Comparison of computer algebra systems
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The following tables provide a comparison of computer algebra systems (CAS).
Contents |
[edit] General
| System | Creator | Development started | First public release | Latest stable release | Cost (USD) | Open source | License | Notes |
|---|---|---|---|---|---|---|---|---|
| Algebrator | Neven Jurkovic | 1986 | 1999 | 2009 (4.2) | $58.99 | No | Proprietary | Elementary algebra; step-by-step solutions |
| Axiom | Tim Daly | 1971 | 2002 | January 2012 | Free | Yes | modified BSD license | Forked in 2007 to OpenAxiom and FriCAS |
| bergman | Jörgen Backelin | 1972 | 1972 | 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 | 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 | 2001 (5.0) | Discontinued | No | Proprietary | Version of Maple 5 for CASSIOPEIA |
| CoCoA | The CoCoA Team | 1987 | 1995 | 2007 (4.7.3) | Free | Yes | GPL | For polynomial calculations |
| Derive | Soft Warehouse | 1979 | 1988 | 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 | 2005 (1.0) | Free | Yes | GPL | |
| Eigenmath | George Weigt | 2004 | 2005 | 2010 (137) | Free | Yes | GPL | OS supported: Windows, Mac, Android, Poket PC, Nintendo DS[1] |
| Euler Math Toolbox | R. Grothmann | 1987 | 1988 | 2011 (12.3) | Free | Yes | GPL | Extension of Maxima, symbolic and numeric computation, interval arithmetic |
| Fermat | Robert H. Lewis | 1986 | 1993 | 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 | March 2011 (0.11) | Free | Yes | GPL | Symbolic and numeric math, plotting, functions |
| FriCAS | Waldek Hebisch | 2007 | 2007 | 2011 (1.1.5) | Free | Yes | modified BSD license | Forked from Axiom in 2007. |
| GAP | GAP Group | 1986 | 1986 | 2008 (4.4.12) | Free | Yes | GPL | groups, character theory, discrete mathematics |
| JACAL | Aubrey Jaffer | 1989 | 1991 | 2010 (1c2) | Free | Yes | GPL | Scheme-based |
| Jasymca | Helmut Dersch | 2003 | 2006 | 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 | 2007 (3.5.9) | $149, $45 student (1 year) | No | Proprietary | interactive solving and graphing |
| Macaulay2 | Daniel Grayson and Michael Stillman | 1992 | 1994 | 2010 (1.4) | Free | Yes | GPL | algebraic geometry, commutative algebra |
| Macsyma | MIT Project MAC and Symbolics | 1968 | 1978 | 1999 (2.4) | $500 | No | Proprietary | Lisp-based. Continues as the open-source Maxima. |
| Magma | University of Sydney | ~1990 | 1993 | 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 | ? | 2009 | Free | Yes | GPL | Infinite group theory |
| Maple | Symbolic Computation Group, University of Waterloo | 1980 | 1984 | 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 | ? | 1998 (1.01) | Free | ? | unspecified | Modula-2 source code available |
| Mathcad | Parametric Technology Corporation | 1985 | 1985 | 2010 (15) | $1,195[3] | No | Proprietary | standard mathematical notation, plotting, unit-aware calculations |
| MathEclipse/Symja | Axel Kramer | 2002 | 2002 | 2007 | Free | Yes | CPL | Java symbolic computing library (uses JAS and Apache Commons-Math) |
| Mathematica | Wolfram Research | 1986 | 1988 | 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 | 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 | 2009 (0.0.1) | Free | No | Proprietary | Complex number manipulation |
| Mathomatic | George Gesslein II | 1986 | 1987 | 2012 (15.7.3) | Free | Yes | LGPL | Elementary algebra, calculus, complex number and polynomial manipulations. |
| MathPiper | Ted Kosan, Sherm Ostrowsky | 2008 | 2010 | 2010 (.80n) | Free | Yes | GPL | Specifically designed for use in education. |
| MathXpert | Michael Beeson | 1985 | 1997 | 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 | 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 | 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 | 2008 (5.1) | Discontinued | No | Proprietary | MathWorks has incorporated MuPAD technology into Symbolic Math Toolbox |
| NCAlgebra and NCGB | Helton, deOliveira,Stankus,Miller | 1990 | 1991 | 2010 (4.0) | Free | Yes | NCAlgebraBSD | Non-commutative algebra in Mathematica; NCGroebner Bases; block matrices |
| NCLab | FEMhub | 2011 | 2012 | 2012 (1.0) | Free | No | Proprietary | Wide range of symbolic and numerical methods including algebra, calculus, differential equations |
| OpenAxiom | Gabriel Dos Reis | 2007 | 2007 | 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 | 2011 (2.5.0) | Free | Yes | GPL | Number theory, elliptic curves, arbitrary-precision arithmetic |
| Reduce | Anthony C. Hearn | 1960s | 1968 | 2009 | Free | Yes | modified BSD license | open-sourced and freed in December 2008 |
| Sage | William A. Stein | 2005 | 2005 | 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 | 2011 (3.1.2) | Free | Yes | GPL | polynomials, rings, ideals |
| SMath Studio | Andrey Ivashov | ? | 2005 | 2012 (0.91) | Free | No | Creative Commons Attribution-NoDerivs (CC-BY-ND) | Mathematical notebook program similar to Mathcad |
| SpaceTime Mathematics | SpaceTime Mathematics | 2006 | 2009 | 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 | 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 | 2009 (3.29) | Free | Yes | GPL | C++ -based |
| SymPy | Ondřej Čertík | 2006 | 2007 | 2011 (0.7.1) | Free | Yes | modified BSD license | Python-based |
| SympyCore | Pearu Peterson | 2008 | 2008 | 2008 (0.1) | Free | Yes | modified BSD license | Python-based |
| TI-Nspire CAS (Computer Software) | Texas Instruments | 2006 | 2009 | 3.1.0.392 | 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 | 2011 (1.1.12) | Free | No | Academic license | celestial mechanics |
| Wolfram Alpha | Wolfram Research | 2009 | 2012 | Pro version: $4.99 / month, Pro version for students: $2.99 / month, Regular version free. | No | Proprietary | Online computer algebra system with step-by step solutions. | |
| WIRIS | Maths for More | 1997 | 2001 | 2.0 | No | Proprietary | Online computer algebra system and interactive geometry software | |
| Xcas | Bernard Parisse | 2004 | 2008 | 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] | ? | 2012 (1.3.2) | 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.
[edit] 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 | No |
| 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 |
| 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 |
[edit] 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 |
|---|---|---|---|---|---|---|
| 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 |
[edit] 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 | George Weigt | 2008 | 2008 | 137 | Free | Yes | free | Handhelds available: Android, Nintendo DS, Poket PC. |
| 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 | 1.2.1 | $15 | No | Proprietary | Native iPhone and iPad implementation of REDUCE. |
| i41CX+ | AL Software | 2008 | 2008 | 4.9.2 | $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 |
- ^ 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.
[edit] See also
- Mathematical software
- List of information graphics software
- List of numerical analysis software
- List of statistical packages
- Comparison of numerical analysis software
- Comparison of statistical packages
- Web-based simulation
[edit] References
- ^ "SourceForge.net: Eigenmath DS". http://eigenmatds.sourceforge.net/. Retrieved 2008-06-22.
- ^ "Maplesoft Web Store". https://webstore.maplesoft.com. Retrieved 2011-10-21.
- ^ "Parametric Technology Corporation Web Store". http://store.ptc.com. Retrieved 2008-06-28.
- ^ "Wolfram Worldwide Web Store". http://store.wolfram.com. Retrieved 2008-11-20.
- ^ Mathematica Home Edition Released Macworld, Feb 2009
- ^ "HelpWithMath". http://www.HelpWithMath.com. Retrieved 2008-08-25.
- ^ "Xcas ARM". http://www-fourier.ujf-grenoble.fr/~parisse/install_en#xcaswince. Retrieved 2010-10-12.
- ^ "Big changes ahead for Yacas". http://yacas.sourceforge.net/homepage.html?recent.html&newdesign.html. Retrieved 2011-04-19.
[edit] External links
There are various lists of computer algebra systems available on-line:
- http://directory.google.com/Top/Science/Math/Algebra/Software/[dead link]
- http://www.cs.ru.nl/~freek/digimath/xindex.html
- Math Software at the Open Directory Project
- http://www.mat.univie.ac.at/~slc/divers/software.html
- Use Maxima in a web browser without downloading any software
- http://orms.mfo.de/about
- Rosetta Translations: a collection of synonyms for various operations in the computer algebra systems
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