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 release Cost (USD) License Notes
Axiom Tim Daly 1971 2002 May 2012 Free modified BSD license General purpose CAS. The first one with strong typing for mathematical expressions.
Cadabra Kasper Peeters 2001 2007 July 2013 (1.33) Free GNU GPL CAS for tensor field theory
CoCoA The CoCoA Team 1987 1995 2007 (4.7.3) Free GNU GPL Specialized CAS for commutative algebra
Derive Soft Warehouse 1979 1988 November 2007 (6.1) Discontinued Proprietary CAS designed for pocket calculators; it was discontinued in 2007
Fermat Robert H. Lewis 1986 1993 2010 (3.9.9x) $60 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 4.0 Free GNU GPL CAS designed mainly for particle physics
GAP GAP Group 1986 1986 2013 (4.7.2) Free GNU GPL Specialized CAS for group theory and combinatorics.
KANT/KASH KANT Group ? ? KASH3 (2005/2008) Free for non-commercial use own license Specialized CAS for algebraic number theory
Macaulay2 Daniel Grayson and Michael Stillman 1992 1994 2013 (1.6) Free GNU GPL Specialized CAS for algebraic geometry and commutative algebra
Macsyma MIT Project MAC and Symbolics 1968 1978 1999 (2.4) $500 Proprietary The oldest general purpose CAS. Still alive as Maxima.
Magma University of Sydney ~1990 1993 2014 (2.20) $1,150 Proprietary General purpose CAS, originally specialized in group theory. Works with elements of algebraic structures rather than with non typed mathematical expressions
Maple Symbolic Computation Group, University of Waterloo 1980 1984 2014 (18) $2,275 (Commercial), $2,155 (Government), $1245 (Academic), $239 (Personal Edition), $99 (Student), $79 (Student, 12-Month term)[7] Proprietary One of the major general purpose CAS
Mathcad Parametric Technology Corporation 1985 1985 2010 (15) $1,195[8] Proprietary Numerical software with some CAS capabilities
Mathematica Wolfram Research 1986 1988 2014 $2,495 (Professional), $1095 (Education), $295 (Personal),[9] $140 (Student), $69.95 (Student annual license),[10] free on Raspberry Pi hardware[11] Proprietary One of the major general purpose CAS
Mathics Jan Pöschko 2011 2011 2013 Free GPL Mathematica-like syntax
Mathomatic George Gesslein II 1986 1987 2012 (16.0.5) Free LGPL Elementary algebra, calculus, complex number and polynomial manipulations.
Maxima MIT Project MAC and Bill Schelter et al. 1967 1998 2014 (5.33.0) Free GNU GPL General purpose CAS. Continuation of Macsyma.
MuMATH Soft Warehouse 1970s 1980 MuMATH-83 Discontinued Proprietary Predecessor of Derive
MuPAD SciFace Software 1989 2008 2008 (5.1) Discontinued Proprietary MathWorks has incorporated MuPAD technology into Symbolic Math Toolbox
OpenAxiom Gabriel Dos Reis 2007 2007 2013 (1.4.2) Free modified BSD license General purpose CAS. A fork of Axiom.
PARI/GP Henri Cohen, Karim Belabas, Bill Allombert et al. 1985 1990 2014 (2.7.1) 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
Sage William A. Stein 2005 2005 6.2 (6 May 2014; 2 months ago (2014-05-06)) [±][12] Free GNU GPL Mathematics software system combining a number of existing packages, including numerical computation, statistics and image processing
SCaVis S.Chakanov 2005 2013 2013 (1.3) Free GNU GPL Mathematics software system including numerical computation, statistics and image processing
SINGULAR University of Kaiserslautern 1984 1997 2012 (3.1.5) 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 2014 (0.97) Free Proprietary (CC-BY-ND) Mathematical notebook program similar to Mathcad.
Symbolic Math Toolbox (MATLAB) MathWorks 1989 2008 2013 (5.10(2013a)) $3150 including required Simulink Proprietary Provides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic.
SymbolicC++ W.-H. Steeb 1997 1997 2010 (3.35) Free GNU GPL C++ -based
Symbolism E. Cavazos 2012 2013 2013 Free modified BSD license C# library for automatic simplification of algebraic expressions
SymPy Ondřej Čertík 2006 2007 2014 (0.7.5) 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/Voyager 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 Bernard Parisse 2004 2008 2011 (0.9.4) Free GNU GPL 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[13]
Yacas Ayal Pinkus et al. 1998[14] ? 2014 (1.3.4) Free GNU GPL
Creator Development started First public release Latest stable version 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
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
GNU Octave No No Yes Yes Yes Yes No Yes Yes Yes No No Yes Yes Yes Yes No No
Magma No Yes No No Yes No Yes No No Yes Yes No No No ? ? Yes Yes
Maple Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes No Yes
Mathcad Yes No Yes No Yes No No No No No No No No No No No No No
Mathematica Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes[15] Yes Yes No Yes
Mathomatic No No Yes Yes Yes No No No No No Yes No No No No No No No
Symbolic Math Toolbox (MATLAB) No Yes Yes Yes Yes No No Yes No No No No No No No No No No
Maxima No Yes Yes Yes Yes Yes No Yes Yes Yes Yes No Yes Yes Yes No No Yes
Sage No Yes Yes Yes Yes Yes Yes[A] Yes Yes Yes Yes No Yes Yes No No Yes Yes
SCaVis No Yes Yes Yes Yes Yes No Yes Yes Yes Yes No Yes Yes Yes No Yes Yes
SymPy No Yes Yes Yes Yes Yes Yes[16] Yes Yes No Yes No Yes Yes Yes No No Yes
Wolfram Alpha Pro version only Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No ? ? No Yes
GAP No Yes No No Yes Yes Yes No Yes Yes Yes Yes Yes Yes No No Yes Yes
Yacas No Yes Yes No Yes No No No No No No No No No ? ? No No
Xcas Yes Yes Yes No Yes Yes No Yes Yes No Yes No No No ? ? No ?
  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.

