Comparison of computer algebra systems

Comparison of computer algebra systems

The following tables provide a comparison of computer algebra systems (CAS).

Contents

General

System Creator Development started First public release Latest stable release Cost (USD) Open source License Notes
Algebrator Neven Jurkovic 1986 1999 02009 2009 (4.2) $58.99 No Proprietary Elementary algebra; step-by-step solutions
Axiom Tim Daly 1971 2002 02011-09 September 2011 Free Yes modified BSD license Forked in 2007 to OpenAxiom and FriCAS
bergman Jörgen Backelin 1972 1972 01999 1999 (0.96) Free Yes GPL-style license Non-commutative and commutative Gröbner bases; mainly homogeneous and non-linear; Lisp-based
Cadabra Kasper Peeters 2001 2007 02011 2011 (1.29) Free Yes GPL tensor algebra, field theory
calc Dave Gillespie  ?  ? in GNU emacs 23 Free Yes GPL Advanced calculator integrated in the Emacs editor. Supports a simple CAS and physical units.
ClassPad Manager CASIO 1999 2001 3.03 (2008) $45.45 No Proprietary
CASSIOPEIA CASIO-MAPLE 1997 2001 02001 2001 (5.0) Discontinued No Proprietary Version of Maple 5 for CASSIOPEIA
CoCoA The CoCoA Team 1987 1995 02007 2007 (4.7.3) Free Yes GPL For polynomial calculations
Derive Soft Warehouse 1979 1988 02007-11 November 2007 (6.1) Discontinued No Proprietary Owned by TI; it was discontinued 2007
DoCon Serge D. Mechveliani 1993 1995 2.11 Free Yes non-OSI approved license Haskell library
DCAS Robert Fenichel ? 2005 02005 2005 (1.0) Free Yes GPL
Eigenmath George Weigt 2004 2005 02010 2010 (137) Free Yes GPL A version is available for the Nintendo DS[1]
Euler Math Toolbox R. Grothmann 1987 1988 02011 2011 (12.3) Free Yes GPL Extension of Maxima, symbolic and numeric computation, interval arithmetic
Fermat Robert H. Lewis 1986 1993 02010 2010 (3.9.9x) $60 if grant money available, otherwise $0 No Proprietary polynomials, matrices
FORM J.A.M. Vermaseren 1984 1989 3.3 Free Yes GPL high speed, arbitrary size of expressions, multi-threaded
Franklin Math Allen Franklin Jordan 2008 2009 02011-03 March 2011 (0.11) Free Yes GPL Symbolic and numeric math, plotting, functions
FriCAS Waldek Hebisch 2007 2007 02011 2011 (1.1.4) Free Yes modified BSD license Forked from Axiom in 2007.
GAP GAP Group 1986 1986 02008 2008 (4.4.12) Free Yes GPL groups, character theory, discrete mathematics
JACAL Aubrey Jaffer 1989 1991 02009 2009 (1c1) Free Yes GPL Scheme-based
Jasymca Helmut Dersch 2003 2006 02011 2011 (3) Free Yes GPL Algebra, Calculus, Polynomials, Matrices, graphing
Java Algebra System Heinz Kredel 2000 2005 2.0 Free Yes GPL or LGPL Commutative and non-commutative, Gröbner bases, gcd, Java library
KANT/KASH KANT Group ? ? KASH3 (2005/2008) free for non-commercial use No own license algebraic number theory
LiveMath
(formerly Theorist)		 Math Monkeys  ? 1991 02007 2007 (3.5.9) $149, $45 student (1 year) No Proprietary interactive solving and graphing
Macaulay2 Daniel Grayson and Michael Stillman 1992 1994 02010 2010 (1.4) Free Yes GPL algebraic geometry, commutative algebra
Macsyma MIT Project MAC and Symbolics 1968 1978 01999 1999 (2.4) $500 No Proprietary Lisp-based. Continues as the open-source Maxima.
Magma University of Sydney ~1990 1993 02011 2011 (2.17) $1,150 No Proprietary Algebra, Cryptography, Group Theory, Number Theory
Magnus Computational Group Theory Package The New York Group Theory Cooperative 1994  ? 02002 2002 Free/Discontinued Yes GPL Infinite group theory. As of 2011-10 it is no longer available at NY GTC web page
Maple Symbolic Computation Group, University of Waterloo 1980 1984 02011 2011 (15.01) $2,275 (Commercial), $2,155 (Government), $1245(Academic), $239 (Personal Edition), $99 (Student), $79 (Student, 12-Month term)[2] No Proprietary Library source code is viewable
MAS Heinz Kredel, Michael Pesch 1989 ? 01998 1998 (1.01) Free ? unspecified Modula-2 source code available
Mathcad Parametric Technology Corporation 1985 1985 02010 2010 (15) $1,195[3] No Proprietary standard mathematical notation, plotting, unit-aware calculations
MathEclipse/Symja Axel Kramer 2002 2002 02007 2007 Free Yes CPL Java symbolic computing library (uses JAS and Apache Commons-Math)
Mathematica Wolfram Research 1986 1988 02011 2011 (8.0.4) $2,495 (Professional), $1095 (Education), $140 (Student), $69.95 (Student annual license) [4] $295 (Personal)[5] No Proprietary System also includes extensive numeric capabilities, statistics, image processing, number theory, boolean computation and is a development environment.
Mathination Orion Math 2010 2010 02010 2010 (1.0) $4.99 No Proprietary Basic algebra for the iPad, with a multi-touch interface to manipulate equations.
Mathiverse Calculator Mathiverse 2009 2009 02009 2009 (0.0.1) Free No Proprietary Complex number manipulation
Mathomatic George Gesslein II 1986 1987 02011 2011 (15.7.0) Free Yes LGPL Elementary algebra, calculus, complex number and polynomial manipulations.
MathPiper Ted Kosan, Sherm Ostrowsky 2008 2010 02010 2010 (.80n) Free Yes GPL Specifically designed for use in education.
MathXpert Michael Beeson 1985 1997 02008 2008 (3.0.4) Algebra Assistant $49.95, Calculus Assistant $89.95[6] No Proprietary Step-by-step solutions, correct graphs, keeps track of assumptions for logical correctness of results.
Maxima MIT Project MAC and Bill Schelter et al. 1967 1998 02011 2011 (5.25) Free Yes GPL Common Lisp-based full-featured CAS
meditor Raphael Jolly 2000 2000 2.0_01 Free Yes GPL Java symbolic computing library and math editor
Microsoft Mathematics Microsoft 2005 02011 2011 (4.0.1108) Free No Proprietary Elementary algebra and calculus; unit conversion; graphing; step-by-step solutions
MuMATH Soft Warehouse 1970s 1980 MuMATH-83 Discontinued No Proprietary
MuPAD SciFace Software 1989 2008 02008 2008 (5.1) Discontinued No Proprietary MathWorks has incorporated MuPAD technology into Symbolic Math Toolbox
NCAlgebra and NCGB Helton, deOliveira,Stankus,Miller 1990 1991 02010 2010 (4.0) Free Yes NCAlgebraBSD Non-commutative algebra in Mathematica; NCGroebner Bases; block matrices
OpenAxiom Gabriel Dos Reis 2007 2007 02011 2011 (1.4.1) Free Yes modified BSD license Forked from Axiom in 2007
PARI/GP Henri Cohen, Karim Belabas, Bill Allombert et al. 1985 1990 02011 2011 (2.5.0) Free Yes GPL Number theory, elliptic curves, arbitrary-precision arithmetic
Reduce Anthony C. Hearn 1960s 1968 02009 2009 Free Yes modified BSD license open-sourced and freed in December 2008
Sage William A. Stein 2005 2005 02011 2011 (4.7) Free Yes GPL Includes extensive numeric capabilities, statistics, image processing, number theory and is a development environment using a web-based interface via HTTP or HTTPS.
SINGULAR University of Kaiserslautern 1984 1997 02011 2011 (3.1.2) Free Yes GPL polynomials, rings, ideals
SMath Studio Andrey Ivashov 2005 02010 2010 (0.89) Free No Creative Commons Attribution-NoDerivs (CC-BY-ND) Mathematical notebook program similar to Mathcad
SpaceTime Mathematics SpaceTime Mathematics 2006 2009 02010 2010 (4.0) $39, free and discontinued for Windows Mobile Devices. No Proprietary Computer algebra and calculus, mobile device scientific computing
Symbolic MATLAB Toolbox MathWorks 1989 2008 02011 2011 (5.7(2011b)) $2900 including required MATLAB No Proprietary Provides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic.
SymbolicC++ W.-H. Steeb 1997 1997 02009 2009 (3.29) Free Yes GPL C++ -based
SymPy Ondřej Čertík 2006 2007 02011 2011 (0.7.1) Free Yes modified BSD license Python-based
SympyCore Pearu Peterson 2008 2008 02008 2008 (0.1) Free Yes modified BSD license Python-based
TI-Nspire CAS (Computer Software) Texas Instruments 2006 2009 2.1 No Proprietary Successor to Derive. Based on Derive's engine used in TI-89/Voyager 200 and TI-Nspire handheld
TRIP J. Laskar, M. Gastineau 1989 2002 02011 2011 (1.1.12) Free No Academic license celestial mechanics
WIRIS Maths for More 1997 2001 2.0 No Proprietary Online computer algebra system and interactive geometry software
Xcas Bernard Parisse 2004 2008 02011 2011 (0.9.4) Free Yes 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[7]
Yacas Ayal Pinkus et al. 1998[8] ? 02007 2007 (1.2.2) Free Yes GPL
Creator Development started First public release Latest stable version Cost (USD) Open source 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

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
Integration Integral transforms Equations Inequalities Diophantine equations Differential equations Recurrence relations
Axiom No Yes Yes Yes Yes  ?  ?  ?  ?  ?  ?  ?  ?  ?
Algebrator Yes No No No Yes Yes No No No No No No No No
Cadabra Yes No No No No No No No No No No No No Yes
FriCAS No Yes Yes Yes Yes No  ? Yes  ?  ?  ?  ?  ?  ?
Jacal No No No No No No No No No No No No No Yes
Jasymca No No Yes Yes Yes No No Yes No No No No No No
Magma No Yes No No Yes No Yes No No Yes Yes No No No
Maple Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes No No Yes
Mathcad Yes No Yes No Yes No No No No No No No No No
Math Eclipse No Yes 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
Mathomatic No No Yes Yes Yes No No No No No Yes No No No
Symbolic MATLAB toolbox  ? Yes Yes Yes Yes  ?  ? Yes  ?  ?  ?  ?  ?  ?
Maxima No Yes Yes Yes Yes Yes No Yes No Yes Yes Yes No Yes
Microsoft Mathematics Yes No Yes No Yes Yes No No No No No No Yes No
Sage Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes
SymPy No Yes Yes No Yes Yes No Yes Yes No Yes No Yes Yes
Yacas No Yes 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

Operating system support

The operating systems the software can run on 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
Algebrator Yes Yes Yes No No ?
Axiom Yes Yes Yes No No ?
bergman Yes ? Yes Yes Yes ?
Cadabra No Yes Yes Yes Yes ?
ClassPad Manager Yes No No No No ?
CoCoA Yes Yes Yes Yes Yes Tru64 UNIX, HP-UX, IRIX
Derive Yes No No No No ?
DoCon ? ? Yes ? ? ?
DCAS Yes ? ? ? ? ?
Eigenmath Yes Yes No No No ?
Euler Yes No No No No ?
Fermat Yes Yes Yes No Yes (SPARC only) ?
FORM No Yes Yes Yes Yes ?
Franklin Math Yes Yes Yes Yes Yes Any system that supports Java
FriCAS Yes Yes Yes Yes Yes ?
GAP Yes Yes Yes Yes Yes ?
JACAL Yes Yes Yes Yes Yes ?
Jasymca Yes Yes Yes Yes Yes Any system that supports Java
Java Algebra System Yes Yes Yes Yes Yes Any system that supports Java
KANT/KASH Yes Yes Yes No No No
Macaulay2 Yes Yes Yes Yes Yes ?
Magma Yes Yes Yes Yes Yes ?
Magnus ? ? Yes ? ? ?
Maple Yes Yes Yes No Yes No
Mathcad Yes No No No No No
MathEclipse Yes Yes Yes Yes Yes Any system that supports Java
Mathematica Yes Yes Yes No No No
Mathomatic Yes Yes Yes Yes Yes All POSIX platforms
MathXpert Yes No No No No ?
Maxima Yes Yes Yes Yes Yes All POSIX platforms with Common Lisp
Meditor Yes Yes Yes Yes Yes ?
Microsoft Mathematics Yes No No No No
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
SINGULAR Yes Yes Yes Yes Yes ?
SMath Studio Yes No Yes No No Many handhelds supported
SymbolicC++ Yes Yes Yes Yes Yes ?
Symbolic MATLAB toolbox Yes Yes Yes Yes Yes ?
SymPy Yes Yes Yes Yes Yes Any system that supports Python
SympyCore Yes Yes Yes Yes Yes Any system that supports Python
TI-Nspire (desktop software) Yes Yes No No No ?
WIRIS Yes Yes Yes Yes Yes ?
Xcas Yes Yes Yes Yes Yes ?
Yacas Yes Yes Yes Yes Yes ?
TRIP Yes Yes Yes Yes Yes ?
Windows Mac OS X Linux BSD Solaris Other

Hand-held calculator CAS

System Creator Development started First public release Latest stable version Cost (USD) Open source License Notes
Alg48 & Erable Bernard Parisse 1996 1998 3.2 Free Symbolic Math packages for HP48 series
Casio CFX-9970G CASIO Computer Co. ? 1998 No Proprietary
Casio Algebra FX 2.0 CASIO Computer Co. ? 1999 No Proprietary
Casio ClassPad 330 CASIO Computer Co. ? 2003 3.04.5000 $140 No Proprietary There is also an emulator: "ClassPad Manager" which runs on a PC.
Eigenmath DS Leonel Hernandez 2008 2008 1.0 Free Yes free This software runs on a Nintendo DS
HP 49 series Hewlett-Packard ? 1999 2.15 $110 and up Yes[h 1] Proprietary with some LGPL Based on Erable. Intended for problems which occur in engineering applications. Also used in HP-50 calculators.
iCAS AL Software 2010 2010 1.1.2 $15 No Proprietary Native iPhone and iPad implementation of REDUCE.
i41CX+ AL Software 2008 2008 4.8.1 $25 No Proprietary iPhone and iPad application that combines the capabilities of the HP-41CX with a CAS based on REDUCE.
TI-89 Texas Instruments ? 1996 2.09 No longer in production No Proprietary
TI-89 Titanium Texas Instruments ? 2004 3.10 $150 No Proprietary
TI-92 Texas Instruments ? 1995 ? No longer in production No Proprietary
TI-92 Plus Texas Instruments 1997 1998 2.09 No longer in production No Proprietary
TI-Nspire CAS Texas Instruments 2006 2008 2.0.1.60 $160 No Proprietary TI-Nspire CAS handheld has a built-in Computer Algebra System for mathematical expressions in symbolic form. Features include: Symbolic calculations in addition to standard numeric calculations
Voyage 200 Texas Instruments 2001 2002 3.10 $150 No Proprietary
ZoomMath300 IQ Joe ?  ? 1.03 $60 No Proprietary TI-83 and TI-84 application that adds CAS capabilities
  1. ^ There are several different definitions for open source. While the source code of the HP49 CAS is available to the public, the use of certain parts of it is restricted by a proprietary license. Therefore, the source code does not qualify under all definitions of open source as such.

See also

References

  1. ^ "SourceForge.net: Eigenmath DS". http://eigenmatds.sourceforge.net/. Retrieved 2008-06-22. 
  2. ^ "Maplesoft Web Store". https://webstore.maplesoft.com. Retrieved 2011-10-21. 
  3. ^ "Parametric Technology Corporation Web Store". http://store.ptc.com. Retrieved 2008-06-28. 
  4. ^ "Wolfram Worldwide Web Store". http://store.wolfram.com. Retrieved 2008-11-20. 
  5. ^ Mathematica Home Edition Released Macworld, Feb 2009
  6. ^ "HelpWithMath". http://www.HelpWithMath.com. Retrieved 2008-08-25. 
  7. ^ "Xcas ARM". http://www-fourier.ujf-grenoble.fr/~parisse/install_en#xcaswince. Retrieved 2010-10-12. 
  8. ^ "Big changes ahead for Yacas". http://yacas.sourceforge.net/homepage.html?recent.html&newdesign.html. Retrieved 2011-04-19. 

External links

There are various lists of computer algebra systems available on-line:

v · d · eComputer algebra systems
Retail
Open source
Axiom · Cadabra · CoCoA · DoCon · Eigenmath · FriCAS · GAP · GiNaC · Macaulay2 · Mathomatic · Maxima · OpenAxiom · PARI/GP · Reduce · Sage · SINGULAR · SymPy · Xcas
Free/shareware
Discontinued
Derive · DCAS · Macsyma · muMATH · Yacas
Category  • Comparison

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