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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
System | Creator | Development started | First public release | Latest stable release | Cost (USD) | License | Notes |
---|---|---|---|---|---|---|---|
Axiom | Tim Daly | 1971 | 2002 | mai 2012 | Gratuit | 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) | Gratuit | GPL | Specialized CAS for commutative algebra |
Derive | Soft Warehouse | 1979 | 1988 | novembre 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) | Gratuit | 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 | 4.0 | Gratuit | GPL | CAS designed mainly for particle physics |
GAP | GAP Group | 1986 | 1986 | 2013 (4.6.2) | Gratuit | GPL | Specialized CAS for group theory and combinatorics. Subpackage of Sage[7] |
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) | Gratuit | 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)[8] | Proprietary | One of the major general purpose CAS |
Mathcad | Parametric Technology Corporation | 1985 | 1985 | 2010 (15) | $1,195[9] | Proprietary | Numerical software with some CAS capabilities |
Mathematica | Wolfram Research | 1986 | 1988 | 2012 (9.0.0) | $2,495 (Professional), $1095 (Education), $140 (Student), $69.95 (Student annual license) [10] $295 (Personal)[11] | Proprietary | One of the major general purpose CAS |
Mathomatic | George Gesslein II | 1986 | 1987 | 2012 (16.0.5) | Gratuit | LGPL | Elementary algebra, calculus, complex number and polynomial manipulations. |
Maxima | MIT Project MAC and Bill Schelter et al. | 1967 | 1998 | 2012 (5.28) | Gratuit | GPL | General purpose CAS. Continuation of Macsyma. Subpackage of Sage.[7] |
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) | Gratuit | 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) | Gratuit | GPL | Specialized CAS for Number theory. A major reference in this domain. Subpackage of Sage.[7] |
Reduce | Anthony C. Hearn | 1960s | 1968 | 2009 | Gratuit | modified BSD license | Historically important general purpose CAS. Still alive, as open-sourced and freed in December 2008 |
Sage | William A. Stein | 2005 | 2005 | 2013 (5.8) | Gratuit | 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 | 2012 (3.1.5) | Gratuit | GPL | computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebra, algebraic geometry, and singularity theory. |
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) | Gratuit | GPL | C++ -based |
Symbolism | E. Cavazos | 2012 | 2013 | 2013 | Gratuit | modified BSD license | C# library for automatic simplification of algebraic expressions |
SymPy | Ondřej Čertík | 2006 | 2007 | 2012 (0.7.2) | Gratuit | 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 | 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) | Gratuit | 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[12] |
Yacas | Ayal Pinkus et al. | 1998[13] | ? | 2012 (1.3.3) | Gratuit | 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 | Coding theory | Group theory | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Integration | Integral transforms | Equations | Inequalities | Diophantine equations | Differential equations | Recurrence relations | ||||||||||||
Axiom | Non | Oui | Oui | Oui | Oui | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | Non | Oui |
Magma | Non | Oui | Non | Non | Oui | Non | Oui | Non | Non | Oui | Oui | Non | Non | Non | ? | ? | Oui | Oui |
Maple | Oui | Oui | Oui | Oui | Oui | Oui | Non | Oui | Oui | Oui | Oui | Non | Non | Oui | Oui | Oui | Non | Oui |
Mathcad | Oui | Non | Oui | Non | Oui | Non | Non | Non | Non | Non | Non | Non | Non | Non | Non | Non | Non | Non |
Mathematica | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui[14] | Oui | Oui | Non | Oui |
