List of computer algebra systems

The following tables provide a comparison of computer 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

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System Creator Development started First public release Latest stable version Latest stable release date Cost (USD) License Notes
Axiom Richard Jenks 1977 1993 and 2002[7] August 2014[8] Free modified BSD license General purpose CAS. Continuous Release using Docker Containers
Cadabra Kasper Peeters 2001 2007 2.4.0 25 August 2022 Free GNU GPL CAS for tensor field theory
CoCoA John Abbott, Anna M. Bigatti, Giovanni Lagorio 1987 1995 5.2.0 2 May 2017 Free GNU GPL Specialized CAS for commutative algebra
Derive Soft Warehouse 1979 1988 6.1 November 2007 Discontinued Proprietary CAS designed for DOS and Windows microcomputers; it was discontinued in 2007
Erable (aka ALGB) Bernard Parisse [fr], Mika Heiskanen, Claude-Nicolas Fiechter 1993 1993 4.20060919 21 April 2009 Free LGPL CAS designed for Hewlett-Packard scientific graphing calculators of the HP 48/49/40/50 series; discontinued in 2009
Fermat Robert H. Lewis 1986 1993 6.5 21 June 2021 $70 if grant money available, otherwise $0 GNU GPL Specialized CAS for resultant computation and linear algebra with polynomial entries
FORM J.A.M. Vermaseren 1984 1989 4.3.1 11 April 2023[9] Free GNU GPL CAS designed mainly for particle physics
FriCAS Waldek Hebisch 2007 2007 1.3.11 1 July 2024 Free modified BSD license Full-featured general purpose CAS. Especially strong at symbolic integration.
GAP GAP Group 1986 1986 4.13.1 13 June 2024[10] Free GNU GPL[11] Specialized CAS for group theory and combinatorics.
GeoGebra CAS Markus Hohenwarter et al. 2013 6.0.753.0 3 January 2023 Free for non-commercial use[12] Freeware[12] Web-based or Desktop CAS Calculator
GiNaC Christian Bauer, Alexander Frink, Richard B. Kreckel, et al. 1999 1999 1.8.3 23 March 2022 Free GNU GPL Integrate symbolic computation into C++ programs; no high-level interface, but emphasis on interoperability.
GNU Octave John W. Eaton 1993 1994 7.3.0 2022 Free GPLv3+ A high-level programming language for scientific computing and numerical computation mostly compatible with MATLAB
KANT/KASH KANT Group ? ? 3 2005/2008 Free for non-commercial use own license Specialized CAS for algebraic number theory
LiveMath MathMonkeys, LLC 1991 1993 3.6 2018 $399 (Commercial), $299 (Academic), $199 (Personal Edition), $69 (Student), $29 (Student, 3-Month term)[13] Proprietary More interface than computing power
Macaulay2 Daniel Grayson and Michael Stillman 1992 1994 1.24.05 15 May 2024 Free GNU GPL Specialized CAS for algebraic geometry and commutative algebra
Macsyma MIT Project MAC and Symbolics 1968 1978 2.4 1999 $500 Proprietary The oldest general purpose CAS. Still alive as Maxima.
Magma University of Sydney ~1990 1993 2.27-8 22 February 2023 $1,440 Proprietary General purpose CAS, originally specialized in group theory. Works with elements of algebraic structures rather than with non typed mathematical expressions
Magnus The New York Group Theory Cooperative 1994 1997 2005 Free GNU GPL Specialized CAS for group theory providing facilities for doing calculations in and about infinite groups. Discontinued in 2005.
Maple Symbolic Computation Group, University of Waterloo 1980[14] 1984 2024 (6 March 2024; 8 months ago (2024-03-06)) [±][15] 15 March 2022 $2,390(Commercial), $2,265 (Government), $995 (Academic), $239 (Personal Edition), $99 (Student), $79 (Student, 12-Month term)[16] Proprietary One of the major general purpose CAS
Mathcad Parametric Technology Corporation 1985 1985 15.0 M045 27 February 2021 $1,600 (Commercial), $105 (Student), Free (Express Edition)[17] Proprietary Numerical software with some CAS capabilities
Mathematica Wolfram Research 1986 1988 14.1.0 (July 31, 2024; 3 months ago (2024-07-31)) [±][18] 29 June 2022 $2,495 (Professional), $1,095 (Education), $295 (Personal),[19] $140 (Student), $69.95 (Student annual license),[20] free on Raspberry Pi hardware[21] Proprietary One of the major general purpose CAS
Mathics Jan Pöschko 2016 2016 7.0.0 9 August 2024 Free GPL3 Uses Mathematica syntax.
Mathomatic George Gesslein II 1986 1987 16.0.5 2012 Discontinued LGPL Elementary algebra, calculus, complex number and polynomial manipulations.
Maxima MIT Project MAC and Bill Schelter et al. 1967 1998 5.46.0[22] 13 April 2022 Free GNU GPL General purpose CAS. Continuation of Macsyma; new releases occur approximately two times per year.
MuMATH Soft Warehouse 1970s 1980 MuMATH-83 Discontinued Proprietary Predecessor of Derive
MuPAD SciFace Software 1989 2008 5.1 2008 Discontinued Proprietary MathWorks has incorporated MuPAD technology into Symbolic Math Toolbox
OpenAxiom Gabriel Dos Reis 2007 2007 1.4.2 2013 Free modified BSD license General purpose CAS. A fork of Axiom.
PARI/GP Henri Cohen, Karim Belabas, Bill Allombert et al. 1985 1990 2.11.4 17 April 2020 Free GNU GPL Specialized CAS for number theory.
Reduce Anthony C. Hearn 1960s 1968 2018 Free modified BSD license Historically important general purpose CAS. Still alive, as open-sourced and freed in December 2008
SageMath William A. Stein 2005 2005 9.8 11 February 2023[23] Free GNU GPL Mathematics software system combining a number of existing packages, including numerical computation, statistics and image processing
Scilab Scilab Enterprises 1990 1990 2023.0 10 March 2023 Free CeCILL (GPL-compatible) until version 5.5.2 GPL v2.0 since version 6.0.2 Matlab alternative.
SICMUtils Colin Smith, Sam Ritchie 2014 2016 0.13.0 9 November 2020 Free GNU GPL Clojure and Clojurescript computer algebra system optimized for classical mechanics and differential geometry investigations.
SINGULAR University of Kaiserslautern 1984 1997 4-3-0 14 January 2022 Free GNU GPL Computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory.
SMath Studio Andrey Ivashov 2004 2006 1.0.8348 9 November 2022 Free Proprietary Mathematical notebook program similar to Mathcad.
Symbolica Ben Ruijl 2023 2024 July 2024 Free for hobbyists - One core and one instance free for non-commercial use - At a cost otherwise Proprietary but source available CAS Library written in Rust with Python bindings, focused on performance for large expressions.[24][25][26]
Symbolic Manipulation Program Stephen Wolfram 1979[27] 1981 1988 Discontinued Proprietary This software was eventually replaced by Mathematica, and the newer program still retains much of the syntax and functionality of the earlier SMP.[28]
Symbolic Math Toolbox (MATLAB) MathWorks 1989 2008 9.4(2018a) 2018 $3,150 (Commercial), $99 (Student Suite), $700 (Academic), $194 (Home) including required Matlab Proprietary Provides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic.
Symbolics.jl (https://symbolics.juliasymbolics.org/stable/) Shashi Gowda, Yingbo Ma, Chris Rackauckas 2021 2021 v5.3.1 25 April 2023 Free MIT License A fast and modern Computer Algebra System for the Julia programming language.[29]
SymPy Ondřej Čertík 2006 2007 1.13.2 11 August 2024 Free modified BSD license Python-based
TI-Nspire CAS (Computer Software) Texas Instruments 2006 2009 5.1.3 2020 Proprietary Successor to Derive. Based on Derive's engine used in TI-89/Voyage 200 and TI-Nspire handheld
Wolfram Alpha Wolfram Research 2009 2013 Pro version: $4.99 / month, Pro version for students: $2.99 / month, ioRegular version: free Proprietary Online computer algebra system with step-by step solutions.
Xcas/Giac Bernard Parisse [fr] 2000 2000 1.9.0-99 May 2024 Free GPL General 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 WinCE[30]
Yacas Ayal Pinkus et al. 1998[31] 1999 1.9.1 4 July 2020 Free GNU GPL
Creator Development started First public release Latest stable version Latest stable release date Cost (USD) License Notes

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

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

System Formula editor Arbitrary precision Calculus Solvers Graph theory Number theory Quantifier elimination Boolean algebra Tensors Probability Control theory Group theory System
Integration Integral transforms Equations Inequalities Diophantine equations Differential equations Recurrence relations
Axiom No Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes No Yes Axiom
Cadabra No Yes Yes Yes Yes Yes No Yes No No No No No Yes No No Yes Cadabra
FriCAS Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes FriCAS
GAP No Yes No No Yes Yes Yes No Yes Yes Yes Yes Yes Yes No No Yes GAP
Magma No Yes No No Yes No Yes No No Yes Yes No No No ? ? Yes Magma
Magnus No Yes No No No No No No No ? ? No ? No No No Yes Magnus
Maple Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Maple
Mathcad Yes No Yes No Yes No No No No No No No No No No No No Mathcad
Mathematica Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes[32] Yes Yes Yes Mathematica
Mathics No Yes[A] Yes[A] Yes[A] Yes[A] Yes[A] Yes[A] Yes[A] Yes[A] Yes[33] Yes No Yes Yes Yes No Yes Mathics
Mathomatic No No Yes Yes Yes No No No No No Yes No No No No No No Mathomatic
Maxima No Yes Yes Yes Yes Yes No Yes Yes Yes Yes No Yes Yes Yes Yes Yes Maxima
Reduce No Yes Yes ? Yes Yes ? Yes ? ? Yes Yes Yes Yes ? ? ? Reduce
SageMath No Yes Yes Yes Yes Yes Yes[A] Yes Yes Yes Yes Yes[B] Yes Yes Yes No Yes SageMath
SICMUtils No Yes Yes No Yes No No Yes No No No No Yes Yes No No No SICMUtils
SMath Studio Yes No Yes No Yes No No No No No No No No No No No No SMath Studio
Symbolic Math Toolbox (MATLAB) Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes No Yes No Yes Yes No Symbolic Math Toolbox (MATLAB)
SymPy No Yes Yes Yes Yes Yes Yes[34] Yes Yes No Yes No Yes Yes Yes No Yes SymPy
Wolfram Alpha Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No ? ? Yes Wolfram Alpha
Xcas/Giac Yes Yes Yes No Yes Yes No Yes Yes No Yes No No No Yes ? ? Xcas/Giac
Yacas No Yes Yes No Yes No No No No No No No No No ? ? No Yacas
  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

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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.

System DOS Windows macOS Linux BSD Solaris Android iOS SaaS Other
Axiom ? Emulator Yes Yes No No ? ? No
Cadabra No Yes Yes Yes Yes No No No No
CoCoA No Yes Yes Yes Yes Yes ? ? No Tru64 UNIX, HP-UX, IRIX
Derive Yes Yes No No No No ? ? No
Erable No Emulator Emulator Emulator No No No No No System RPL on HP 48/49/50/40 series
Euler ? Yes No Yes No No ? ? No
Fermat ? Cygwin Yes Yes No No ? ? No
FORM ? Cygwin Yes Yes Yes Yes ? ? No
FriCAS ? Cygwin+native Yes Yes Yes Yes Yes ? No
GAP ? Yes Yes Yes Yes Yes ? ? No
KANT/KASH ? Yes Yes Yes No No ? ? No
Macaulay2 ? Cygwin Yes Yes Yes Yes ? ? No
Magma ? Yes Yes Yes Yes Yes ? ? No
Magnus No Yes ? Yes ? Yes No No No SunOs
Maple No Yes Yes Yes No No No No No
Mathcad Yes Yes No No No No No No No
Mathematica Yes Yes Yes Yes No No No No Yes Raspberry Pi[21]
Mathics No Yes Yes Yes Yes No No No No All POSIX platforms
Mathomatic Yes Yes Yes Yes Yes Yes No Yes No All POSIX platforms
Maxima ? Yes Yes Yes Yes Yes Yes ? No All POSIX platforms with Common Lisp
MuMATH Yes No No No No No ? ? No
OpenAxiom ? Yes Yes Yes Yes Yes ? ? No
PARI/GP ? Yes Yes Yes Yes Yes Yes ? No
Reduce ? Yes Yes Yes Yes Yes Yes Yes No
SageMath No Yes Yes Yes No Yes No Yes Yes
SICMUtils No Yes Yes Yes Yes Yes Yes Yes Yes Any system that supports Clojure or Clojurescript
SINGULAR ? Yes Yes Yes Yes Yes ? ? No
SMath Studio No Yes Mono Mono Mono Mono Yes Yes Yes Universal Windows Platform
Symbolic Math Toolbox (MATLAB) No Yes Yes Yes No No No No Yes
SymbolicC++ ? Yes Yes Yes Yes Yes ? ? No
SymPy ? Yes Yes Yes Yes Yes Yes Yes Yes[35] Any system that supports Python
TI-Nspire (desktop software) No Yes Yes No No No No Yes No
Xcas/Giac No Yes Yes Yes Yes Yes Yes Yes No HP Prime CAS, KhiCAS for TI Nspire
Yacas No Yes Yes Yes Yes Yes ? ? No

Graphing calculators

[edit]

Some graphing calculators have CAS features.