System Img Aud eqn PHYS CHEM
Axiom No No No
GNU Octave Yes No No
Magma ? ? ?
Maple Yes Yes Yes
Mathcad Yes Yes ?
Mathematica Yes Yes Yes
Mathomatic ? ? ?
Symbolic Math Toolbox (MATLAB) ? ? ?
Maxima No No No
Sage ? ? ?
SCaVis ? ? ?
SymPy ? ? ?
Wolfram Alpha Yes Yes Yes
GAP No No No
Yacas No No No
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.

System Windows Mac OS X Linux BSD Solaris Other
Axiom Yes Yes Yes No No ?
CoCoA Yes Yes Yes Yes Yes Tru64 UNIX, HP-UX, IRIX
Derive Yes No No No No ?
Euler Yes No No 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 ?
Maple Yes Yes Yes No Yes iPad
Mathcad Yes No No No No No
Mathematica Yes Yes Yes No No Raspberry Pi[11]
Mathomatic Yes Yes Yes Yes Yes Android, and all POSIX platforms
Maxima Yes Yes Yes Yes Yes All POSIX platforms with Common Lisp
GNU Octave Yes Yes Yes Yes Yes All POSIX platforms, uses BLAS
MuMATH No No No No No ?
MuPAD Yes Yes Yes No No ?
OpenAxiom Yes Yes Yes Yes Yes ?
PARI/GP Yes Yes Yes Yes Yes ?
Reduce Yes Yes Yes Yes Yes ?
Sage No Yes Yes No Yes VMware image for MS-Windows users
SCaVis Yes Yes Yes Yes Yes All Java enabled platforms
SINGULAR Yes Yes Yes Yes Yes ?
SMath Studio Yes ? Yes ? ? ?
SymbolicC++ Yes Yes Yes Yes Yes ?
Symbolic Math Toolbox (MATLAB) Yes Yes Yes Yes Yes ?
SymPy Yes Yes Yes Yes Yes Any system that supports Python
TI-Nspire (desktop software) Yes Yes No No No iPad
Xcas Yes Yes Yes Yes Yes Android, iOS
Yacas Yes Yes Yes Yes Yes ?

Graphing calculators[edit]

Some graphing calculators have CAS features.

System Creator Development started First public release Latest stable version Cost (USD) Notes
Casio CFX-9970G CASIO Computer Co. ? 1998
Casio Algebra FX 2.0 CASIO Computer Co. ? 1999
Casio ClassPad 330
Casio ClassPad Manager
CASIO Computer Co. ? 2003 3.04.5000 $140 ClassPad Manager is an emulator which runs on a PC.
HP 49 series
HP 50g
Hewlett-Packard ? 1999 2.15 $110 and up Based on Erable. Intended for problems which occur in engineering applications. Source code openly available.
HP Prime Hewlett-Packard ? 2013 Based on Giac/XCAS. Source code openly available.
TI-89 Texas Instruments ? 1996 2.09 No longer in production
TI-89 Titanium Texas Instruments ? 2004 3.10 $150
TI-92 Texas Instruments ? 1995 ? No longer in production
TI-92 Plus Texas Instruments 1997 1998 2.09 No longer in production
TI-Nspire CAS Texas Instruments 2006 2008 3.6.0.550 $160
Voyage 200 Texas Instruments 2001 2002 3.10 $150
ZoomMath300 IQ Joe ? ? 1.03 $60 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. ^ "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 6.2 Changelog". sagemath.org. 2014-05-06. Retrieved 2014-06-19. 
  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:

Other: