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下表提供了计算机代数系统(CAS)的比较。CAS是一个包,包含一组算法,用于对代数对象执行符号操作,一种语言来实现它们,以及使用该语言的环境。CAS可以包括用户界面和图形功能;要想有效,可能需要大量的算法库、高效的数据结构和一个快速的内核

General

System Creator Development started First public release Latest stable version Latest stable release date Cost (USD) License Notes
Axiom Richard Jenks 1977 1993 and 2002[7]   August 2014[8] Free modified BSD license General purpose CAS. Continuous Release using Docker Containers
Cadabra Kasper Peeters 2001 2007 2.2.0 29 March 2018 Free GNU GPL CAS for tensor field theory
CoCoA John Abbott, Anna M. Bigatti, Giovanni Lagorio 1987 1995 5.2.0 2 May 2017 Free GNU GPL Specialized CAS for commutative algebra
Derive Soft Warehouse 1979 1988 6.1 November 2007 Discontinued Proprietary CAS designed for pocket calculators; it was discontinued in 2007
Erable (aka ALGB) Bernard Parisse, Mika Heiskanen, Claude-Nicolas Fiechter 1993 1993 4.20060919 21 April 2009 Free LGPL CAS designed for Hewlett-Packard scientific graphing calculators of the HP 48/49/40/50 series; discontinued in 2009
Fermat Robert H. Lewis 1986 1993 6.21 13 July 2018 $70 if grant money available, otherwise $0 GNU GPL Specialized CAS for resultant computation and linear algebra with polynomial entries
FORM J.A.M. Vermaseren 1984 1989 4.2 6 July 2017[9] Free GNU GPL CAS designed mainly for particle physics
FriCAS Waldek Hebisch 2007 2007 1.3.5 3 February 2019 Free modified BSD license Full-featured general purpose CAS. Especially strong at symbolic integration.
GAP GAP Group 1986 1986 4.9.3 5 September 2018 Free GNU GPL[10] Specialized CAS for group theory and combinatorics.
GiNaC Christian Bauer, Alexander Frink, Richard B. Kreckel, et al. 1999 1999 1.7.5 17 February 2019 Free GNU GPL Integrate symbolic computation into C++ programs; no high-level interface, but emphasis on interoperability.
KANT/KASH KANT Group ? ? 3 2005/2008 Free for non-commercial use own license Specialized CAS for algebraic number theory
Macaulay2 Daniel Grayson and Michael Stillman 1992 1994 1.14 2019 Free GNU GPL Specialized CAS for algebraic geometry and commutative algebra
Macsyma MIT Project MAC and Symbolics 1968 1978 2.4 1999 $500 Proprietary The oldest general purpose CAS. Still alive as Maxima.
Magma University of Sydney ~1990 1993 2.22-3 20 July 2016 $1,440 Proprietary General purpose CAS, originally specialized in group theory. Works with elements of algebraic structures rather than with non typed mathematical expressions
Magnus The New York Group Theory Cooperative 1994 1997   2005 Free GNU GPL Specialized CAS for group theory providing facilities for doing calculations in and about infinite groups. Discontinued in 2005.
Maple Symbolic Computation Group, University of Waterloo 1980 1984 2019.1 (May 28, 2019; 3 months ago) [±][11] 14 March 2019 $2,390(Commercial), $2,265 (Government), $995 (Academic), $239 (Personal Edition), $99 (Student), $79 (Student, 12-Month term)[12] Proprietary One of the major general purpose CAS
Mathcad Parametric Technology Corporation 1985 1985 15.0 M045 November 2015 $1,600 (Commercial), $105 (Student), Free (Express Edition)[13] Proprietary Numerical software with some CAS capabilities
Mathematica Wolfram Research 1986 1988 12.0.0 (April 16, 2019; 5 months ago) [±][14] 16 April 2019 $2,495 (Professional), $1095 (Education), $295 (Personal),[15] $140 (Student), $69.95 (Student annual license),[16] free on Raspberry Pi hardware[17] Proprietary One of the major general purpose CAS
Mathomatic George Gesslein II 1986 1987 16.0.5 2012 Discontinued LGPL Elementary algebracalculuscomplex number and polynomial manipulations.
Maxima MIT Project MAC and Bill Schelter et al. 1967 1998 5.42.0 22 January 2019 Free GNU GPL General purpose CAS. Continuation of Macsyma; new releases occur two times a year.
MuMATH Soft Warehouse 1970s 1980 MuMATH-83   Discontinued Proprietary Predecessor of Derive
MuPAD SciFace Software 1989 2008 5.1 2008 Discontinued Proprietary MathWorks has incorporated MuPAD technology into Symbolic Math Toolbox
OpenAxiom Gabriel Dos Reis 2007 2007 1.4.2 2013 Free modified BSD license General purpose CAS. A fork of Axiom.
PARI/GP Henri Cohen, Karim Belabas, Bill Allombert et al. 1985 1990 2.11.0 18 July 2018 Free GNU GPL Specialized CAS for number theory.
Reduce Anthony C. Hearn 1960s 1968   2018 Free modified BSD license Historically important general purpose CAS. Still alive, as open-sourced and freed in December 2008
Scilab Scilab Enterprises 1990 1990 6.0.2 14 February 2019 Free CeCILL (GPL-compatible) Matlab alternative.
SageMath William A. Stein 2005 2005 8.8 27 June 2019[18] Free GNU GPL Mathematics software system combining a number of existing packages, including numerical computationstatistics and image processing
SINGULAR University of Kaiserslautern 1984 1997 4-1-2 25 March 2019 Free GNU GPL Computer algebra system for polynomial computations, with special emphasis on commutative and non-commutative algebraalgebraic geometry, and singularity theory.
SMath Studio Andrey Ivashov 2004 2006 0.99.6839 22 September 2018 Free Proprietary Mathematical notebook program similar to Mathcad.
Symbolic Math Toolbox (MATLAB) MathWorks 1989 2008 9.4(2018a) 2018 $3,150 (Commercial), $99 (Student Suite), $700 (Academic), $194 (Home) including required Matlab Proprietary Provides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic.
SymPy Ondřej Čertík 2006 2007 1.4 10 April 2019 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/Voyage 200 and TI-Nspire handheld
Wolfram Alpha Wolfram Research   2009   2013 Pro version: $4.99 / month, Pro version for students: $2.99 / month, ioRegular version: free Proprietary Online computer algebra system with step-by step solutions.
Xcas/Giac Bernard Parisse 2000 2000 1.2.3 January 2017 Free GPL General CAS, also adapted for the HP Prime. 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[19]
Yacas Ayal Pinkus et al. 1998[20] 1999 1.7.0 26 June 2019 Free GNU GPL  
  Creator Development started First public release Latest stable version Latest stable release date Cost (USD) License Notes

These computer algebra systems are sometimes combined with "front end" programs that provide a better 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 System
Integration Integral transforms Equations Inequalities Diophantine equations Differential equations Recurrence relations
Axiom No Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes No No Yes Axiom
Cadabra No Yes Yes Yes Yes Yes No Yes No No No No No Yes No No No Yes Cadabra
FriCAS Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No Yes FriCAS
Magma No Yes No No Yes No Yes No No Yes Yes No No No ? ? Yes Yes Magma
Magnus No Yes No No No No No No No ? ? No ? No No No No Yes Magnus
Maple Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes No Yes Maple
Mathcad Yes No Yes No Yes No No No No No No No No No No No No No Mathcad
Mathematica Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes[21] Yes Yes No Yes Mathematica
Mathomatic No No Yes Yes Yes No No No No No Yes No No No No No No No Mathomatic
Symbolic Math Toolbox (MATLAB) Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes No Yes No Yes Yes No No Symbolic Math Toolbox (MATLAB)
Maxima No Yes Yes Yes Yes Yes No Yes Yes Yes Yes No Yes Yes Yes Yes No Yes Maxima
SageMath No Yes Yes Yes Yes Yes Yes[A] Yes Yes Yes Yes Yes[B] Yes Yes Yes No Yes Yes SageMath
SMath Studio Yes No Yes No Yes No No No No No No No No No No No No No SMath Studio
SymPy No Yes Yes Yes Yes Yes Yes[22] Yes Yes No Yes No Yes Yes Yes No No Yes SymPy
Wolfram Alpha Pro version only Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No ? ? No Yes Wolfram Alpha
GAP No Yes No No Yes Yes Yes No Yes Yes Yes Yes Yes Yes No No Yes Yes GAP
Xcas/Giac Yes Yes Yes No Yes Yes No Yes Yes No Yes No No No Yes ? No ? Xcas/Giac
Yacas No Yes Yes No Yes No No No No No No No No No ? ? No No Yacas
Reduce No Yes Yes ? Yes Yes ? Yes ? ? Yes Yes Yes Yes ? ? ? ? Reduce
  1. ^ via SymPy
  2. ^ via qepcad optional package
 

Those which do not "edit equations" may have a GUI, plotting, ASCII graphic formulae and math font printing. The ability to generate plaintext files is also a sought-after feature because it allows a work to be understood by people who do not have a computer algebra system installed.

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. For some platforms, only older releases of the software may be available.

System DOS Windows macOS Linux BSD Solaris Android iOS SaaS Other
Axiom ? Emulator Yes Yes No No ? ? No  
Cadabra No Yes Yes Yes Yes No No No No  
CoCoA No Yes Yes Yes Yes Yes ? ? No Tru64 UNIXHP-UXIRIX
Derive Yes Yes No No No No ? ? No  
Erable No Emulator Emulator Emulator No No No No No System RPL on HP 48/49/50/40 series
Euler ? Yes No Yes No No ? ? No  
Fermat ? Cygwin Yes Yes No No ? ? No  
FORM ? Cygwin Yes Yes Yes Yes ? ? No  
FriCAS ? Cygwin+native Yes Yes Yes Yes ? ? No  
GAP ? Yes Yes Yes Yes Yes ? ? No  
KANT/KASH ? Yes Yes Yes No No ? ? No  
Macaulay2 ? Cygwin Yes Yes Yes Yes ? ? No  
Magma ? Yes Yes Yes Yes Yes ? ? No  
Magnus No Yes ? Yes ? Yes No No No SunOs
Maple No Yes Yes Yes No No No No No  
Mathcad Yes Yes No No No No No No No  
Mathematica No Yes Yes Yes No No No No Yes Raspberry Pi[17]
Mathomatic Yes Yes Yes Yes Yes Yes No Yes No All POSIX platforms
Maxima ? Yes Yes Yes Yes Yes Yes ? No All POSIX platforms with Common Lisp
MuMATH Yes No No No No No ? ? No  
OpenAxiom ? Yes Yes Yes Yes Yes ? ? No  
PARI/GP ? Yes Yes Yes Yes Yes Yes ? No  
Reduce ? Yes Yes Yes Yes Yes ? ? No  
SageMath No Yes Yes Yes No Yes No Yes Yes  
SINGULAR ? Yes Yes Yes Yes Yes ? ? No  
SMath Studio No Yes Mono Mono Mono Mono Yes Yes Yes Universal Windows Platform
SymbolicC++ ? Yes Yes Yes Yes Yes ? ? No  
Symbolic Math Toolbox (MATLAB) No Yes Yes Yes No No No No Yes  
SymPy ? Yes Yes Yes Yes Yes Yes Yes Yes[23] Any system that supports Python
TI-Nspire (desktop software) No Yes Yes No No No No Yes No  
Xcas/Giac No Yes Yes Yes Yes Yes Yes Yes No HP Prime CASKhiCAS for TI Nspire
Yacas No Yes Yes Yes Yes Yes ? ? No  

Graphing calculators

Some graphing calculators have CAS features.

System Creator Development started First public release / OS version Latest stable version / OS version Notes
Casio CFX-9970G CASIO Computer Co. ? 1998    
Casio Algebra FX 2.0 CASIO Computer Co. ? 1999    
Casio ClassPad 300Casio ClassPad 300 PlusCasio ClassPad 330Casio ClassPad 330 PlusCasio ClassPad fx-CP400

Casio ClassPad Manager
CASIO Computer Co. 2002 2003 3.10.7000 ClassPad Manager is an emulator which runs on a PC.
HP 49GHP 49g+HP 48gIIHP 50gHP 40GHP 40gs Hewlett-Packard 1993 1.??(1999) / 4 2.15 (2006-09-19, 2009-04-21) / 4 Based on Erable, which is also available as an add-on for the HP 48SHP 48SXHP 48GHP 48G+HP 48GX. Intended for problems which occur in engineering applications. Source code openly available.
HP Prime Hewlett-Packard 2000 2013 6975 (2014-12-03) / v1.1.0-46 (2014-03-31) Based on Xcas/Giac. Source code openly available.
TI-89 Texas Instruments 1995 1996 2.09  
TI-89 Titanium Texas Instruments 2003 2004 7/18/2005 v3.10  
TI-92 Texas Instruments 1994 1995 ?  
TI-92 Plus Texas Instruments 1997 1998 3/27/2003 v2.09  
TI-Nspire CASTI-Nspire CX CAS Texas Instruments 2006 2008 2014 v3.6.0.550  
Voyage 200 Texas Instruments 2001 2002 7/18/2005 v3.10  

 

See also

 

原文:https://en.wikipedia.org/wiki/List_of_computer_algebra_systems

本文:https://pub.intelligentx.net/wikipedia-list-computer-algebra-systems

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星期四, 一月 5, 2023 - 21:55
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