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List of computer algebra systems

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(Redirected fromComparison of computer algebra systems)

The following tables provide acomparison ofcomputer algebra systems (CAS).[1][2][3] 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.[4][5] 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.[6]

General

[edit]
SystemCreatorDevelopment startedFirst public releaseLatest stable versionLatest stable release dateCost (USD)LicenseNotes
AxiomRichard Jenks19771993 and 2002[7]August 2014[8]FreemodifiedBSD licenseGeneral purpose CAS. Continuous Release using Docker Containers
CadabraKasper Peeters200120072.5.14[9] Edit this on Wikidata31 July 2025FreeGNU GPLCAS fortensor field theory
CoCoAJohn Abbott,Anna M. Bigatti, Giovanni Lagorio198719955.2.02 May 2017FreeGNU GPLSpecialized CAS forcommutative 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 forHewlett-Packard scientificgraphing calculators of theHP 48/49/40/50 series; discontinued in 2009
FermatRobert H. Lewis198619936.521 June 2021$70 if grant money available, otherwise $0GNU GPLSpecialized CAS forresultant computation andlinear algebra withpolynomial entries
FORMJ.A.M. Vermaseren198419894.3.111 April 2023[10]FreeGNU GPLCAS designed mainly forparticle physics
FriCASWaldek Hebisch200720071.3.123 June 2025FreemodifiedBSD licenseFull-featured general purpose CAS. Especially strong at symbolic integration.
GAPGAP Group198619864.15.1[11] Edit this on Wikidata18 October 2025FreeGNU GPL[12]Specialized CAS forgroup theory andcombinatorics.
GeoGebra CASMarkus Hohenwarter et al.20136.0.753.03 January 2023Free for non-commercial use[13]Freeware[13]Web-based or Desktop CAS Calculator
GiNaCChristian Bauer, Alexander Frink, Richard B. Kreckel, et al.199919991.8.9[14] Edit this on Wikidata15 May 2025FreeGNU GPLIntegrate symbolic computation into C++ programs; no high-level interface, but emphasis on interoperability.
GNU OctaveJohn W. Eaton1993199410.3.0[15] Edit this on Wikidata23 September 2025FreeGPLv3+A high-level programming language for scientific computing and numerical computation mostly compatible withMATLAB
KANT/KASHKANT Group??32005/2008Free for non-commercial useown licenseSpecialized CAS foralgebraic number theory
Macaulay2Daniel Grayson andMichael Stillman199219941.24.0515 May 2024FreeGNU GPLSpecialized CAS foralgebraic geometry andcommutative algebra
MacsymaMIT Project MAC andSymbolics196819782.41999$500ProprietaryOne of the oldest general purpose CAS. Still alive asMaxima.
MagmaUniversity of Sydney~199019932.28-19[16] Edit this on Wikidata21 February 2025$1,440ProprietaryGeneral purpose CAS, originally specialized ingroup theory. Works with elements ofalgebraic structures rather than with non typedmathematical expressions
MagnusThe New York Group Theory Cooperative199419972005FreeGNU GPLSpecialized CAS forgroup theory providing facilities for doing calculations in and aboutinfinite groups. Discontinued in 2005.
MapleSymbolic Computation Group,University of Waterloo1980[17]19842025[18] Edit this on Wikidata25 March 2025$2,390(Commercial), $2,265 (Government), $995 (Academic), $239 (Personal Edition), $99 (Student), $79 (Student, 12-Month term)[19]ProprietaryOne of the major general purpose CAS
MathcadParametric Technology Corporation1985198515.0 M04527 February 2021$1,600 (Commercial), $105 (Student), Free (Express Edition)[20]ProprietaryNumerical software with some CAS capabilities
MathemagixJoris van der Hoeven19992002FreeGNU GPLComputer algebraand analysis system
MathematicaWolfram Research1986198814.3[21] Edit this on Wikidata5 August 2025$2,495 (Professional), $1,095 (Education), $295 (Personal),[22] $140 (Student), $69.95 (Student annual license),[23] free onRaspberry Pi hardware[24]ProprietaryOne of the major general purpose CAS
MathomaticGeorge Gesslein II1986198716.0.52012DiscontinuedLGPLElementary algebra,calculus,complex number andpolynomial manipulations.
MaximaMIT Project MAC andBill Schelter et al.196719985.48.1[25] Edit this on Wikidata6 August 2025FreeGNU GPLGeneral purpose CAS. Continuation ofMacsyma; new releases occur approximately two times per year.
MuMATHSoft Warehouse1970s1980MuMATH-83DiscontinuedProprietaryPredecessor ofDerive
MuPADSciFace Software198920085.12008DiscontinuedProprietaryMathWorks has incorporated MuPAD technology into Symbolic Math Toolbox
OpenAxiomGabriel Dos Reis200720071.4.22013FreemodifiedBSD licenseGeneral purpose CAS. A fork of Axiom.
PARI/GPHenri Cohen, Karim Belabas, Bill Allombert et al.198519902.17.2[26] Edit this on Wikidata5 March 2025FreeGNU GPLSpecialized CAS fornumber theory.
REDUCEAnthony C. Hearn196319686860 (August 2024; 1 year ago (2024-08)) [±][27]See "Latest stable version".FreemodifiedBSD licenseOne of the oldest and historically important general purpose CAS. Still alive, as open-sourced and freed in December 2008
SageMathWilliam A. Stein2005200510.7[28] Edit this on Wikidata9 August 2025FreeGNU GPLMathematics software system combining a number of existing packages, includingnumerical computation,statistics andimage processing
ScilabScilab Enterprises199019902026.0.0[29] Edit this on Wikidata16 October 2025FreeCeCILL (GPL-compatible) until version 5.5.2 GPL v2.0 since version 6.0.2MATLAB alternative.
SINGULARUniversity of Kaiserslautern198419974.4.1[30] Edit this on Wikidata16 January 2025FreeGNU GPLComputer algebra system for polynomial computations, with special emphasis oncommutative andnon-commutative algebra,algebraic geometry, andsingularity theory.
SMath StudioAndrey Ivashov200420061.0.83489 November 2022FreeProprietaryMathematical notebook program similar to Mathcad.
Symbolic Manipulation ProgramStephen Wolfram1979[31]19811988DiscontinuedProprietaryThis software was eventually replaced byMathematica, and the newer program still retains much of the syntax and functionality of the earlier SMP.[32]
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 Čertík200620071.14.0[33] Edit this on Wikidata27 April 2025FreemodifiedBSD 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: freeProprietaryOnlinecomputer algebra system with step-by step solutions.
Xcas/GiacBernard Parisse [fr]200020002.0.0-15[34] Edit this on WikidataNovember 2025FreeGPLGeneral CAS, also adapted for theHP 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 orWinCE[35]
YacasAyal Pinkus et al.1998[36]19991.9.1[37] Edit this on Wikidata4 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-purposeGNU TeXmacs.

Functionality

[edit]

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

SystemCalculusSolversSystem
AxiomNoYesYesYesYesYesYesYesYesNoYesYesYesYesYesNoYesAxiom
CadabraNoYesYesYesYesYesNoYesNoNoNoNoNoYesNoNoYesCadabra
FriCASYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesNoYesFriCAS
GAPNoYesNoNoYesYesYesNoYesYesYesYesYesYesNoNoYesGAP
GNU OctaveYesYesYes?YesYes?Yes????Yes?YesYes?GNU Octave
MagmaNoYesNoNoYesNoYesNoNoYesYesNoNoNo??YesMagma
MagnusNoYesNoNoNoNoNoNoNo??No?NoNoNoYesMagnus
MapleYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesYesMaple
MathcadYesNoYesNoYesNoNoNoNoNoNoNoNoNoNoNoNoMathcad
MathematicaYesYesYesYesYesYesYesYesYesYesYesYesYesYes[38]YesYesYesMathematica
MathomaticNoNoYesYesYesNoNoNoNoNoYesNoNoNoNoNoNoMathomatic
MaximaNoYesYesYesYesYesNoYesYesYesYesNoYesYesYesYesYesMaxima
PARI/GPNoYesYesNoYesNoYes*NoYes*NoYesNoYes??NoYesPARI/GP
REDUCEYesYesYesYesYesYesNoYesNoNoYesYesYesYesNoNoNoREDUCE
SageMathNoYesYesYesYesYesYes[A]YesYesYesYesYes[B]YesYesYesNoYesSageMath
ScilabYesYesYes?YesYes?Yes????Yes?YesYes?Scilab
SMath StudioYesNoYesNoYesNoNoNoNoNoNoNoNoNoNoNoNoSMath Studio
Symbolic Math Toolbox (MATLAB)YesYesYesYesYesYesYesYesNoYesYesNoYesNoYesYesNoSymbolic Math Toolbox (MATLAB)
SymPyNoYesYesYesYesYesYes[39]YesYesNoYesNoYesYesYesNoYesSymPy
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 aGUI, 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

[edit]

The software can run under their respectiveoperating systems natively withoutemulation. 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
CadabraNoYesYesYesYesNoNoNoYes
CoCoANoYesYesYesYesYes??NoTru64 UNIX,HP-UX,IRIX
DeriveYesYesNoNoNoNoNoNoNo
ErableNoEmulatorEmulatorEmulatorNoNoNoNoNoSystem RPL onHP 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
MathematicaYesYesYesYesSomeNoSomeSomeYesRaspberry Pi[24]
MathomaticYesYesYesYesYesYesNoYesNoAllPOSIX platforms
Maxima?YesYesYesYesYesYes?NoAll POSIX platforms withCommon 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?YesYesYesYesYesYesYesYes[40]Any system that supportsPython
TI-Nspire (desktop software)NoYesYesNoNoNoNoYesNo
Xcas/GiacNoYesYesYesYesYesYesYesNoHP Prime CAS,KhiCAS for TI Nspire
YacasNoYesYesYesYesYes??No

Graphing calculators

[edit]

Somegraphing 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-CG500
Casio ClassPad Manager		CASIO 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 onErable, which is also available as an add-on for theHP 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 onXcas/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

[edit]

References

[edit]
  1. ^"Computer Algebra Software".Special Interest Group on Symbolic and Algebraic Manipulation. Association for Computing Machinery. 2008-07-11. Retrieved2012-11-16.
  2. ^"Systems and Packages". Computer Algebra Information Network. 1998-05-07. Retrieved2012-11-17.
  3. ^"SAC Systems Listing". SymbolicNet. Archived fromthe original on 2012-04-15. Retrieved2012-11-17.
  4. ^Aladjev, V.Z. (2004).Computer algebra systems : a new software toolbox for Maple. [S.l.]: Fultus Books. p. 9.ISBN 9781596820005.
  5. ^Labahn, K.O. Geddes; S.R. Czapor; G. (1999).Algorithms for computer algebra (6. pr. ed.). Boston: Kluwer. pp. xv.ISBN 9780792392590.{{cite book}}: CS1 maint: multiple names: authors list (link)
  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)
  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". Retrieved2016-04-29.
  9. ^"Release 2.5.14". 31 July 2025. Retrieved15 August 2025.
  10. ^"Releases - vermaseren/form - GitHub".GitHub. Retrieved2016-04-29.
  11. ^"Release 4.15.1". 18 October 2025. Retrieved18 October 2025.
  12. ^"GAP Copyright". 2012-06-14. Retrieved2015-02-26.
  13. ^ab"GeoGebra License". Retrieved15 July 2023.
  14. ^"release 1.8.9".
  15. ^"Version 10.3.0 released". 23 September 2025. Retrieved16 October 2025.
  16. ^"Change Log for V2.28-19 (Released 21/2/2025)". Retrieved12 March 2025.
  17. ^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.
  18. ^"Announcing Maple 2025". 25 March 2025. Retrieved12 November 2025.
  19. ^"Maplesoft Web Store". Retrieved2019-03-14.
  20. ^"PTC Web Store". Retrieved2015-02-01.
  21. ^"New Features Everywhere: Launching Version 14.3 of Wolfram Language & Mathematica". 5 August 2025. Retrieved12 November 2025.
  22. ^Cohen, Peter (2009-02-05)."Mathematica Home Edition Released".Macworld. Retrieved2014-07-03.
  23. ^"Wolfram Worldwide Web Store". Retrieved2008-11-20.
  24. ^abKastrenakes, Jacob (2013-11-21)."Raspberry Pi now includes Mathematica and Wolfram Language for free".The Verge. Retrieved2014-07-03.
  25. ^"Announcing Maxima 5.48.1". 6 August 2025. Retrieved12 November 2025.
  26. ^"pari-2.17.2 (STABLE) released". 5 March 2025.
  27. ^"REDUCE Files on SourceForge".
  28. ^"Release 10.7". 9 August 2025. Retrieved16 August 2025.
  29. ^"Scilab 2026.0.0". Retrieved16 October 2025.
  30. ^"Release 4.4.1". 16 January 2025. Retrieved29 January 2025.
  31. ^"Wolfram Announcements Archive » Computer Algebra Pioneer Wins Nobel Prize". Wolfram Archive. 1999-10-15. Retrieved2021-01-19.
  32. ^Wolfram, Stephen (April 1985)."Symbolic Mathematical Computation"(PDF).Communications of the ACM.28 (4):390–394.doi:10.1145/3341.3347.S2CID 15577857.
  33. ^"Release 1.14.0". 27 April 2025. Retrieved1 May 2025.
  34. ^"Version 2.0.0-15". 28 October 2025.
  35. ^"Xcas ARM". Retrieved2010-10-12.
  36. ^"Big changes ahead for Yacas". Retrieved2011-04-19.
  37. ^"Release 1.9.1". 4 July 2020. Retrieved5 July 2020.
  38. ^"Symbolic Tensors". Mathematica Documentation. Retrieved2014-07-03.
  39. ^"SymPy release notes for 0.7.4".GitHub. Retrieved2014-07-03.
  40. ^ThroughSymPy Gamma

External links

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Open-source
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Discontinued
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