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]

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 1.45 September 6, 2016 Free GNU GPL CAS for tensor field theory
Calcinator George J. Paulos 2013 2016 2.0 February 2015 Free Proprietary Browser-based CAS for desktop and mobile devices
CoCoA-4 The CoCoA Team 1987 1995 4.7.5 2009 Free for non-commercial use own license Specialized CAS for commutative algebra
CoCoA-5 Abbott, Bigatti, Lagorio 2000 2011 5.1.1 2014 Free GNU GPL Specialized CAS for commutative algebra
Derive Soft Warehouse 1979 1988 6.1 November 2007 Discontinued Proprietary CAS designed for pocket calculators; it was discontinued in 2007
DataMelt (DMelt) jWork.ORG (Sergei Chekanov) 2005 2015 1.5 May 14, 2016 $0 for academic usage, commercial license unknown Proprietary Java-based. Runs on the Java platform. Supports Python, Ruby, Groovy, Java and Octave.
Erable (aka ALGB) Bernard Parisse, Mika Heiskanen, Claude-Nicolas Fiechter 1993 1993 4.20060919 April 21, 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 5.25 July 5, 2016 $70 if grant money available, otherwise $0 Proprietary Specialized CAS for resultant computation and linear algebra with polynomial entries
FORM J.A.M. Vermaseren 1984 1989 4.1 October 25, 2013[9] Free GNU GPL CAS designed mainly for particle physics
FriCAS Waldek Hebisch 2007 2007 1.3.0 August 31, 2016 Free modified BSD license Full-featured general purpose CAS. Especially strong at symbolic integration.
FxSolver Equanalysis UG 2010 2014 2016 Free Proprietary General online computer algebra system
GAP GAP Group 1986 1986 4.8.6 November 12, 2016 Free GNU GPL[10] Specialized CAS for group theory and combinatorics.
GiNaC Christian Bauer, Alexander Frink, Richard B. Kreckel, et al. 1999 1999 1.7.1 October 2, 2016 Free GNU GPL Integrate symbolic computation into C++ programs; no high-level interface, but emphasis on interoperability.
KANT/KASH KANT Group ? ? 3 2005/2008 Free for non-commercial use own license Specialized CAS for algebraic number theory
Macaulay2 Daniel Grayson and Michael Stillman 1992 1994 1.8 2015 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 2.22-3 July 20, 2016 $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 1984 2016 March 2, 2016 $2,275 (Commercial), $2,155 (Government), $1245 (Academic), $239 (Personal Edition), $99 (Student), $79 (Student, 12-Month term)[11] Proprietary One of the major general purpose CAS
Mathcad Parametric Technology Corporation 1985 1985 15.0 M045 November 2015 $1,600 (Commercial), $105 (Student), Free (Express Edition)[12] Proprietary Numerical software with some CAS capabilities
Mathematica Wolfram Research 1986 1988 11.0.1 (September 28, 2016 (2016-09-28)) [±][13] April 18, 2016 $2,495 (Professional), $1095 (Education), $295 (Personal),[14] $140 (Student), $69.95 (Student annual license),[15] free on Raspberry Pi hardware[16] Proprietary One of the major general purpose CAS
MathHandbook DrHuang.com 1986 1987 2016 Free GPL former SymbMath, online computer algebra system to calculate fractional calculus and fractional differential equation and more
Mathics Jan Pöschko 2011 2011 0.9 March 1, 2016 Free GPL Mathematica-like 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 5.38.1 May 12, 2016 Free GNU GPL General purpose CAS. Continuation of Macsyma; New releases occur two times a 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 2.9.1 November 22, 2016 Free GNU GPL Specialized CAS for number theory.
Reduce Anthony C. Hearn 1960s 1968 2009 Free modified BSD license Historically important general purpose CAS. Still alive, as open-sourced and freed in December 2008
Scilab Scilab Enterprises 1990 1990 5.5.2 April 1, 2015 Free CeCILL (GPL-compatible) Matlab alternative.
SageMath William A. Stein 2005 2005 7.2 May 15, 2016[17] Free GNU GPL Mathematics software system combining a number of existing packages, including numerical computation, statistics and image processing
SINGULAR University of Kaiserslautern 1984 1997 4-1-0 November 21, 2016 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 A. Ivashov 2005 2005 0.97.5346 August 21, 2014 Free Proprietary (CC-BY-ND) Mathematical notebook program similar to Mathcad.
Symbolic Math Toolbox (MATLAB) MathWorks 1989 2008 8.5(2015a) 2015 $3150 including required Simulink Proprietary Provides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic.
SyMAT Netsyms Technologies 2014 2015 2.1 December 28, 2015 Free for personal use modified BSD license Written in Java and runs JavaScript and Python scripts.
SymbolicC++ W.-H. Steeb 1997 1997 3.35 September 15, 2010 Free GNU GPL C++ -based
Symbolism E. Cavazos 2012 2013 2013 Free modified BSD license C# library for automatic simplification of algebraic expressions
Symja A. Kramer 2007 2011 2016 Free LGPL Java library for symbolic mathematics
Symengine (CSymPy) Ondřej Čertík 2012 Free modified BSD license C++ port of selected SymPy functionality
SymPy Ondřej Čertík 2006 2007 1.0 March 8, 2016 Free modified BSD license Python-based
TI-Nspire CAS (Computer Software) Texas Instruments 2006 2009 3.1.0.392 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, Regular version: free Proprietary Online computer algebra system with step-by step solutions.
Xcas/Giac Bernard Parisse 2000 2000 1.2.2-81 September 2016 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[18]
Yacas Ayal Pinkus et al. 1998[19] 1999 1.5.0 May 9, 2016 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 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.