System Creator Development started First public release / OS version Latest stable version / OS version Notes
Casio CFX-9970G CASIO Computer Co. ? 1998
Casio Algebra FX 2.0, Casio Algebra FX 2.0 Plus CASIO 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. 2002 2003 3.10.7000 (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 40gs Hewlett-Packard 1993 1.??(1999) / 4 2.15 (2006-09-19, 2009-04-21) / 4 Based 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 Prime Hewlett-Packard 2000 2013 2.1.14433 (2020 01 21) CAS ver. 1.5.0 Based on Xcas/Giac. Source code openly available.
TI-89 Texas Instruments 1995 1996 2.09
TI-89 Titanium Texas Instruments 2003 2004 7/18/2005 v3.10
TI-92 Texas Instruments 1994 1995 ?
TI-92 Plus Texas Instruments 1997 1998 3/27/2003 v2.09
TI-Nspire CAS, TI-Nspire CX CAS, TI-Nspire CX II CAS Texas Instruments 2006 2008 2021 v4.5.5.79 (For TI-Nspire CX CAS), 2022 v5.4.0.259 (For TI-Nspire CX II CAS)
Voyage 200 Texas Instruments 2001 2002 7/18/2005 v3.10


See also

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References

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  1. ^ "Computer Algebra Software". Special Interest Group on Symbolic and Algebraic Manipulation. Association for Computing Machinery. 2008-07-11. Retrieved 2012-11-16.
  2. ^ "Systems and Packages". Computer Algebra Information Network. 1998-05-07. Retrieved 2012-11-17.
  3. ^ "SAC Systems Listing". SymbolicNet. Archived from the original on 2012-04-15. Retrieved 2012-11-17.
  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". Retrieved 2016-04-29.
  9. ^ "Releases - vermaseren/form - GitHub". GitHub. Retrieved 2016-04-29.
  10. ^ "Release v4.13.1 · gap-system/gap". GitHub. Retrieved 2024-06-22.
  11. ^ "GAP Copyright". 2012-06-14. Retrieved 2015-02-26.
  12. ^ a b "GeoGebra License". Retrieved 15 July 2023.
  13. ^ "LiveMath Store". Retrieved 2020-02-25.
  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.
  15. ^ "Maplesoft Media Releases". www.maplesoft.com. Retrieved 2024-05-12.
  16. ^ "Maplesoft Web Store". Retrieved 2019-03-14.
  17. ^ "PTC Web Store". Retrieved 2015-02-01.
  18. ^ "Yet More New Ideas and New Functions: Launching Version 14.1 of Wolfram Language & Mathematica". Retrieved 2024-07-31.
  19. ^ Cohen, Peter (2009-02-05). "Mathematica Home Edition Released". Macworld. Retrieved 2014-07-03.
  20. ^ "Wolfram Worldwide Web Store". Retrieved 2008-11-20.
  21. ^ a b Kastrenakes, Jacob (2013-11-21). "Raspberry Pi now includes Mathematica and Wolfram Language for free". The Verge. Retrieved 2014-07-03.
  22. ^ Maxima, a Computer Algebra System
  23. ^ "SageMath – Open-Source Mathematical Software System". Retrieved 2022-02-18.
  24. ^ Zeng, M.; Smirnov, A.V.; Mokrov, K.S. (2023). "Упрощение рациональных функций для редукции с использованием соотношений интегрирования по частям и не только". Numerical Methods and Programming (Vychislitel'nye Metody I Programmirovanie). 24 (4): 352–367. arXiv:2304.13418. doi:10.26089/NumMet.v24r425.
  25. ^ Belitsky, A. V.; Smirnov, V. A. (2023). "Near mass-shell double boxes". arXiv:2312.00641 [hep-th].
  26. ^ Smirnov, Alexander V.; Zeng, Mao (2023). "FIRE 6.5: Feynman Integral Reduction with New Simplification Library". arXiv:2311.02370 [hep-ph].
  27. ^ "Wolfram Announcements Archive » Computer Algebra Pioneer Wins Nobel Prize". Wolfram Archive. 1999-10-15. Retrieved 2021-01-19.
  28. ^ Wolfram, Stephen (April 1985). "Symbolic Mathematical Computation" (PDF). Communications of the ACM. 28 (4): 390–394. doi:10.1145/3341.3347. S2CID 15577857.
  29. ^ "JuliaSymbolics". Retrieved 2022-06-16.
  30. ^ "Xcas ARM". Retrieved 2010-10-12.
  31. ^ "Big changes ahead for Yacas". Retrieved 2011-04-19.
  32. ^ "Symbolic Tensors". Mathematica Documentation. Retrieved 2014-07-03.
  33. ^ "What makes up Mathics?". Mathics's Developer Reference. Retrieved 2021-07-08.
  34. ^ "SymPy release notes for 0.7.4". GitHub. Retrieved 2014-07-03.
  35. ^ Through SymPy Gamma
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