List of computer algebra systems: Difference between revisions

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Revision as of 17:16, 17 November 2012

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

General

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
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
Euler Math Toolbox	R. Grothmann	1987	1988	2011 (12.3)	Free	GNU GPL	Numerical software linked to Maxima
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	3.3	Free	GNU GPL	CAS designed mainly for particle physics
GAP	GAP Group	1986	1986	2012 (4.5.6)	Free	GNU GPL	Specialized CAS for group theory and combinatorics. Subpackage of Sage
KANT/KASH	KANT Group	?	?	KASH3 (2005/2008)	free for non-commercial use	own license	Specialized CAS for algebraic number theory
LiveMath (formerly Theorist)	Math Monkeys	?	1991	2007 (3.5.9)	$149, $45 student (1 year)	Proprietary	Numerical software for interactive solving and mathematical graphing
Macaulay2	Daniel Grayson and Michael Stillman	1992	1994	2010 (1.4)	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. Was the state of the art during almost 20 years. Still alive as Maxima
Magma	University of Sydney	~1990	1993	2011 (2.17)	$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	2012 (16)	$2,275 (Commercial), $2,155 (Government), $1245(Academic), $239 (Personal Edition), $99 (Student), $79 (Student, 12-Month term)	Proprietary	One of the major general purpose CAS
Mathcad	Parametric Technology Corporation	1985	1985	2010 (15)	$1,195	Proprietary	Numerical software with some CAS capabilities
Mathematica	Wolfram Research	1986	1988	2011 (8.0.4)	$2,495 (Professional), $1095 (Education), $140 (Student), $69.95 (Student annual license) $295 (Personal)	Proprietary	One of the major general purpose CAS
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	2012 (5.28)	Free	GNU GPL	General purpose CAS. Continuation of Macsyma. Subpackage of Sage.
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	2011 (1.4.1)	Free	modified BSD license	General purpose CAS, the first one to have a strong typing for mathematical objects and expressions
PARI/GP	Henri Cohen, Karim Belabas, Bill Allombert et al.	1985	1990	2012 (2.5.1)	Free	GNU GPL	Specialized CAS for Number theory. A major reference in this domain. Subpackage of Sage.
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	2012 (5.3)	Free	GNU GPL	Mathematics software system combining a number of existing packages, including computer algebra, numerical computation, statistics and image processing
SINGULAR	University of Kaiserslautern	1984	1997	2011 (3.1.2)	Free	GNU GPL	Specialized CAS, initially for singularity theory, now extended to all polynomial algebra. Subpackage of Sage.
Symbolic MATLAB Toolbox	MathWorks	1989	2008	2011 (5.7(2011b))	$2900 including required MATLAB	Proprietary	Provides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic.
SymbolicC++	W.-H. Steeb	1997	1997	2009 (3.29)	Free	GNU GPL	C++ -based
SymPy	Ondřej Čertík	2006	2007	2012 (0.7.2)	Free	modified BSD license	Python-based. Subpackage of Sage.
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	2012	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
Yacas	Ayal Pinkus et al.	1998	?	2012 (1.3.3)	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

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
System	Formula editor	Arbitrary precision	Integration	Integral transforms	Equations	Inequalities	Diophantine equations	Differential equations	Recurrence relations	Graph theory	Number theory	Quantifier elimination	Boolean algebra	Tensors	Probability	Control Theory
Axiom	No	Yes	Yes	Yes	Yes	?	?	?	?	?	?	?	?	?	?	?
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	Yes	Yes
Mathcad	Yes	No	Yes	No	Yes	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	No	Yes	Yes
Mathomatic	No	No	Yes	Yes	Yes	No	No	No	No	No	Yes	No	No	No	No	No
Symbolic MATLAB toolbox	No	Yes	Yes	Yes	Yes	No	No	Yes	?	No	?	No	No	?	?	?
Maxima	No	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	?	?
Sage	Yes	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes	No	No
SymPy	No	Yes	Yes	Yes	Yes	Yes	No	Yes	Yes	No	Yes	No	Yes	Yes	Yes	No
Wolfram Alpha	Pro version only	Yes	Yes	Yes	Yes	Yes	?	Yes	Yes	Yes	Yes	Yes	Yes	No	?	?
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 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	Yes	Yes	Yes	Yes	Yes	?
Magma	Yes	Yes	Yes	Yes	Yes	?
Maple	Yes	Yes	Yes	No	Yes	No
Mathcad	Yes	No	No	No	No	No
Mathematica	Yes	Yes	Yes	No	No	No
Mathomatic	Yes	Yes	Yes	Yes	Yes	Android, and all POSIX platforms
Maxima	Yes	Yes	Yes	Yes	Yes	All POSIX platforms with Common Lisp
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	?
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
TI-Nspire (desktop software)	Yes	Yes	No	No	No	?
Xcas	Yes	Yes	Yes	Yes	Yes	?
Yacas	Yes	Yes	Yes	Yes	Yes	?

Graphing calculators

Some graphing calculators have CAS features.

System	Creator	Development started	First public release	Latest stable version	Cost (USD)	Open source	License	Notes
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.
HP 49 series	Hewlett-Packard	?	1999	2.15	$110 and up	Yes	Proprietary with some LGPL	Based on Erable. Intended for problems which occur in engineering applications. Also used in HP-50 calculators.
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	3.2.0	$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

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.

References

"Computer Algebra Software". Special Interest Group on Symbolic and Algebraic Manipulation. Association for Computing Machinery. 11 July 2008. Retrieved 16 November 2012.
^ Sage components
"Maplesoft Web Store". Retrieved 2011-10-21.
"Parametric Technology Corporation Web Store". Retrieved 2008-06-28.
"Wolfram Worldwide Web Store". Retrieved 2008-11-20.
Mathematica Home Edition Released Macworld, Feb 2009
"Xcas ARM". Retrieved 2010-10-12.
"Big changes ahead for Yacas". Retrieved 2011-04-19.

External links

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

v t e Computer algebra systems
Open-source	Axiom Cadabra CoCoA Fermat FriCAS FORM GAP GiNaC Macaulay2 Maxima Normaliz PARI/GP REDUCE SageMath Singular SymPy Xcas/Giac Yacas
Proprietary	ClassPad Manager KANT Magma Maple Mathcad Mathematica muPAD (MATLAB symbolic math toolbox) SMath Studio TI InterActive! Engineering Equation Solver
Discontinued	CAMAL Derive Erable LiveMath Macsyma Mathomatic muMATH ALTRAN
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