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]

General[edit]

SystemCreatorDevelopment startedFirst public releaseLatest stable releaseCost (USD)LicenseNotes
AxiomTim Daly19712002May 2012Freemodified BSD licenseGeneral purpose CAS. The first one with strong typing for mathematical expressions.
CoCoAThe CoCoA Team198719952007 (4.7.3)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
GAPGAP Group198619862013 (4.7.2)FreeGNU GPLSpecialized 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 Waterloo198019842013 (17)$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 Research198619882014Free on Raspberry Pi hardware,[9] $2,495 (Professional), $1095 (Education), $140 (Student), $69.95 (Student annual license) [10] $295 (Personal)[11]ProprietaryOne of the major general purpose CAS
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.196719982013 (5.29.1)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.198519902013 (2.5.4)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. Stein200520056.1 (30 January 2014; 17 days ago (2014-01-30)) [±][12]FreeGNU GPLMathematics software system combining a number of existing packages, including numerical computation, statistics and image processing
SCaVisS.Chakanov200520132013 (1.3)FreeGNU GPLMathematics software system 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.
Symbolic Math Toolbox (MATLAB)MathWorks198920082013 (5.10(2013a))$3150 including required MATLABProprietaryProvides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic.
SymbolicC++W.-H. Steeb199719972010 (3.35)FreeGNU GPLC++ -based
SymbolismE. Cavazos201220132013Freemodified BSD licenseC# library for automatic simplification of algebraic expressions
SymPyOndřej Čertík200620072013 (0.7.3)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 free.ProprietaryOnline computer algebra system with step-by step solutions.
XcasBernard Parisse200420082011 (0.9.4)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 (1.3.4)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.

Functionality[edit]

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
AxiomNoYesYesYesYesYesYesYesYesNoYesYesYesYesYesNoNoYes
GNU OctaveNoNoYesYesYesYesNoYesYesYesNoNoYesYesYesYesNoNo
MagmaNoYesNoNoYesNoYesNoNoYesYesNoNoNo ? ?YesYes
MapleYesYesYesYesYesYesYesYesYesYesYesNoYesYesYesYesNoYes
MathcadYesNoYesNoYesNoNoNoNoNoNoNoNoNoNoNoNoNo
MathematicaYesYesYesYesYesYesYesYesYesYesYesYesYesYes[15]YesYesNoYes
MathomaticNoNoYesYesYesNoNoNoNoNoYesNoNoNoNoNoNoNo
Symbolic Math Toolbox (MATLAB)NoYesYesYesYesNoNoYesNoNoNoNoNoNoNoNoNoNo
MaximaNoYesYesYesYesYesNoYesYesYesYesNoYesYesYesNoNoYes
SageNoYesYesYesYesYesNoYesYesYesYesNoYesYesNoNoYesYes
SCaVisNoYesYesYesYesYesNoYesYesYesYesNoYesYesYesNoYesYes
SymPyNoYesYesYesYesYesYes[16]YesYesNoYesNoYesYesYesNoNoYes
Wolfram AlphaPro version onlyYesYesYesYesYesYesYesYesYesYesYesYesNo ? ?NoYes
GAPNoYesNoNoYesYesYesNoYesYesYesYesYesYesNoNoYesYes
YacasNoYesYesNoYesNoNoNoNoNoNoNoNoNo ? ?NoNo
XcasYesYesYesNoYesYesNoYesYesNoYesNoNoNo ? ?No ?

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 eqnPHYCHEM
AxiomNoNoNo
GNU OctaveYesNoNo
Magma ? ? ?
MapleYesYesYes
MathcadYesYes ?
MathematicaYesYesYes
Mathomatic ? ? ?
Symbolic Math Toolbox (MATLAB) ? ? ?
MaximaNoNoNo
Sage ? ? ?
SCaVis ? ? ?
SymPy ? ? ?
Wolfram AlphaYesYesYes
GAPNoNoNo
YacasNoNoNo
Xcas ? ? ?

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 XLinuxBSDSolarisOther
AxiomYesYesYesNoNo?
CoCoAYesYesYesYesYesTru64 UNIX, HP-UX, IRIX
DeriveYesNoNoNoNo?
EulerYesNoNoNoNo?
FermatCygwinYesYesNoNo?
FORMCygwinYesYesYesYes?
GAPYesYesYesYesYes?
KANT/KASHYesYesYesNoNoNo
Macaulay2CygwinYesYesYesYes?
MagmaYesYesYesYesYes?
MapleYesYesYesNoYesiPad
MathcadYesNoNoNoNoNo
MathematicaYesYesYesNoNoRaspberry Pi[17]
MathomaticYesYesYesYesYesAndroid, and all POSIX platforms
MaximaYesYesYesYesYesAll POSIX platforms with Common Lisp
GNU OctaveYesYesYesYesYesAll POSIX platforms, uses BLAS
MuMATHNoNoNoNoNo?
MuPADYesYesYesNoNo?
OpenAxiomYesYesYesYesYes?
PARI/GPYesYesYesYesYes?
ReduceYesYesYesYesYes?
SageNoYesYesNoYesVMware image for MS-Windows users
SCaVisYesYesYesYesYesAll Java enabled platforms
SINGULARYesYesYesYesYes?
SymbolicC++YesYesYesYesYes?
Symbolic Math Toolbox (MATLAB)YesYesYesYesYes?
SymPyYesYesYesYesYesAny system that supports Python
TI-Nspire (desktop software)YesYesNoNoNoiPad
XcasYesYesYesYesYes?
YacasYesYesYesYesYes?

Graphing calculators[edit]

Some graphing calculators have CAS features.

SystemCreatorDevelopment startedFirst public releaseLatest stable 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.?20033.04.5000$140ClassPad Manager is an emulator which runs on a PC.
HP 49 series
HP 50g
Hewlett-Packard?19992.15$110 and upBased on Erable. Intended for problems which occur in engineering applications. Source code openly available.
TI-89Texas Instruments?19962.09No longer in production
TI-89 TitaniumTexas Instruments?20043.10$150
TI-92Texas Instruments?1995?No longer in production
TI-92 PlusTexas Instruments199719982.09No longer in production
TI-Nspire CASTexas Instruments200620083.2.0$160
Voyage 200Texas Instruments200120023.10$150
ZoomMath300IQ Joe? ?1.03$60TI-83 and TI-84 application that adds CAS capabilities. Proprietary


See also[edit]

References[edit]

  1. ^ "Computer Algebra Software". Special Interest Group on Symbolic and Algebraic Manipulation. Association for Computing Machinery. 11 July 2008. Retrieved 16 November 2012. 
  2. ^ "Systems and Packages". Computer Algebra Information Network. 7 May 1998. Retrieved 17 November 2012. 
  3. ^ "SAC Systems Listing". SymbolicNet. Retrieved 17 November 2012. 
  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. ^ [1]
  10. ^ "Wolfram Worldwide Web Store". Retrieved 2008-11-20. 
  11. ^ Mathematica Home Edition Released Macworld, Feb 2009
  12. ^ "http://www.sagemath.org/mirror/src/changelogs/sage-6.1.txt". 
  13. ^ "Xcas ARM". Retrieved 2010-10-12. 
  14. ^ "Big changes ahead for Yacas". Retrieved 2011-04-19. 
  15. ^ Symbolic Tensors Mathematica Documentation
  16. ^ [2] SymPy release notes
  17. ^ [3]

External links[edit]

Lists of computer algebra systems:

Other: