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컴퓨터 대수학 시스템

위키백과, 우리 모두의 백과사전.

컴퓨터 대수학 시스템(Computer algebra system)은 수학 기호로 구성된 대수 구조를 해결하는 컴퓨터 시스템을 말한다.

[편집]내용

  • 기호와 함수로 구성된 대수 구조에 대해 연산
  • 집합, 행렬, 기하, 대수, 미적분, 해석함수, 통계, 증명과 검증, 수론 등의 대다수 수학적 대상물에 대해 자동화된 처리를 지원한다.

[편집]일반적으로 포함되는 기능

  • 자체 프로그래밍 언어와 IDE
  • 코드 에디터
  • 그래프, 도표, 테이블, 다이어그램의 표현
  • 외부 시스템에 연계할 수 있는 API
  • 소수점 이하를 자유롭게 지정하는 기능 (부동소수점 연산과 대비됨)
  • 다양한 수론 함수 지원 및 정확한 정수 표현 (부동소수점 형태로 표현하지 않음)
  • 수학 표현식 (적분, 극한, 행렬 등의 복잡한 수학 표현을 입출력)
  • 응용 수학, 물리학, 생물학, 화학 등에 관한 확장 패키지

 

 

 

비교 내용 :  http://en.wikipedia.org/wiki/Comparison_of_computer_algebra_systems

 

 

Comparison of computer algebra systems

From Wikipedia, the free encyclopedia

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

Contents

  [hide] 

