristic
• Taylor series (Laurent series)

• Systems of linear equations
• Systems of algebraic equations that are solvable by radicals
• Differential equations
• Difference equations

• Binomial coefficients
• Summations
• Products
• Number theory: generating Prime numbers, primality testing, integer factorization, etc.
• Logic expressions{{Cite web|url=https://docs.sympy.org/latest/modules/assumptions/index.html|title=Assumptions Module — SymPy 1.4 documentation|website=docs.sympy.org|access-date=2019-07-05}}

• Basic arithmetic
• Eigenvalues and their eigenvectors when the characteristic polynomial is solvable by radicals
• Determinants
• Inversion
• Solving

• Points, lines, rays, ellipses, circles, polygons, etc.
• Intersections
• Tangency
• Similarity

Note, plotting requires the external Matplotlib or Pyglet module.

• Coordinate models
• Plotting Geometric Entities
• 2D and 3D
• Interactive interface
• Colors
• Animations

• Units
• Classical mechanics
• Continuum mechanics{{Cite web|url=https://docs.sympy.org/latest/modules/physics/continuum_mechanics/index.html|title=Continuum Mechanics — SymPy 1.4 documentation|website=docs.sympy.org|access-date=2019-07-05}}
• Quantum mechanics
• Gaussian optics
• Linear control

• Normal distributions
• Uniform distributions
• Probability

• Permutations
• Combinations
• Partitions
• Subsets
• Permutation group: Polyhedral, Rubik, Symmetric, etc.
• Prufer sequence and Gray codes

• Pretty-printing: ASCII/Unicode pretty-printing, LaTeX
• Code generation: C, Fortran, Python

• SageMath: an open source alternative to Mathematica, Maple, MATLAB, and Magma (SymPy is included in Sage)
• SymEngine: a rewriting of SymPy's core in C++, in order to increase its performance. Work is currently in progress{{As of?|date=August 2021}} to make SymEngine the underlying engine of Sage too.{{Cite web|title=GitHub - symengine/symengine: SymEngine is a fast symbolic manipulation library, written in C++|url=https://github.com/symengine/symengine|access-date=2021-08-25|website=GitHub|language=en}}
• mpmath: a Python library for arbitrary-precision floating-point arithmetic{{Cite web|title=mpmath - Python library for arbitrary-precision floating-point arithmetic|url=https://mpmath.org/|access-date=2021-08-25|website=mpmath.org}}
• SympyCore: another Python computer algebra system{{Cite web|title=GitHub - pearu/sympycore: Automatically exported from code.google.com/p/sympycore|url=https://github.com/pearu/sympycore|access-date=2021-08-25|website=GitHub|date=January 2021|language=en}}
• SfePy: Software for solving systems of coupled partial differential equations (PDEs) by the finite element method in 1D, 2D and 3D.{{Cite web|last=Developers|first=SfePy|title=SfePy: Simple Finite Elements in Python — SfePy version: 2021.2+git.13ca95f1 documentation|url=http://sfepy.org/doc-devel/index.html|access-date=2021-08-25|website=sfepy.org|language=en}}
• GAlgebra: Geometric algebra module (previously {{Not a typo|sympy.galgebra}}).{{Cite web|title=GitHub - pygae/galgebra: Symbolic Geometric Algebra/Calculus package for SymPy|url=https://github.com/pygae/galgebra|access-date=2021-08-25|website=GitHub|language=en}}
• Quameon: Quantum Monte Carlo in Python.{{Cite web|title=Quameon - Quantum Monte Carlo in Python|url=http://quameon.sourceforge.net/|access-date=2021-08-25|website=quameon.sourceforge.net}}
• Lcapy: Experimental Python package for teaching linear circuit analysis.{{Cite web|date=2021-01-16|title=Welcome to Lcapy's documentation! — Lcapy 0.76 documentation|url=http://lcapy.elec.canterbury.ac.nz/|access-date=2021-08-25|archive-url=https://web.archive.org/web/20210116185108/http://lcapy.elec.canterbury.ac.nz/|archive-date=2021-01-16}}
• LaTeX Expression project: Easy LaTeX typesetting of algebraic expressions in symbolic form with automatic substitution and result computation.{{Cite web|title=LaTeX Expression project documentation — LaTeX Expression 0.3.dev documentation|url=http://mech.fsv.cvut.cz/~stransky/software/latexexpr/doc/|access-date=2021-08-25|website=mech.fsv.cvut.cz}}
• Symbolic statistical modeling: Adding statistical operations to complex physical models.{{Cite web|title=Symbolic Statistics with SymPy|url=https://www.researchgate.net/publication/260585491|access-date=2021-08-25|website=ResearchGate|language=en}}
• Diofant: a fork of SymPy, started by Sergey B Kirpichev{{Cite web|title=Diofant's documentation — Diofant 0.13.0a4.dev13+g8c5685115 documentation|url=https://diofant.readthedocs.io/en/latest/|access-date=2021-08-25|website=diofant.readthedocs.io}}

Since version 1.0, SymPy has the mpmath package as a dependency.

There are several optional dependencies that can enhance its capabilities:

• {{Not a typo|gmpy}}: If {{Not a typo|gmpy}} is installed, SymPy's polynomial module will automatically use it for faster ground types. This can provide a several times boost in performance of certain operations.
• matplotlib: If matplotlib is installed, SymPy can use it for plotting.
• Pyglet: Alternative plotting package.

{{Portal|Free and open-source software|Mathematics}}

• Comparison of computer algebra systems

{{Reflist}}

• {{Official website}}
• [http://planet.sympy.org/ Planet SymPy]
• [https://coderslegacy.com/python/sympy-tutorial/ SymPy Tutorials Collection]
• [https://github.com/sympy/sympy/ Code Repository on GitHub]
• [https://groups.google.com/forum/#!forum/sympy Support and development forum]
• [https://gitter.im/sympy/sympy Gitter chat room]

{{Computer algebra systems}}

{{DEFAULTSORT:Sympy}}

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