Mathomatic | Non | Non | Oui | Oui | Oui | Non | Non | Non | Non | Non | Oui | Non | Non | Non | Non | Non | Non | Non |
Symbolic MATLAB toolbox | Non | Oui | Oui | Oui | Oui | Non | Non | Oui | ? | Non | ? | Non | Non | Non | Non | ? | Non | Non |
Maxima | Non | Oui | Oui | Oui | Oui | Oui | Non | Oui | Oui | Oui | Oui | Non | Oui | Oui | ? | ? | Non | Oui |
Sage | Non | Oui | Oui | Oui | Oui | Oui | Non | Oui | Oui | Oui | Oui | Non | Oui | Oui | Non | Non | Oui | Oui |
SymPy | Non | Oui | Oui | Oui | Oui | Oui | Non | Oui | Oui | Non | Oui | Non | Oui | Oui | Oui | Non | Non | Oui |
Wolfram Alpha | Pro version only | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Oui | Non | ? | ? | Non | Oui |
Yacas | Non | Oui | Oui | Non | Non | Non | Non | Non | Non | Non | Non | Non | Non | Non | ? | ? | Non | Non |
Xcas | Oui | Oui | Oui | Non | Oui | Oui | Non | Oui | Oui | Non | Oui | Non | Non | Non | ? | ? | Non | ? |
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 | Oui | Oui | Oui | Non | Non | ? |
CoCoA | Oui | Oui | Oui | Oui | Oui | Tru64 UNIX, HP-UX, IRIX |
Derive | Oui | Non | Non | Non | Non | ? |
Euler | Oui | Non | Non | Non | Non | ? |
Fermat | Cygwin | Oui | Oui | Non | Non | ? |
FORM | Cygwin | Oui | Oui | Oui | Oui | ? |
GAP | Oui | Oui | Oui | Oui | Oui | ? |
KANT/KASH | Oui | Oui | Oui | Non | Non | Non |
Macaulay2 | Cygwin | Oui | Oui | Oui | Oui | ? |
Magma | Oui | Oui | Oui | Oui | Oui | ? |
Maple | Oui | Oui | Oui | Non | Oui | Non |
Mathcad | Oui | Non | Non | Non | Non | Non |
Mathematica | Oui | Oui | Oui | Non | Non | Non |
Mathomatic | Oui | Oui | Oui | Oui | Oui | Android, and all POSIX platforms |
Maxima | Oui | Oui | Oui | Oui | Oui | All POSIX platforms with Common Lisp |
MuMATH | Non | Non | Non | Non | Non | ? |
MuPAD | Oui | Oui | Oui | Non | Non | ? |
OpenAxiom | Oui | Oui | Oui | Oui | Oui | ? |
PARI/GP | Oui | Oui | Oui | Oui | Oui | ? |
Reduce | Oui | Oui | Oui | Oui | Oui | ? |
Sage | Non | Oui | Oui | Non | Oui | VMware image for MS-Windows users |
SINGULAR | Oui | Oui | Oui | Oui | Oui | ? |
SymbolicC++ | Oui | Oui | Oui | Oui | Oui | ? |
Symbolic MATLAB toolbox | Oui | Oui | Oui | Oui | Oui | ? |
SymPy | Oui | Oui | Oui | Oui | Oui | Any system that supports Python |
TI-Nspire (desktop software) | Oui | Oui | Non | Non | Non | ? |
Xcas | Oui | Oui | Oui | Oui | Oui | ? |
Yacas | Oui | Oui | Oui | Oui | Oui | ? |
Graphing calculators
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. |
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 | 3.2.0 | $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
- Mathematical software
- List of information graphics software
- List of numerical analysis software
- List of numerical libraries
- List of statistical packages
- Comparison of numerical analysis software
- Comparison of statistical packages
- Web-based simulation
References
External links
Lists of computer algebra systems:
- http://directory.google.com/Top/Science/Math/Algebra/Software/ Modèle:Dead link
- Modèle:Dmoz
- Alphabetically sorted list compiled by Freed Wiedijk
- Combinatorial Software and Databases (Séminaire Lotharingien de Combinatoire)
- ORMS (Oberwolfach References on Mathematical Software)
Other:
- Use Maxima in a web browser without downloading any software
- Rosetta Translations: a collection of synonyms for various operations in the computer algebra systems
Modèle:Computer algebra systems
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- ↑ Modèle:Cite web
- ↑ Modèle:Cite web
- ↑ Modèle:Cite web
- ↑ Modèle:Cite book
- ↑ Modèle:Cite book
- ↑ Modèle:Cite book
- ↑ 7,0 7,1 et 7,2 Sage components
- ↑ Modèle:Cite web
- ↑ Modèle:Cite web
- ↑ Modèle:Cite web
- ↑ Mathematica Home Edition Released Macworld, Feb 2009
- ↑ Modèle:Cite web
- ↑ Modèle:Cite web
- ↑ Symbolic Tensors Mathematica Documentation