SymPy

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SymPy
[[Programmer|DeveloperTemplate:Pluralize from text]]SymPy Development Team
Initial release2007; 19 years ago (2007)
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Written inPython
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Operating systemCross-platform
TypeComputer algebra system
License3-clause BSD
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SymPy is an open-source Python library for symbolic computation. It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live[2] or SymPy Gamma.[3] SymPy is simple to install and to inspect because it is written entirely in Python with few dependencies.[4][5][6] This ease of access combined with a simple and extensible codebase in a well-known language make SymPy a computer algebra system with a relatively low barrier to entry.

SymPy includes features ranging from basic symbolic arithmetic to calculus, algebra, discrete mathematics, and quantum physics. It is capable of formatting the result of the computations as LaTeX code.[4][5]

SymPy is free software and is licensed under the 3-clause BSD. The lead developers are Ondřej Čertík and Aaron Meurer. It was started in 2005 by Ondřej Čertík.[7]

Features

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

Currently, the core of SymPy has around 260,000 lines of code[8] (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:[4][5][9][10][11]

Core capabilities

Polynomials

Calculus

Solving equations

Discrete math

Matrices

Geometry

Plotting

Note, plotting requires the external Matplotlib or Pyglet module.

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

Physics

Statistics

Combinatorics

Printing

  • 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?] to make SymEngine the underlying engine of Sage too.[14]
  • mpmath: a Python library for arbitrary-precision floating-point arithmetic[15]
  • SympyCore: another Python computer algebra system[16]
  • SfePy: Software for solving systems of coupled partial differential equations (PDEs) by the finite element method in 1D, 2D and 3D.[17]
  • GAlgebra: Geometric algebra module (previously sympy.galgebra).[18]
  • Quameon: Quantum Monte Carlo in Python.[19]
  • Lcapy: Experimental Python package for teaching linear circuit analysis.[20]
  • LaTeX Expression project: Easy LaTeX typesetting of algebraic expressions in symbolic form with automatic substitution and result computation.[21]
  • Symbolic statistical modeling: Adding statistical operations to complex physical models.[22]
  • Diofant: a fork of SymPy, started by Sergey B Kirpichev[23]

Dependencies

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

There are several optional dependencies that can enhance its capabilities:

  • gmpy: If 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.

See also

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References

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  1. ^ Page Module:Citation/CS1/styles.css has no content."Releases - sympy/sympy". Retrieved 14 May 2025 – via GitHub.
  2. ^ Page Module:Citation/CS1/styles.css has no content."SymPy Live". live.sympy.org. Retrieved 2021-08-25.
  3. ^ Page Module:Citation/CS1/styles.css has no content."SymPy Gamma". www.sympygamma.com. Retrieved 2021-08-25.
  4. ^ a b c Page Module:Citation/CS1/styles.css has no content."SymPy homepage". Retrieved 2014-10-13.
  5. ^ a b c Page Module:Citation/CS1/styles.css has no content.Joyner, David; Čertík, Ondřej; Meurer, Aaron; Granger, Brian E. (2012). "Open source computer algebra systems: SymPy". ACM Communications in Computer Algebra. 45 (3/4): 225–234. doi:10.1145/2110170.2110185. S2CID 44862851.
  6. ^ Page Module:Citation/CS1/styles.css has no content.Meurer, Aaron; Smith, Christopher P.; Paprocki, Mateusz; Čertík, Ondřej; Kirpichev, Sergey B.; Rocklin, Matthew; Kumar, AMiT; Ivanov, Sergiu; Moore, Jason K. (2017-01-02). "SymPy: symbolic computing in Python" (PDF). PeerJ Computer Science. 3: e103. doi:10.7717/peerj-cs.103. ISSN 2376-5992.
  7. ^ Page Module:Citation/CS1/styles.css has no content."SymPy vs. Mathematica · sympy/Sympy Wiki". GitHub.
  8. ^ Page Module:Citation/CS1/styles.css has no content."Sympy project statistics on Open HUB". Retrieved 2014-10-13.
  9. ^ Page Module:Citation/CS1/styles.css has no content.Gede, Gilbert; Peterson, Dale L.; Nanjangud, Angadh; Moore, Jason K.; Hubbard, Mont (2013). Constrained multibody dynamics with Python: From symbolic equation generation to publication. ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers. pp. V07BT10A051. doi:10.1115/DETC2013-13470. ISBN 978-0-7918-5597-3.
  10. ^ Page Module:Citation/CS1/styles.css has no content.Rocklin, Matthew; Terrel, Andy (2012). "Symbolic Statistics with SymPy". Computing in Science & Engineering. 14 (3): 88–93. Bibcode:2012CSE....14c..88R. doi:10.1109/MCSE.2012.56. S2CID 18307629.
  11. ^ Page Module:Citation/CS1/styles.css has no content.Asif, Mushtaq; Olaussen, Kåre (2014). "Automatic code generator for higher order integrators". Computer Physics Communications. 185 (5): 1461–1472. arXiv:1310.2111. Bibcode:2014CoPhC.185.1461M. doi:10.1016/j.cpc.2014.01.012. S2CID 42041635.
  12. ^ Page Module:Citation/CS1/styles.css has no content."Assumptions Module — SymPy 1.4 documentation". docs.sympy.org. Retrieved 2019-07-05.
  13. ^ Page Module:Citation/CS1/styles.css has no content."Continuum Mechanics — SymPy 1.4 documentation". docs.sympy.org. Retrieved 2019-07-05.
  14. ^ Page Module:Citation/CS1/styles.css has no content."GitHub - symengine/symengine: SymEngine is a fast symbolic manipulation library, written in C++". GitHub. Retrieved 2021-08-25.
  15. ^ Page Module:Citation/CS1/styles.css has no content."mpmath - Python library for arbitrary-precision floating-point arithmetic". mpmath.org. Retrieved 2021-08-25.
  16. ^ Page Module:Citation/CS1/styles.css has no content."GitHub - pearu/sympycore: Automatically exported from code.google.com/p/sympycore". GitHub. January 2021. Retrieved 2021-08-25.
  17. ^ Page Module:Citation/CS1/styles.css has no content.Developers, SfePy. "SfePy: Simple Finite Elements in Python — SfePy version: 2021.2+git.13ca95f1 documentation". sfepy.org. Retrieved 2021-08-25.
  18. ^ Page Module:Citation/CS1/styles.css has no content."GitHub - pygae/galgebra: Symbolic Geometric Algebra/Calculus package for SymPy". GitHub. Retrieved 2021-08-25.
  19. ^ Page Module:Citation/CS1/styles.css has no content."Quameon - Quantum Monte Carlo in Python". quameon.sourceforge.net. Retrieved 2021-08-25.
  20. ^ Page Module:Citation/CS1/styles.css has no content."Welcome to Lcapy's documentation! — Lcapy 0.76 documentation". 2021-01-16. Archived from the original on 2021-01-16. Retrieved 2021-08-25.
  21. ^ Page Module:Citation/CS1/styles.css has no content."LaTeX Expression project documentation — LaTeX Expression 0.3.dev documentation". mech.fsv.cvut.cz. Retrieved 2021-08-25.
  22. ^ Page Module:Citation/CS1/styles.css has no content."Symbolic Statistics with SymPy". ResearchGate. Retrieved 2021-08-25.
  23. ^ Page Module:Citation/CS1/styles.css has no content."Diofant's documentation — Diofant 0.13.0a4.dev13+g8c5685115 documentation". diofant.readthedocs.io. Retrieved 2021-08-25.

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