List of computer algebra systems

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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]


SystemCreatorDevelopment startedFirst public releaseLatest stable releaseCost (USD)LicenseNotes
AxiomTim Daly19652002August 2014Freemodified BSD licenseGeneral purpose CAS. The first one with strong typing for mathematical expressions.
CadabraKasper Peeters20012007July 2013 (1.33)FreeGNU GPLCAS for tensor field theory
CoCoA-4The CoCoA Team198719952009 (4.7.5)Free for non-commercial useown licenseSpecialized CAS for commutative algebra
CoCoA-5Abbott,Bigatti,Lagorio200020112014 (5.1.1)FreeGNU GPLSpecialized CAS for commutative algebra
DeriveSoft Warehouse19791988November 2007 (6.1)DiscontinuedProprietaryCAS designed for pocket calculators; it was discontinued in 2007
FermatRobert H. Lewis198619932010 (3.9.9x)$60 if grant money available, otherwise $0ProprietarySpecialized CAS for resultant computation and linear algebra with polynomial entries
FORMJ.A.M. Vermaseren198419894.0FreeGNU GPLCAS designed mainly for particle physics
FxSolverEquanalysis UG201020142014FreeProprietarygeneral online computer algebra system
GAPGAP Group198619862013 (4.7.2)FreeProprietarySpecialized CAS for group theory and combinatorics.
KANT/KASHKANT Group??KASH3 (2005/2008)Free for non-commercial useown licenseSpecialized CAS for algebraic number theory
Macaulay2Daniel Grayson and Michael Stillman199219942013 (1.6)FreeGNU GPLSpecialized CAS for algebraic geometry and commutative algebra
MacsymaMIT Project MAC and Symbolics196819781999 (2.4)$500ProprietaryThe oldest general purpose CAS. Still alive as Maxima.
MagmaUniversity of Sydney~199019932014 (2.20)$1,150ProprietaryGeneral purpose CAS, originally specialized in group theory. Works with elements of algebraic structures rather than with non typed mathematical expressions
MapleSymbolic Computation Group, University of Waterloo198019842014 (18)$2,275 (Commercial), $2,155 (Government), $1245 (Academic), $239 (Personal Edition), $99 (Student), $79 (Student, 12-Month term)[7]ProprietaryOne of the major general purpose CAS
MathcadParametric Technology Corporation198519852010 (15)$1,195[8]ProprietaryNumerical software with some CAS capabilities
MathematicaWolfram Research198619882014$2,495 (Professional), $1095 (Education), $295 (Personal),[9] $140 (Student), $69.95 (Student annual license),[10] free on Raspberry Pi hardware[11]ProprietaryOne of the major general purpose CAS
MathHandbookDrHuang.com198620002013FreeGPLformer SymbMath, now online computer algebra system
MathicsJan Pöschko201120112013FreeGPLMathematica-like syntax
MathomaticGeorge Gesslein II198619872012 (16.0.5)FreeLGPLElementary algebra, calculus, complex number and polynomial manipulations.
MaximaMIT Project MAC and Bill Schelter et al.196719982014 (5.34.1)FreeGNU GPLGeneral purpose CAS. Continuation of Macsyma.
MuMATHSoft Warehouse1970s1980MuMATH-83DiscontinuedProprietaryPredecessor of Derive
MuPADSciFace Software198920082008 (5.1)DiscontinuedProprietaryMathWorks has incorporated MuPAD technology into Symbolic Math Toolbox
OpenAxiomGabriel Dos Reis200720072013 (1.4.2)Freemodified BSD licenseGeneral purpose CAS. A fork of Axiom.
PARI/GPHenri Cohen, Karim Belabas, Bill Allombert et al.198519902014 (2.7.1)FreeGNU GPLSpecialized CAS for number theory.
ReduceAnthony C. Hearn1960s19682009Freemodified BSD licenseHistorically important general purpose CAS. Still alive, as open-sourced and freed in December 2008
SageWilliam A. Stein200520056.4.1 (23 November 2014; 43 days ago (2014-11-23)) [±][12]FreeGNU GPLMathematics software system combining a number of existing packages, including numerical computation, statistics and image processing
SINGULARUniversity of Kaiserslautern198419972012 (3.1.5)FreeGNU GPLComputer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory.
SMath StudioA. Ivashov200520052014 (0.97)FreeProprietary (CC-BY-ND)Mathematical notebook program similar to Mathcad.
Symbolic Math Toolbox (MATLAB)MathWorks198920082013 (5.10(2013a))$3150 including required SimulinkProprietaryProvides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic.
SyMATApocalypse Laboratories201420152015 (0.9)$4.00 - $10.00, first 15 days freeOpen-sourceWritten in Java and runs JavaScript and Python scripts.
SymbolicC++W.-H. Steeb199719972010 (3.35)FreeGNU GPLC++ -based
SymbolismE. Cavazos201220132013Freemodified BSD licenseC# library for automatic simplification of algebraic expressions
SymPyOndřej Čertík200620072014 (0.7.5)Freemodified BSD licensePython-based
TI-Nspire CAS (Computer Software)Texas Instruments200620093.1.0.392ProprietarySuccessor to Derive. Based on Derive's engine used in TI-89/Voyager 200 and TI-Nspire handheld
Wolfram AlphaWolfram Research20092013Pro version: $4.99 / month, Pro version for students: $2.99 / month, Regular version: freeProprietaryOnline computer algebra system with step-by step solutions.
XcasBernard Parisse200420082014 (1.1.2)FreeGNU GPLCompatible 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[13]
YacasAyal Pinkus et al.1998[14]?2014 (1.3.5)FreeGNU GPL
CreatorDevelopment startedFirst public releaseLatest stable versionCost (USD)LicenseNotes

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


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

SystemFormula editorArbitrary precisionCalculusSolversGraph theoryNumber theoryQuantifier eliminationBoolean algebraTensorsProbabilityControl theoryCoding theoryGroup theory
IntegrationIntegral transformsEquationsInequalitiesDiophantine equationsDifferential equationsRecurrence relations
GNU OctaveNoNoYesYesYesYesNoYesYesYesNoNoYesYesYesYesNoNo
Symbolic Math Toolbox (MATLAB)NoYesYesYesYesNoNoYesNoNoNoNoNoNoNoNoNoNo
Wolfram AlphaPro version onlyYesYesYesYesYesYesYesYesYesYesYesYesNo??NoYes
  1. ^ via SymPy

Those which don't "edit equations" may have a GUI, gnu plotting, ascii graphic formulae, math font printing. A major feature is how well others can share and read contributions.

Check the language of math files (and system include files): some programs hide or make these illegible; making study or editing user and non-user files illegible.

Application areas[edit]

Partial noted but important is how much Applied science is available as file and data, readily used. Mathematica and other major brands even include geography, though none do a (best) job compared to field specific software.

SystemImg Aud eqnPHYSCHEM
GNU OctaveYesNoNo
Symbolic Math Toolbox (MATLAB)???
Wolfram AlphaYesYesYes

Operating system support[edit]

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.

SystemWindowsMac OS XLinuxBSDSolarisAndroidiOSOther
CoCoAYesYesYesYesYes??Tru64 UNIX, HP-UX, IRIX
MathematicaYesYesYesNoNo??Raspberry Pi[11]
MathomaticYesYesYesYesYesYes?All POSIX platforms
MaximaYesYesYesYesYesYes?All POSIX platforms with Common Lisp
GNU OctaveYesYesYesYesYes??All POSIX platforms, uses BLAS
SageVirtual MachineYesYesNoYes??VMware image for MS-Windows users
SMath StudioYes?Yes?????
SyMATYesYesYesYesYesNoNoAll platforms that run Java
Symbolic Math Toolbox (MATLAB)YesYesYesYesYes???
SymPyYesYesYesYesYes??Any system that supports Python
TI-Nspire (desktop software)YesYesNoNoNoNoYes?
XcasYesYesYesYesYesYesYesHP Prime CAS, KhiCAS for TI Nspire

Graphing calculators[edit]

Some graphing calculators have CAS features.

SystemCreatorDevelopment startedFirst public release / OS versionLatest stable version / OS versionCost (USD)Notes
Casio CFX-9970GCASIO Computer Co.?1998
Casio Algebra FX 2.0CASIO Computer Co.?1999
Casio ClassPad 330
Casio ClassPad Manager
CASIO Computer Co.200220033.04.5000$140ClassPad Manager is an emulator which runs on a PC.
HP 49 series
HP 50g
Hewlett-Packard199819992.15$110 and upBased on Erable. Intended for problems which occur in engineering applications. Source code openly available.
HP PrimeHewlett-Packard201320133/31/2014 v1.1.0-46$130Based on Giac/XCAS. Source code openly available.
TI-89Texas Instruments199519962.09No longer in production
TI-89 TitaniumTexas Instruments200320047/18/2005 v3.10$150
TI-92Texas Instruments19941995?No longer in production
TI-92 PlusTexas Instruments199719983/27/2003 v2.09No longer in production
TI-Nspire CASTexas Instruments200620082014 v3.6.0.550$160
Voyage 200Texas Instruments200120027/18/2005 v3.10$150
ZoomMath300IQ Joe??1.03$60TI-83 and TI-84 application that adds CAS capabilities. Proprietary

See also[edit]


  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. 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. 
  6. ^ Gerhard, Joachim von Zur Gathen ; Jürgen (2003). Modern computer algebra (2. ed.). Cambridge: Cambridge Univ. Press. p. 4. ISBN 9780521826464. 
  7. ^ "Maplesoft Web Store". Retrieved 2011-10-21. 
  8. ^ "Parametric Technology Corporation Web Store". Retrieved 2008-06-28. 
  9. ^ Cohen, Peter (2009-02-05). "Mathematica Home Edition Released". Macworld. Retrieved 2014-07-03. 
  10. ^ "Wolfram Worldwide Web Store". Retrieved 2008-11-20. 
  11. ^ a b Kastrenakes, Jacob (2013-11-21). "Raspberry Pi now includes Mathematica and Wolfram Language for free". The Verge. Retrieved 2014-07-03. 
  12. ^ "Sage 6.4.1 Changelog". Retrieved 2014-12-29. 
  13. ^ "Xcas ARM". Retrieved 2010-10-12. 
  14. ^ "Big changes ahead for Yacas". Retrieved 2011-04-19. 
  15. ^ "Symbolic Tensors". Mathematica Documentation. Retrieved 2014-07-03. 
  16. ^ "SymPy release notes for 0.7.4". GitHub. Retrieved 2014-07-03. 

External links[edit]

Lists of computer algebra systems: