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]
Contents |
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 |
| 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 | 4.0 | Free | GNU GPL | CAS designed mainly for particle physics |
| GAP | GAP Group | 1986 | 1986 | 2013 (4.6.2) | Free | GNU 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) | 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 | 2013 (17) | $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 | 2013 (9.0.1) | $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) | 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.[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) | 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.[7] |
| 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 | 2013 (5.8) | 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 | 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. |
| 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 |
| Symbolism | E. Cavazos | 2012 | 2013 | 2013 | Free | modified BSD license | C# library for automatic simplification of algebraic expressions |
| SymPy | Ondřej Čertík | 2006 | 2007 | 2012 (0.7.2) | 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 | 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[12] |
| Yacas | Ayal Pinkus et al. | 1998[13] | ? | 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 [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 | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | ? | No | Yes |
| Magma | No | Yes | No | No | Yes | No | Yes | No | No | Yes | Yes | No | No | No | ? | ? | Yes | Yes |
| Maple | Yes | Yes | Yes | Yes | Yes | Yes | No | Yes | Yes | Yes | Yes | No | No | 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[14] | Yes | Yes | No | Yes |
| Mathomatic | No | No | Yes | Yes | Yes | No | No | No | No | No | Yes | No | No | No | No | No | No | No |
| Symbolic MATLAB toolbox | No | Yes | Yes | Yes | Yes | No | No | Yes | ? | No | ? | No | No | No | No | ? | No | No |
| Maxima | No | Yes | Yes | Yes | Yes | Yes | No | Yes | Yes | Yes | Yes | No | Yes | Yes | ? | ? | No | Yes |
| Sage | No | Yes | Yes | Yes | Yes | Yes | No | Yes | Yes | Yes | Yes | No | Yes | Yes | No | No | Yes | Yes |
| SymPy | No | Yes | Yes | Yes | Yes | Yes | No | 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 |
| Yacas | No | Yes | Yes | No | No | 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 | ? |
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 | 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 | iPad |
| Xcas | Yes | Yes | Yes | Yes | Yes | ? |
| 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. |
| 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 [edit]
- 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 [edit]
- ^ "Computer Algebra Software". Special Interest Group on Symbolic and Algebraic Manipulation. Association for Computing Machinery. 11 July 2008. Retrieved 16 November 2012.
- ^ "Systems and Packages". Computer Algebra Information Network. 7 May 1998. Retrieved 17 November 2012.
- ^ "SAC Systems Listing". SymbolicNet. Retrieved 17 November 2012.
- ^ Aladjev, V.Z. (2004). Computer algebra systems : a new software toolbox for Maple. [S.l.]: Fultus Books. p. 9. ISBN 9781596820005.
- ^ Labahn, K.O. Geddes ; S.R. Czapor ; G. (1999). Algorithms for computer algebra (6. pr. ed.). Boston: Kluwer. pp. xv. ISBN 9780792392590.
- ^ Gerhard, Joachim von Zur Gathen ; Jürgen (2003). Modern computer algebra (2. ed.). Cambridge: Cambridge Univ. Press. p. 4. ISBN 9780521826464.
- ^ a b c 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.
- ^ Symbolic Tensors Mathematica Documentation
External links [edit]
Lists of computer algebra systems:
- http://directory.google.com/Top/Science/Math/Algebra/Software/[dead link]
- Math Software at the Open Directory Project
- 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
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