System Formula editor Arbitrary precision Calculus Solvers Graph theory Number theory Quantifier elimination Boolean algebra Tensors Probability Control theory Coding 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 No Yes Axiom
Calcinator Yes No Yes Yes Yes No Yes No No No No No No No No No No No Calcinator
Magma No Yes No No Yes No Yes No No Yes Yes No No No ? ? Yes Yes Magma
Magnus No Yes No 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 No Yes Yes Yes Yes No Yes Maple
Mathcad Yes No Yes No Yes No 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[20] Yes Yes No Yes Mathematica
MathHandbook No Yes Yes Yes Yes Yes No Yes No No Yes No Yes No Yes No No No MathHandbook
Mathomatic No No Yes Yes Yes No No No No No Yes No No No No No No No Mathomatic
Symbolic Math Toolbox (MATLAB) No Yes Yes Yes Yes No No Yes No No No No No No No No No No Symbolic Math Toolbox (MATLAB)
Maxima No Yes Yes Yes Yes Yes No Yes Yes Yes Yes No Yes Yes Yes Yes No Yes Maxima
SageMath No Yes Yes Yes Yes Yes Yes[A] Yes Yes Yes Yes No Yes Yes Yes No Yes Yes SageMath
SymPy No Yes Yes Yes Yes Yes Yes[21] Yes Yes No Yes No Yes Yes Yes No No Yes SymPy
Wolfram Alpha Pro version only Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No ? ? No Yes Wolfram Alpha
GAP No Yes No No Yes Yes Yes No Yes Yes Yes Yes Yes Yes No No Yes Yes GAP
Xcas/Giac Yes Yes Yes No Yes Yes No Yes Yes No Yes No No No Yes ? No ? Xcas/Giac
Yacas No Yes Yes No Yes No No No No No No No No No ? ? No No Yacas
  1. ^ via SymPy

Those which don't "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[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. For some platforms, only older releases of the software may be available.

