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List of computer algebra systems
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The following tables provide a comparison of computer algebra systems (CAS). A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them, and an environment in which to use the language. A CAS may include a user interface and graphics capability; and to be effective may require a large library of algorithms, efficient data structures and a fast kernel.

General

SystemCreatorDevelopment startedFirst public releaseLatest stable versionLatest stable release dateCost (USD)LicenseNotes
AxiomRichard Jenks19771993 and 20027August 20148Freemodified BSD licenseGeneral purpose CAS. Continuous Release using Docker Containers
CadabraKasper Peeters200120072.4.025 August 2022FreeGNU GPLCAS for tensor field theory
CoCoAJohn Abbott, Anna M. Bigatti, Giovanni Lagorio198719955.2.02 May 2017FreeGNU GPLSpecialized CAS for commutative algebra
DeriveSoft Warehouse197919886.1November 2007DiscontinuedProprietaryCAS designed for DOS and Windows microcomputers; it was discontinued in 2007
Erable (aka ALGB)Bernard Parisse [fr], Mika Heiskanen, Claude-Nicolas Fiechter199319934.2006091921 April 2009FreeLGPLCAS designed for Hewlett-Packard scientific graphing calculators of the HP 48/49/40/50 series; discontinued in 2009
FermatRobert H. Lewis198619936.521 June 2021$70 if grant money available, otherwise $0GNU GPLSpecialized CAS for resultant computation and linear algebra with polynomial entries
FORMJ.A.M. Vermaseren198419894.3.111 April 20239FreeGNU GPLCAS designed mainly for particle physics
FriCASWaldek Hebisch200720071.3.111 July 2024Freemodified BSD licenseFull-featured general purpose CAS. Especially strong at symbolic integration.
GAPGAP Group198619864.13.113 June 202410FreeGNU GPL11Specialized CAS for group theory and combinatorics.
GeoGebra CASMarkus Hohenwarter et al.20136.0.753.03 January 2023Free for non-commercial use12Freeware13Web-based or Desktop CAS Calculator
GiNaCChristian Bauer, Alexander Frink, Richard B. Kreckel, et al.199919991.8.323 March 2022FreeGNU GPLIntegrate symbolic computation into C++ programs; no high-level interface, but emphasis on interoperability.
GNU OctaveJohn W. Eaton199319947.3.02022FreeGPLv3+A high-level programming language for scientific computing and numerical computation mostly compatible with MATLAB
KANT/KASHKANT Group??32005/2008Free for non-commercial useown licenseSpecialized CAS for algebraic number theory
Macaulay2Daniel Grayson and Michael Stillman199219941.24.0515 May 2024FreeGNU GPLSpecialized CAS for algebraic geometry and commutative algebra
MacsymaMIT Project MAC and Symbolics196819782.41999$500ProprietaryOne of the oldest general purpose CAS. Still alive as Maxima.
MagmaUniversity of Sydney~199019932.27-822 February 2023$1,440ProprietaryGeneral purpose CAS, originally specialized in group theory. Works with elements of algebraic structures rather than with non typed mathematical expressions
MagnusThe New York Group Theory Cooperative199419972005FreeGNU GPLSpecialized CAS for group theory providing facilities for doing calculations in and about infinite groups. Discontinued in 2005.
MapleSymbolic Computation Group, University of Waterloo19801419842024 (6 March 2024; 12 months ago (2024-03-06)) [±]1515 March 2022$2,390(Commercial), $2,265 (Government), $995 (Academic), $239 (Personal Edition), $99 (Student), $79 (Student, 12-Month term)16ProprietaryOne of the major general purpose CAS
MathcadParametric Technology Corporation1985198515.0 M04527 February 2021$1,600 (Commercial), $105 (Student), Free (Express Edition)17ProprietaryNumerical software with some CAS capabilities
MathemagixJoris van der Hoeven19992002FreeGNU GPLComputer algebra and analysis system
MathematicaWolfram Research1986198814.2.0 (January 23, 2025; 2 months ago (2025-01-23)) [±]1829 June 2022$2,495 (Professional), $1,095 (Education), $295 (Personal),19 $140 (Student), $69.95 (Student annual license),20 free on Raspberry Pi hardware21ProprietaryOne of the major general purpose CAS
MathomaticGeorge Gesslein II1986198716.0.52012DiscontinuedLGPLElementary algebra, calculus, complex number and polynomial manipulations.
MaximaMIT Project MAC and Bill Schelter et al.196719985.46.02213 April 2022FreeGNU GPLGeneral purpose CAS. Continuation of Macsyma; new releases occur approximately two times per year.
MuMATHSoft Warehouse1970s1980MuMATH-83DiscontinuedProprietaryPredecessor of Derive
MuPADSciFace Software198920085.12008DiscontinuedProprietaryMathWorks has incorporated MuPAD technology into Symbolic Math Toolbox
OpenAxiomGabriel Dos Reis200720071.4.22013Freemodified BSD licenseGeneral purpose CAS. A fork of Axiom.
PARI/GPHenri Cohen, Karim Belabas, Bill Allombert et al.198519902.11.417 April 2020FreeGNU GPLSpecialized CAS for number theory.
REDUCEAnthony C. Hearn196319686860 (August 2024; 7 months ago (2024-08)) [±]23See "Latest stable version".Freemodified BSD licenseOne of the oldest and historically important general purpose CAS. Still alive, as open-sourced and freed in December 2008
SageMathWilliam A. Stein2005200510.524  (4 December 2024; 3 months ago (4 December 2024))4 December 2024FreeGNU GPLMathematics software system combining a number of existing packages, including numerical computation, statistics and image processing
ScilabScilab Enterprises199019902023.010 March 2023FreeCeCILL (GPL-compatible) until version 5.5.2 GPL v2.0 since version 6.0.2MATLAB alternative.
SINGULARUniversity of Kaiserslautern198419974-3-014 January 2022FreeGNU GPLComputer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory.
SMath StudioAndrey Ivashov200420061.0.83489 November 2022FreeProprietaryMathematical notebook program similar to Mathcad.
Symbolic Manipulation ProgramStephen Wolfram19792519811988DiscontinuedProprietaryThis software was eventually replaced by Mathematica, and the newer program still retains much of the syntax and functionality of the earlier SMP.26
Symbolic Math Toolbox (MATLAB)MathWorks198920082024b2024$3,150 (Commercial), $99 (Student Suite), $700 (Academic), $194 (Home) including price of MATLAB.ProprietaryProvides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic.
SymPyOndřej Čertík200620071.13.211 August 2024Freemodified BSD licensePython-based
TI-Nspire CAS (Computer Software)Texas Instruments200620095.1.32020ProprietarySuccessor to Derive. Based on Derive's engine used in TI-89/Voyage 200 and TI-Nspire handheld
Wolfram AlphaWolfram Research20092013Pro version: $4.99 / month, Pro version for students: $2.99 / month, ioRegular version: freeProprietaryOnline computer algebra system with step-by step solutions.
Xcas/GiacBernard Parisse [fr]200020001.9.0-99May 2024FreeGPLGeneral CAS, also adapted for the HP Prime. Compatible modes for Maple, MuPAD and TI89 syntax. Symbolic spreadsheets, Giac library for use with other programs. ARM ports for some PDAs with Linux or WinCE27
YacasAyal Pinkus et al.19982819991.9.14 July 2020FreeGNU GPL
CreatorDevelopment startedFirst public releaseLatest stable versionLatest stable release dateCost (USD)LicenseNotes

These computer algebra systems are sometimes combined with "front end" programs that provide a better user interface, such as the general-purpose GNU TeXmacs.

Functionality

Below is a summary of significantly developed symbolic functionality in each of the systems.

SystemFormula editorArbitrary precisionCalculusSolversGraph theoryNumber theoryQuantifier eliminationBoolean algebraTensorsProbabilityControl theoryGroup theorySystem
IntegrationIntegral transformsEquationsInequalitiesDiophantine equationsDifferential equationsRecurrence relations
AxiomNoYesYesYesYesYesYesYesYesNoYesYesYesYesYesNoYesAxiom
CadabraNoYesYesYesYesYesNoYesNoNoNoNoNoYesNoNoYesCadabra
FriCASYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesNoYesFriCAS
GAPNoYesNoNoYesYesYesNoYesYesYesYesYesYesNoNoYesGAP
MagmaNoYesNoNoYesNoYesNoNoYesYesNoNoNo??YesMagma
MagnusNoYesNoNoNoNoNoNoNo??No?NoNoNoYesMagnus
MapleYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesMaple
MathcadYesNoYesNoYesNoNoNoNoNoNoNoNoNoNoNoNoMathcad
MathematicaYesYesYesYesYesYesYesYesYesYesYesYesYesYes29YesYesYesMathematica
MathomaticNoNoYesYesYesNoNoNoNoNoYesNoNoNoNoNoNoMathomatic
MaximaNoYesYesYesYesYesNoYesYesYesYesNoYesYesYesYesYesMaxima
PARI/GPNoYesYesNoYesNoYes*NoYes*NoYesNoYes??NoYesPARI/GP
REDUCEYesYesYesYesYesYesNoYesNoNoYesYesYesYesNoNoNoREDUCE
SageMathNoYesYesYesYesYesYes[A]YesYesYesYesYes[B]YesYesYesNoYesSageMath
SMath StudioYesNoYesNoYesNoNoNoNoNoNoNoNoNoNoNoNoSMath Studio
Symbolic Math Toolbox (MATLAB)YesYesYesYesYesYesYesYesNoYesYesNoYesNoYesYesNoSymbolic Math Toolbox (MATLAB)
SymPyNoYesYesYesYesYesYes30YesYesNoYesNoYesYesYesNoYesSymPy
Wolfram AlphaYesYesYesYesYesYesYesYesYesYesYesYesYesNo??YesWolfram Alpha
Xcas/GiacYesYesYesNoYesYesNoYesYesNoYesNoNoNoYes??Xcas/Giac
YacasNoYesYesNoYesNoNoNoNoNoNoNoNoNo??NoYacas
  1. ^ via SymPy
  2. ^ via qepcad optional package

Those which do not "edit equations" may have a GUI, plotting, ASCII graphic formulae and math font printing. The ability to generate plaintext files is also a sought-after feature because it allows a work to be understood by people who do not have a computer algebra system installed.

Operating system support

The software can run under their respective operating systems natively without emulation. Some systems must be compiled first using an appropriate compiler for the source language and target platform. For some platforms, only older releases of the software may be available.

SystemDOSWindowsmacOSLinuxBSDSolarisAndroidiOSSaaSOther
Axiom?EmulatorYesYesNoNo??No
CadabraNoYesYesYesYesNoNoNoNo
CoCoANoYesYesYesYesYes??NoTru64 UNIX, HP-UX, IRIX
DeriveYesYesNoNoNoNoNoNoNo
ErableNoEmulatorEmulatorEmulatorNoNoNoNoNoSystem RPL on HP 48/49/50/40 series
Euler?YesNoYesNoNo??No
Fermat?CygwinYesYesNoNo??No
FORM?CygwinYesYesYesYes??No
FriCAS?Cygwin+nativeYesYesYesYesYes?No
GAP?YesYesYesYesYes??No
KANT/KASH?YesYesYesNoNo??No
Macaulay2?CygwinYesYesYesYes??No
Magma?YesYesYesYesYes??No
MagnusNoYes?Yes?YesNoNoNoSunOs
MapleNoYesYesYesNoNoNoNoNo
MathcadYesYesNoNoNoNoNoNoNo
MathematicaYesYesYesYesNoNoNoNoYesRaspberry Pi31
MathomaticYesYesYesYesYesYesNoYesNoAll POSIX platforms
Maxima?YesYesYesYesYesYes?NoAll POSIX platforms with Common Lisp
MuMATHYesNoNoNoNoNo??No
OpenAxiom?YesYesYesYesYes??No
PARI/GP?YesYesYesYesYesYes?No
REDUCENoYesYesYesYesYesYesYesNo
SageMathNoYesYesYesNoYesNoYesYes
SINGULAR?YesYesYesYesYes??No
SMath StudioNoYesMonoMonoMonoMonoYesYesYesUniversal Windows Platform
Symbolic Math Toolbox (MATLAB)NoYesYesYesNoNoNoNoYes
SymbolicC++?YesYesYesYesYes??No
SymPy?YesYesYesYesYesYesYesYes32Any system that supports Python
TI-Nspire (desktop software)NoYesYesNoNoNoNoYesNo
Xcas/GiacNoYesYesYesYesYesYesYesNoHP Prime CAS, KhiCAS for TI Nspire
YacasNoYesYesYesYesYes??No

Graphing calculators

Some graphing calculators have CAS features.

SystemCreatorDevelopment startedFirst public release / OS versionLatest stable version / OS versionNotes
Casio CFX-9970GCASIO Computer Co.?1998
Casio Algebra FX 2.0, Casio Algebra FX 2.0 PlusCASIO Computer Co.?1999
Casio ClassPad 300, Casio ClassPad 300 Plus, Casio ClassPad 330, Casio ClassPad 330 Plus, Casio ClassPad fx-CP400, Casio fx-CG500Casio ClassPad ManagerCASIO Computer Co.200220033.10.7000 (ClassPad I)

2.01.7000 (ClassPad II, fx-CG500)

ClassPad Manager is an emulator which runs on a PC.
HP 49G, HP 49g+, HP 48gII, HP 50g, HP 40G, HP 40gsHewlett-Packard19931.??(1999) / 42.15 (2006-09-19, 2009-04-21) / 4Based on Erable, which is also available as an add-on for the HP 48S, HP 48SX, HP 48G, HP 48G+, HP 48GX. Intended for problems which occur in engineering applications. Source code openly available.
HP PrimeHewlett-Packard200020132.1.14433 (2020 01 21) CAS ver. 1.5.0Based on Xcas/Giac. Xcas source code openly available, but not HP Prime implementation.
TI-89Texas Instruments199519962.09
TI-89 TitaniumTexas Instruments200320047/18/2005 v3.10
TI-92Texas Instruments19941995?
TI-92 PlusTexas Instruments199719983/27/2003 v2.09
TI-Nspire CAS, TI-Nspire CX CAS, TI-Nspire CX II CASTexas Instruments200620082021 v4.5.5.79 (For TI-Nspire CX CAS), 2022 v5.4.0.259 (For TI-Nspire CX II CAS)
Voyage 200Texas Instruments200120027/18/2005 v3.10

See also

References

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  2. "Systems and Packages". Computer Algebra Information Network. 1998-05-07. Retrieved 2012-11-17. http://www.computeralgebra.nl/systems_and_packages/systems_and_packages.html ↩

  3. "SAC Systems Listing". SymbolicNet. Archived from the original on 2012-04-15. Retrieved 2012-11-17. https://web.archive.org/web/20120415021413/http://www.symbolicnet.org/systems/Systems.html ↩

  4. Aladjev, V.Z. (2004). Computer algebra systems : a new software toolbox for Maple. [S.l.]: Fultus Books. p. 9. ISBN 9781596820005. 9781596820005 ↩

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  6. Gerhard, Joachim von Zur Gathen; Jürgen (2003). Modern computer algebra (2. ed.). Cambridge: Cambridge Univ. Press. pp. 4. ISBN 9780521826464.{{cite book}}: CS1 maint: multiple names: authors list (link) 9780521826464 ↩

  7. The first date is that of the first commercial release (to be checked), the second one is that of the first free license ↩

  8. "Axiom Computer Algebra System". Retrieved 2016-04-29. http://www.axiom-developer.org/axiom-website/download.html ↩

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  12. "GeoGebra License". Retrieved 15 July 2023. https://www.geogebra.org/license ↩

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  14. MacCallum, Malcolm A. H. (2018). "Computer algebra in gravity research". Living Reviews in Relativity. 21 (1): 6. Bibcode:2018LRR....21....6M. doi:10.1007/s41114-018-0015-6. ISSN 2367-3613. PMC 6105178. PMID 30174551. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6105178 ↩

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  18. "Launching Version 14.2 of Wolfram Language & Mathematica: Big Data Meets Computation & AI". Retrieved 2025-01-23. https://writings.stephenwolfram.com/2025/01/launching-version-14-2-of-wolfram-language-mathematica-big-data-meets-computation-ai/ ↩

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  24. "Release 10.5". 4 December 2024. Retrieved 28 December 2024. https://github.com/sagemath/sage/releases/tag/10.5 ↩

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  26. Wolfram, Stephen (April 1985). "Symbolic Mathematical Computation" (PDF). Communications of the ACM. 28 (4): 390–394. doi:10.1145/3341.3347. S2CID 15577857. https://content.wolfram.com/uploads/sites/34/2020/07/symbolic-mathematical-computation.pdf ↩

  27. "Xcas ARM". Retrieved 2010-10-12. http://www-fourier.ujf-grenoble.fr/~parisse/install_en#xcaswince ↩

  28. "Big changes ahead for Yacas". Retrieved 2011-04-19. http://yacas.sourceforge.net/homepage.html?recent.html&newdesign.html ↩

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  31. Kastrenakes, Jacob (2013-11-21). "Raspberry Pi now includes Mathematica and Wolfram Language for free". The Verge. Retrieved 2014-07-03. https://www.theverge.com/2013/11/21/5130394/raspberry-pi-includes-mathematica-wolfram-language-free ↩

  32. Through SymPy Gamma http://www.sympygamma.com/ ↩