[edit]General

SystemCreatorDevelopment startedFirst public releaseLatest stable releaseCost (USD)LicenseNotes
AlgebratorNeven Jurkovic198619992009 (4.2)$58.99ProprietaryElementary algebra; step-by-step solutions
AxiomTim Daly19712002May 2012Freemodified BSD licenseForked in 2007 to OpenAxiom andFriCAS
bergmanJörgen Backelin197219721999 (0.96)FreeGPL-style licenseNon-commutative and commutative Gröbner bases; mainly homogeneous and non-linear; Lisp-based
CadabraKasper Peeters200120072011 (1.29)FreeGPLtensor algebra, field theory
calcDave Gillespie ? ?in GNU emacs 23FreeGPLAdvanced calculator integrated in the Emacs editor. Supports a simple CAS and physical units.
ClassPad ManagerCASIO199920013.03 (2008)$45.45Proprietary
CASSIOPEIACASIO-MAPLE199720012001 (5.0)DiscontinuedProprietaryVersion of Maple 5 for CASSIOPEIA
CoCoAThe CoCoA Team198719952007 (4.7.3)FreeGPLFor polynomial calculations
DeriveSoft Warehouse19791988November 2007(6.1)DiscontinuedProprietaryOwned by TI; it was discontinued 2007
DoConSerge D. Mechveliani199319952.11Freenon-OSI approved licenseHaskell library
DCASRobert Fenichel ?20052005 (1.0)FreeGPL
EigenmathGeorge Weigt200420052010 (137)FreeGPLOS supported: Windows, Mac, Android, Poket PC, Nintendo DS[1]
Euler Math ToolboxR. Grothmann198719882011 (12.3)FreeGPLExtension of Maxima, symbolic and numeric computation, interval arithmetic
FermatRobert H. Lewis198619932010 (3.9.9x)$60 if grant money available, otherwise $0Proprietarypolynomials, matrices
FORMJ.A.M. Vermaseren198419893.3FreeGPLhigh speed, arbitrary size of expressions, multi-threaded
Franklin MathAllen Franklin Jordan20082009March 2011(0.11)FreeGPLSymbolic and numeric math, plotting, functions
FriCASWaldek Hebisch200720072012 (1.1.7)Freemodified BSD licenseForked from Axiom in 2007.
GAPGAP Group198619862008 (4.4.12)FreeGPLgroups, character theory, discrete mathematics
JACALAubrey Jaffer198919912010 (1c2)FreeGPLScheme-based
JasymcaHelmut Dersch200320062011 (3)FreeGPLAlgebra, Calculus, Polynomials, Matrices, graphing
jMathLab[2]Dr. S.Chekanov201120122012 (3)FreeGPLAlgebra, Calculus (based on Jasymca), Polynomials, Functions, Matrices, Probability, 2D/3D graphics
Java Algebra SystemHeinz Kredel200020052.0FreeGPL or LGPLCommutative and non-commutative, Gröbner bases, gcd, Java library
KANT/KASHKANT Group ? ?KASH3 (2005/2008)free for non-commercial useown licensealgebraic number theory
LiveMath
(formerly Theorist)		Math Monkeys ?19912007 (3.5.9)$149, $45 student (1 year)Proprietaryinteractive solving and graphing
Macaulay2Daniel Grayson and Michael Stillman199219942010 (1.4)FreeGPLalgebraic geometry, commutative algebra
MacsymaMIT Project MAC andSymbolics196819781999 (2.4)$500ProprietaryLisp-based. Continues as the open-source Maxima.
MagmaUniversity of Sydney~199019932011 (2.17)$1,150ProprietaryAlgebra, Cryptography, Group Theory, Number Theory
Magnus Computational Group Theory PackageThe New York Group Theory Cooperative1994 ?2009FreeGPLInfinite group theory
MapleSymbolic Computation Group, University of Waterloo198019842012 (16)$2,275 (Commercial), $2,155 (Government), $1245(Academic), $239 (Personal Edition), $99 (Student), $79 (Student, 12-Month term)[3]ProprietaryLibrary source code is viewable
MASHeinz Kredel, Michael Pesch1989 ?1998 (1.01)FreeunspecifiedModula-2 source code available
MathcadParametric Technology Corporation198519852010 (15)$1,195[4]Proprietarystandard mathematical notation, plotting, unit-aware calculations
MathEclipse/SymjaAxel Kramer200220022007FreeCPLJava symbolic computing library (uses JAS and Apache Commons-Math)
MathematicaWolfram Research198619882011 (8.0.4)$2,495 (Professional), $1095 (Education), $140 (Student), $69.95 (Student annual license) [5] $295 (Personal)[6]ProprietarySystem also includes extensive numeric capabilities, statistics, image processing, number theory, boolean computation and is a development environment.
MathinationOrion Math201020102010 (1.0)$4.99ProprietaryBasic algebra for the iPad, with a multi-touch interface to manipulate equations.
Mathiverse CalculatorMathiverse200920092009 (0.0.1)FreeProprietaryComplex number manipulation
MathomaticGeorge Gesslein II198619872012 (16.0.3)FreeLGPLElementary algebra, calculus,complex number and polynomialmanipulations.
MathPiperTed Kosan, Sherm Ostrowsky200820102010 (.80n)FreeGPLSpecifically designed for use in education.
MathXpertMichael Beeson198519972008 (3.0.4)Algebra Assistant $49.95, Calculus Assistant $89.95[7]ProprietaryStep-by-step solutions, correct graphs, keeps track of assumptions for logical correctness of results.
MaximaMIT Project MAC and Bill Schelter et al.196719982012 (5.28)FreeGPLCommon Lisp-based full-featured CAS
meditorRaphael Jolly200020002.0_01FreeGPLJava symbolic computing library and math editor
Microsoft MathematicsMicrosoft ?20052011 (4.0.1108)FreeProprietaryElementary algebra and calculus; unit conversion; graphing; step-by-step solutions
MuMATHSoft Warehouse1970s1980MuMATH-83DiscontinuedProprietary
MuPADSciFace Software198920082008 (5.1)DiscontinuedProprietaryMathWorks has incorporated MuPAD technology into Symbolic Math Toolbox
NCAlgebra and NCGBHelton, deOliveira,Stankus,Miller199019912010 (4.0)FreeNCAlgebraBSDNon-commutative algebra inMathematica; NCGroebner Bases; block matrices
NCLabFEMhub201120122012 (1.0)FreeProprietaryWide range of symbolic and numerical methods including algebra, calculus, differential equations
OpenAxiomGabriel Dos Reis200720072011 (1.4.1)Freemodified BSD licenseForked from Axiom in 2007
PARI/GPHenri Cohen, Karim Belabas, Bill Allombert et al.198519902012 (2.5.1)FreeGPLNumber theory, elliptic curves,arbitrary-precision arithmetic
ReduceAnthony C. Hearn1960s19682009Freemodified BSD licenseopen-sourced and freed in December 2008
SageWilliam A. Stein200520052012 (5.3)FreeGPLIncludes extensive numeric capabilities, statistics, image processing, number theory and is a development environment using a web-based interface viaHTTP or HTTPS.
SINGULARUniversity of Kaiserslautern198419972011 (3.1.2)FreeGPLpolynomials, rings, ideals
SMath StudioAndrey Ivashov?20052012 (0.91)FreeCreative Commons Attribution-NoDerivs (CC-BY-ND)Mathematical notebook program similar to Mathcad
SpaceTime MathematicsSpaceTime Mathematics200620092010 (4.0)$39, free and discontinued for Windows Mobile Devices.ProprietaryComputer algebra and calculus,mobile device scientific computing
Symbolic MATLABToolboxMathWorks198920082011(5.7(2011b))$2900 including requiredMATLABProprietaryProvides tools for solving and manipulating symbolic math expressions and performing variable-precision arithmetic.
SymbolicC++W.-H. Steeb199719972009 (3.29)FreeGPLC++ -based
SymPyOndřej Čertík200620072012 (0.7.2)Freemodified BSD licensePython-based
SympyCorePearu Peterson200820082008 (0.1)Freemodified BSD licensePython-based
TI-Nspire CAS (Computer Software)Texas Instruments200620093.1.0.392ProprietarySuccessor to Derive. Based on Derive's engine used in TI-89/Voyager 200 and TI-Nspire handheld
TRIPJ. Laskar, M. Gastineau198920022011 (1.1.12)FreeAcademic licensecelestial mechanics
Wolfram AlphaWolfram Research20092012Pro version: $4.99 / month, Pro version for students: $2.99 / month, Regular version free.ProprietaryOnline computer algebra systemwith step-by step solutions.
WIRISMaths for More199720012.0ProprietaryOnline computer algebra systemand interactive geometry software
XcasBernard Parisse200420082011 (0.9.4)FreeGPLCompatible 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[8]
YacasAyal Pinkus et al.1998[9] ?2012 (1.3.3)FreeGPL
CreatorDevelopment startedFirst public releaseLatest stable versionCost (USD)LicenseNotes

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.

SystemFormula editorArbitrary precisionCalculusSolversGraph theoryNumber theoryQuantifier eliminationBoolean algebraTensorsProbabilityControl Theory
IntegrationIntegral transformsEquationsInequalitiesDiophantine equationsDifferential equationsRecurrence relations
AxiomNoYesYesYesYes ? ? ? ? ? ? ? ? ? ? ?
AlgebratorYesNoNoNoYesYesNoNoNoNoNoNoNoNo ? ?
CadabraYesNoNoNoNoNoNoNoNoNoNoNoNoYes ? ?
FriCASNoYesYesYesYesNo ?Yes ? ? ? ? ? ? ? ?
JacalNoNoNoNoNoNoNoNoNoNoNoNoNoYes ? ?
JasymcaNoNoYesYesYesNoNoYesNoNoNoNoNoNo ? ?
jMathLabNoNoYesYesYesNoNoYesNoNoNoNoNoNo ? ?
MagmaNoYesNoNoYesNoYesNoNoYesYesNoNoNo ? ?
MapleYesYesYesYesYesYesNoYesYesYesYesNoNoYesYesYes
MathcadYesNoYesNoYesNoNoNoNoNoNoNoNoNoNoNo
Math EclipseNoYesNoNoNoNoNoNoNoNoNoNoNoNo ? ?
MathematicaYesYesYesYesYesYesYesYesYesYesYesYesYesNoYesYes
MathomaticNoNoYesYesYesNoNoNoNoNoYesNoNoNoNoNo
SymbolicMATLABtoolboxNoYesYesYesYesNoNoYes ?No ?NoNo ? ? ?
MaximaNoYesYesYesYesYesNoYesYesYesYesYesYesYes ? ?
Microsoft MathematicsYesNoYesNoYesYesNoNoNoNoNoNoYesNo ? ?
SageYesYesYesYesYesYesNoYesYesYesYesYesYesYesNoNo
SymPyNoYesYesYesYesYesNoYesYesNoYesNoYesYesYesNo
Wolfram AlphaPro version onlyYesYesYesYesYes ?YesYesYesYesYesYesNo ? ?
YacasNoYesYesNoNoNoNoNoNoNoNoNoNoNo ? ?
XcasYesYesYesNoYesYesNoYesYesNoYesNoNoNo ? ?

[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.

SystemWindowsMac OS XLinuxBSDSolarisOther
AlgebratorYesYesYesNoNo?
AxiomYesYesYesNoNo?
bergmanYes?YesYesYes?
CadabraNoYesYesYesYes?
ClassPad ManagerYesNoNoNoNo?
CoCoAYesYesYesYesYesTru64 UNIX, HP-UX, IRIX
DeriveYesNoNoNoNo?
DoCon??Yes???
DCASYes?????
EigenmathYesYesNoNoNo?
EulerYesNoNoNoNo?
FermatCygwinYesYesNoNo?
FORMCygwinYesYesYesYes?
Franklin MathYesYesYesYesYesAny system that supports Java
FriCASYesYesYesYesYes?
GAPYesYesYesYesYes?
JACALYesYesYesYesYes?
JasymcaYesYesYesYesYesAny system that supports Java
jMathLabYesYesYesYesYesAny system that supports Java
Java Algebra SystemYesYesYesYesYesAny system that supports Java
KANT/KASHYesYesYesNoNoNo
Macaulay2YesYesYesYesYes?
MagmaYesYesYesYesYes?
Magnus??Yes???
MapleYesYesYesNoYesNo
MathcadYesNoNoNoNoNo
MathEclipseYesYesYesYesYesAny system that supports Java
MathematicaYesYesYesNoNoNo
MathomaticYesYesYesYesYesAndroid, and all POSIX platforms
MathXpertYesNoNoNoNo?
MaximaYesYesYesYesYesAll POSIX platforms with Common Lisp
MeditorYesYesYesYesYes?
Microsoft MathematicsYesNoNoNoNo
MuMATHNoNoNoNoNo?
MuPADYesYesYesNoNo?
OpenAxiomYesYesYesYesYes?
PARI/GPYesYesYesYesYes?
ReduceYesYesYesYesYes?
SageNoYesYesNoYesVMware image for MS-Windows users
SINGULARYesYesYesYesYes?
SMath StudioYesNoYesNoNoMany handhelds supported
SymbolicC++YesYesYesYesYes?
Symbolic MATLABtoolboxYesYesYesYesYes?
SymPyYesYesYesYesYesAny system that supports Python
SympyCoreYesYesYesYesYesAndroid (no plots except textplots), Any system that supports Python
TI-Nspire (desktop software)YesYesNoNoNo?
WIRISYesYesYesYesYes?
XcasYesYesYesYesYes?
YacasYesYesYesYesYes?
TRIPYesYesYesYesYes?
WindowsMac OS XLinuxBSDSolarisOther

[edit]Hand-held calculator CAS

SystemCreatorDevelopment startedFirst public releaseLatest stable versionCost (USD)Open sourceLicenseNotes
Alg48 & ErableBernard Parisse199619983.2FreeSymbolic Math packages for HP48 series
Casio CFX-9970GCASIO Computer Co.?1998NoProprietary
Casio Algebra FX 2.0CASIO Computer Co.?1999NoProprietary
Casio ClassPad 330CASIO Computer Co.?20033.04.5000$140NoProprietaryThere is also an emulator: "ClassPad Manager" which runs on a PC.
EigenmathGeorge Weigt20082008137FreeYesfreeHandhelds available: Android, Nintendo DS, Poket PC.
HP 49 seriesHewlett-Packard?19992.15$110 and upYes[h 1]Proprietarywith someLGPLBased on Erable. Intended for problems which occur in engineering applications. Also used in HP-50calculators.
iCASAL Software201020101.2.1$15NoProprietaryNative iPhone and iPad implementation of REDUCE.
i41CX+AL Software200820084.9.2$25NoProprietaryiPhone and iPad application that combines the capabilities of the HP-41CX with a CAS based on REDUCE.
TI-89Texas Instruments?19962.09No longer in productionNoProprietary
TI-89 TitaniumTexas Instruments?20043.10$150NoProprietary
TI-92Texas Instruments?1995?No longer in productionNoProprietary
TI-92 PlusTexas Instruments199719982.09No longer in productionNoProprietary
TI-Nspire CASTexas Instruments200620082.0.1.60$160NoProprietaryTI-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 200Texas Instruments200120023.10$150NoProprietary
ZoomMath300IQ Joe? ?1.03$60NoProprietaryTI-83 and TI-84 application that adds CAS capabilities
  1. ^ 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.

 

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