System DOS Windows macOS Linux BSD Solaris Android iOS Other
Axiom ? Yes Yes Yes No No ? ? ?
Calcinator No Yes Yes Yes Yes Yes Yes Yes ?
CoCoA No Yes Yes Yes Yes Yes ? ? Tru64 UNIX, HP-UX, IRIX
Derive Yes Yes No No No No ? ? ?
Erable No Emulator Emulator Emulator No No No No System RPL on HP 48/49/50/40 series
Euler ? Yes No Yes No No ? ? ?
Fermat ? Cygwin Yes Yes No No ? ? ?
FORM ? Cygwin Yes Yes Yes Yes ? ? ?
GAP ? Yes Yes Yes Yes Yes ? ? ?
KANT/KASH ? Yes Yes Yes No No ? ? No
Macaulay2 ? Cygwin Yes Yes Yes Yes ? ? ?
Magma ? Yes Yes Yes Yes Yes ? ? ?
Magnus No Yes ? Yes ? Yes No No SunOs
Maple No Yes Yes Yes No No No No No
Mathcad Yes Yes No No No No ? ? No
Mathematica No Yes Yes Yes No No No No SaaS, Raspberry Pi[16]
MathHandbook Yes Yes Yes Yes Yes Yes Yes Yes All platforms that run web page
Mathomatic Yes Yes Yes Yes Yes Yes Yes ? All POSIX platforms
Maxima ? Yes Yes Yes Yes Yes Yes ? All POSIX platforms with Common Lisp
MuMATH Yes No No No No No ? ? ?
OpenAxiom ? Yes Yes Yes Yes Yes ? ? ?
PARI/GP ? Yes Yes Yes Yes Yes ? ? ?
Reduce ? Yes Yes Yes Yes Yes ? ? ?
SageMath No Virtual Machine Yes Yes No Yes ? ? VMware image for MS-Windows users
SINGULAR ? Yes Yes Yes Yes Yes ? ? ?
SMath Studio ? Yes ? Yes ? ? ? ? ?
SyMAT ? Yes Yes Yes Yes Yes No No All platforms that run Java
SymbolicC++ ? Yes Yes Yes Yes Yes ? ? ?
Symbolic Math Toolbox (MATLAB) No Yes Yes Yes No No No No No
SymPy ? Yes Yes Yes Yes Yes ? ? Any system that supports Python
TI-Nspire (desktop software) No Yes Yes No No No No Yes ?
Xcas/Giac No Yes Yes Yes Yes Yes Yes Yes HP Prime CAS, KhiCAS for TI Nspire
Yacas No Yes Yes Yes Yes Yes ? ? ?

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 Computer Co. ? 1999
Casio ClassPad 300, Casio ClassPad 300 Plus, Casio ClassPad 330, Casio ClassPad 330 Plus, Casio ClassPad fx-CP400
Casio ClassPad Manager
CASIO Computer Co. 2002 2003 3.06.4000 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 6975 (2014-12-03) / v1.1.0-46 (2014-03-31) 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 Texas Instruments 2006 2008 2014 v3.6.0.550
Voyage 200 Texas Instruments 2001 2002 7/18/2005 v3.10
Zoom Math IQ Joe ? ? 1.03 TI-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. 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. ^ 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". Retrieved 2016-04-29. 
  10. ^ "GAP Copyright". 2012-06-14. Retrieved 2015-02-26. 
  11. ^ "Maplesoft Web Store". Retrieved 2011-10-21. 
  12. ^ "PTC Web Store". Retrieved 2015-02-01. 
  13. ^ "Mathematica Quick Revision History". Retrieved 2016-08-08. 
  14. ^ Cohen, Peter (2009-02-05). "Mathematica Home Edition Released". Macworld. Retrieved 2014-07-03. 
  15. ^ "Wolfram Worldwide Web Store". Retrieved 2008-11-20. 
  16. ^ a b Kastrenakes, Jacob (2013-11-21). "Raspberry Pi now includes Mathematica and Wolfram Language for free". The Verge. Retrieved 2014-07-03. 
  17. ^ "SageMath - Open-Source Mathematical Software System". Retrieved 2016-05-16. 
  18. ^ "Xcas ARM". Retrieved 2010-10-12. 
  19. ^ "Big changes ahead for Yacas". Retrieved 2011-04-19. 
  20. ^ "Symbolic Tensors". Mathematica Documentation. Retrieved 2014-07-03. 
  21. ^ "SymPy release notes for 0.7.4". GitHub. Retrieved 2014-07-03. 

External links[edit]

Lists of computer algebra systems:

Other: