Mathematica

Wolfram Mathematica, normalt omtalt som Mathematica, er en kommerciel^[1] softwarepakke,^[2] som er udviklet af firmaet Wolfram Mathematica. Mathematica kan løse en række problemstillinger indenfor regning, matematik og naturvidenskaber samt ingeniørkundskaber og programmering.

Features[redigér | rediger kildetekst]

Mathematica indeholder bl.a.

Mathematica kan vise matematiske formler som pretty-print.
Computer Algebra System (CAS)^[6]
Numerisk software til numerisk løsning^[7] af ligning^[8]^[9]
beregne differentialkvotient^[10]
beregne integrale^[11]
løse^[12]^[13] differentialligning^[14] (se tabel nedenfor)
beregne multipelt integral^[15]
Virsualiseringsværktøj^[16]
Programmering^[17]

Desuden kan Mathematica vise funktioners grafer (2D såvel som 3D).^[2]

Manualer[redigér | rediger kildetekst]

Der findes flere Mathematica Tutorials^[18] og andre introduktioner^[19] til programmet.^[20]

Styresystemer[redigér | rediger kildetekst]

Mathematica findes til disse fire styresystemer:

Programmeringssprog[redigér | rediger kildetekst]

Mathematica er skrevet i programmeringssproget Wolfram Language,^[22] som minder meget om det funktionale programmeringssprog Lisp. Licensen er proprietær.

Historie[redigér | rediger kildetekst]

Den britiske forfatter og virksomhedsgrundlægger Stephen Wolfram begyndte udviklingsarbejdet i 1986. Mathematica er siden blevet videreudviklet af Wolfram Research of Champaign^[23] i Illinois, USA.^[24] Den 23. juni 1988 kom den første version 1.0 af Mathematica på markedet.^[25] Version 12.0 blev lanceret den 16. april 2019.

Versionshistorie[redigér | rediger kildetekst]

Version	Offentliggørelse
1.0	23. juni 1988
1.1	31. oktober 1988
1.2	1. august 1989
2.0	15. januar 1991
2.1	15. juni 1992
2.2	1. juni 1993
3.0	3. september 1996
4.0	19. maj 1999
4.1	2. november 2000
4.2	1. November 2002
5.0	12. juni 2003
5.1	25. oktober 2004
5.2	20. juni 2005
6.0	1. maj 2007
7.0	18. november 2008
7.0.1	5. marts 2009
8.0	15. november 2010
8.0.1	7. marts 2011
8.0.4	24. oktober 2011
9.0	28. november 2012
9.0.1	30. januar 2013
10	9. juli 2014
10.0.1	17. september 2014
10.0.2	15. december 2014
10.1	31. marts 2015
10.2	14. juli 2015
10.3	15. oktober 2015
10.3.1	16. december 2015
10.4	2. marts 2016
10.4.1	18. april 2016
11	9. august 2016
11.0.1	28. september 2016
11.1	16. marts 2017
11.1.1	25. april 2017
11.2	14. september 2017
11.3	8. marts 2018
12.0	16. april 2019
12.1	18. marts 2020
12.2	16. december 2020
12.3	20. maj 2021

Kritik[redigér | rediger kildetekst]

I 2014 påpegede tre matematikere, at Mathematica beregner forkerte resultater ved beregning af determinant for bestemte matrixer med store heltal (10.000 decimaler).^[26]

Presseomtale o.l.[redigér | rediger kildetekst]

Ifølge techgrabyte.com er Mathematica bedre end Maple.^[27] Disse tre CAS-softwares hjælper kunstig intelligens med at lære matematik: Maple, MATLAB og Mathematica.^[28]

Mathematica i undervisning[redigér | rediger kildetekst]

Mathematica er nævnt på en række danske universiteters hjemmesider: CBS,^[29] ITU,^[30] DTU,^[31]^[32] KU,^[33] AU,^[34] AAU,^[35] SDU^[36] & RUC^[37]

Wolfram Alpha[redigér | rediger kildetekst]

Wolfram Alpha er en matematisk software-pakke, som også er udviklet af firmaet Wolfram Mathematica; Wolfram Alpha er tilgængelig online.^[38]

Features

Wolfram Alpha kan blandt andet:

Se også[redigér | rediger kildetekst]

Wolfram Alpha

Litteratur[redigér | rediger kildetekst]

Hans Benker: MATHEMATICA kompakt: Mathematische Problemlösungen für Ingenieure, Mathematiker und Naturwissenschaftler. Springer, Berlin / Heidelberg 2016, ISBN 978-3-662-49610-7.
Knut Lorenzen: Einführung in Mathematica: Berücksichtigt die kostenlose Version 10 für den Raspberry Pi. mitp Verlags GmbH & Co., 2014. ISBN 978-3-8266-9666-4
Axel Kilian: Programmieren mit Wolfram Mathematica. Springer, Berlin / Heidelberg 2009, ISBN 978-3-642-04671-1.
Michael Trott: The Mathematica GuideBook for Symbolics. Springer, 2006.
Stephen Wolfram: An Elementary Introduction to the Wolfram Language. Wolfram Media, Inc., Champaign, IL. 2015, ISBN 978-1-944183-00-4.
Stephen Wolfram: The Mathematica Book. 5. oplag. Wolfram Media, 2004, ISBN 1-57955-022-3.

Eksterne henvisninger[redigér | rediger kildetekst]

Officiel hjemmeside
List of computer algebra systems (engelsk)

Tabel[redigér | rediger kildetekst]

Mathematica hører til denne gruppe^[41] af CAS-softwares^[42]

Navn	Software licens	Programmeringssprog	MS Windows	macOS	Linux	Andre OS	Kommando løser differentialligning	Note og kilde
CPMP-Tools	freeware eller fri software	java	Windows	macOS	Linux			^[43]
ExpressionsinBar	freeware eller fri software	?		64 bit app for macOS			desolve( $y'=b\cdot y-a$ , $y$ )	^[44]
GeoGebra	freeware eller fri software	java	Windows	macOS	Linux	Android & iOS	SolveODE(^[45]	også som web app^[46]
Maple *	kommerciel	C, Java, Maple	Windows	macOS	Linux		dsolve $(y'(x)=k\cdot y(x)$ , $y(x))$ ^[47]	^[48]
Mathematica *	kommerciel	Wolfram Language, Lisp	Windows	macOS	Linux	Solaris	DSolve( $y'=k\cdot y$ , $y$ )^[12]	også som web^[49] app^[50]
MATLAB	kommerciel	C/C++, MATLAB	Windows	macOS	Linux			^[51]
Maxima	freeware eller fri software	Common Lisp	Windows	macOS	Linux	Android	ode2 (eqn, dvar, ivar)^[52]	også som online app^[53]
SageMath	freeware eller fri software	Python 3	Windows	macOS	Linux		desolve( $y'=b\cdot y-a$ , $y$ )^[54]	^[55]
Singular	freeware eller fri software	C++	Windows	macOS	Linux			findes^[56] også online^[57]
TI-Nspire CX CAS	kommerciel	?	Windows	macOS			deSolve( $y'=b\cdot y-a$ , $x$ , $y$ )^[58]	^[59]^[60]
TI-89 simulator & TI-92 Plus emulator	freeware eller fri software	?	online				deSolve( $y'=b\cdot y-a$ , $x$ , $y$ )	^[61]^[62]
Xcas	freeware eller fri software	C++	Windows	macOS	Linux	Android	desolve( $y'=b\cdot y-a$ , $y$ )^[63]	^[64]
Yacas	freeware eller fri software	C++	Windows	macOS	Linux		OdeSolve( $y''-4*y==0$ )^[65]	^[66]

* løser også triple integraler.

Referencer[redigér | rediger kildetekst]

^ Commercial Software - IT Service Wiki
^ ^a ^b https://www.uni-ulm.de/einrichtungen/kiz/service-katalog/software/softwareliste/mathematische-anwendungssoftware/mathematica/ (Webside ikke længere tilgængelig)
^ "Mathematica 12 System Requirements and Platform Availability". Hentet 16. december 2020.
^ Raspberry Pi Includes Mathematica for Free The Verge
^ "Wolfram Mathematica". Hentet 11. august 2015.
^ Mathematica — Hochschulrechenzentrum
^ http://num.math.uni-goettingen.de/~summer/intro_mathematica.pdf
^ Algebra | Mathematica & Wolfram Language for Math Students—Fast Intro
^ Equation Solving—Wolfram Language Documentation
^ Derivative—Wolfram Language Documentation
^ Integrate—Wolfram Language Documentation
^ ^a ^b Introduction to Differential Equation Solving with DSolve—Wolfram Language Documentation
^ Solve a Differential Equation—Wolfram Language Documentation
^ Wolfram Videos: Solving Differential Equations in Mathematica
^ Multiple Integral - from Wolfram MathWorld
^ Mathematica
^ RRZK: Mathematica
^ "Arkiveret kopi" (PDF). Arkiveret fra originalen (PDF) 15. januar 2021. Hentet 1. januar 2021.
^ Mathematica & Wolfram Language Tutorial: Fast Intro for Math Students
^ Hands-on Start to Mathematica: Wolfram U Class
^ https://www2.uni-mannheim.de/rum/english/about%20us/workgroups/cs/hpc/bwgrid_cluster_englisch/software/mathematica/ (Webside ikke længere tilgængelig)
^ https://www.wolfram.com/language/ Wolfram Language – Wissensbasiertes Programmieren
^ https://uni-tuebingen.de/fakultaeten/wirtschafts-und-sozialwissenschaftliche-fakultaet/faecher/fachbereich-wirtschaftswissenschaft/wirtschaftswissenschaft/fb-wiwi/einrichtungen-und-service/it/services/services/anwendungen-software/mathematica/ (Webside ikke længere tilgængelig)
^ Stephen Wolfram: Simple Solutions; The iconoclastic physicist's Mathematica software nails complex puzzles http://www.businessweek.com/magazine/content/05_40/b3953024.htm, BusinessWeek, October 3, 2005.
^ "Mathematica Latest Version and Quick Revision History". Retrieved 11 August 2015
^ Mathematica rechnet falsch | heise online
^ Facebook’s AI Mathematician Can Solve University Calculus Problems
^ "Facebook trains an artificial intelligence capable of solving equations | Innovation | Spain's News". Arkiveret fra originalen 27. oktober 2020. Hentet 16. december 2020.
^ Software | CBS - Copenhagen Business School
^ Kursusbasen
^ Mathematics and Statistics Software - ITSwiki
^ Mathematica
^ http://web.math.ku.dk/~moller/undervisning/MASO2010/oevelser37.pdf
^ Available software
^ News (Webside ikke længere tilgængelig)
^ TekVideo | Introduktion til mathematica
^ http://entraproject.ruc.dk/wp-content/uploads/2016/03/deliv_1.2.pdf
^ About Wolfram|Alpha: Making the World's Knowledge Computable
^ ^a ^b Wolfram|Alpha Examples: Equation Solving
^ Wolfram|Alpha Widgets: "Triple Integral Calculator" - Free Mathematics Widget
^ Top 20 Best Computer Algebra Systems for Linux in 2020
^ Comparison of computer algebra systems
^ "CPMP-Tools Software". Arkiveret fra originalen 12. januar 2020. Hentet 23. december 2020.
^ ExpressionsinBar
^ SolveODE Command - GeoGebra Manual
^ GeoGebra Classic - GeoGebra
^ interactive symbolic and numeric solution of ordinary differential equations - Maple Programming Help
^ https://www.maplesoft.com/
^ Wolfram|Alpha: Computational Intelligence
^ Wolfram Mathematica: Modern Technical Computing
^ MATLAB - MathWorks - MATLAB & Simulink
^ Functions and Variables for Differential Equations (Maxima 5.44.0 Manual)
^ Online Algebra Calculator | Maxima-online
^ Solving ordinary differential equations — Sage 9.2 Reference Manual: Symbolic Calculus
^ SageMath - Open-Source Mathematical Software System
^ Singular
^ "Singular". Arkiveret fra originalen 20. juli 2017. Hentet 23. december 2020.
^ "Differentialligninger - TI-nspire hjælp". Arkiveret fra originalen 23. oktober 2020. Hentet 20. december 2020.
^ Download Your TI-Nspire™ CAS Student Software - Texas Instruments - US and Canada
^ Undervisningmidler - Texas Instruments
^ TI-89 Online Simulator
^ TI-89 / TI-92+ / TI-V200 / TI-89T emulator (beta version 12-debrouxl)
^ http://www-fourier.ujf-grenoble.fr/~parisse/giac/cascmd_en.pdf
^ Giac/Xcas, a free computer algebra system
^ Differential Equations — Yacas
^ Yacas

Spire

Denne artikel om software og programmering er en spire som bør udbygges. Du er velkommen til at hjælpe Wikipedia ved at udvide den.

[1] Commercial Software - IT Service Wiki

[:0-2] ttps://www.uni-ulm.de/einrichtungen/kiz/service-katalog/software/softwareliste/mathematische-anwendungssoftware/mathematica/ (Webside ikke længere tilgængelig)

[3] "Mathematica 12 System Requirements and Platform Availability". Hentet 16. december 2020.

[4] Raspberry Pi Includes Mathematica for Free The Verge

[5] "Wolfram Mathematica". Hentet 11. august 2015.

[6] Mathematica — Hochschulrechenzentrum

[7] ttp://num.math.uni-goettingen.de/~summer/intro_mathematica.pdf

[8] Algebra | Mathematica & Wolfram Language for Math Students—Fast Intro

[9] Equation Solving—Wolfram Language Documentation

[10] Derivative—Wolfram Language Documentation

[11] Integrate—Wolfram Language Documentation

[autogeneret1-12] Introduction to Differential Equation Solving with DSolve—Wolfram Language Documentation

[13] Solve a Differential Equation—Wolfram Language Documentation

[14] Wolfram Videos: Solving Differential Equations in Mathematica

[15] Multiple Integral - from Wolfram MathWorld

[16] Mathematica

[17] RRZK: Mathematica

[18] "Arkiveret kopi" (PDF). Arkiveret fra originalen (PDF) 15. januar 2021. Hentet 1. januar 2021.

[19] Mathematica & Wolfram Language Tutorial: Fast Intro for Math Students

[20] Hands-on Start to Mathematica: Wolfram U Class

[21] ttps://www2.uni-mannheim.de/rum/english/about%20us/workgroups/cs/hpc/bwgrid_cluster_englisch/software/mathematica/ (Webside ikke længere tilgængelig)

[22] ttps://www.wolfram.com/language/ Wolfram Language – Wissensbasiertes Programmieren

[23] ttps://uni-tuebingen.de/fakultaeten/wirtschafts-und-sozialwissenschaftliche-fakultaet/faecher/fachbereich-wirtschaftswissenschaft/wirtschaftswissenschaft/fb-wiwi/einrichtungen-und-service/it/services/services/anwendungen-software/mathematica/ (Webside ikke længere tilgængelig)

[24] Stephen Wolfram: Simple Solutions; The iconoclastic physicist's Mathematica software nails complex puzzles http://www.businessweek.com/magazine/content/05_40/b3953024.htm, BusinessWeek, October 3, 2005.

[25] "Mathematica Latest Version and Quick Revision History". Retrieved 11 August 2015

[26] Mathematica rechnet falsch | heise online

[27] Facebook’s AI Mathematician Can Solve University Calculus Problems

[28] "Facebook trains an artificial intelligence capable of solving equations | Innovation | Spain's News". Arkiveret fra originalen 27. oktober 2020. Hentet 16. december 2020.

[29] Software | CBS - Copenhagen Business School

[30] Kursusbasen

[31] Mathematics and Statistics Software - ITSwiki

[32] Mathematica

[33] ttp://web.math.ku.dk/~moller/undervisning/MASO2010/oevelser37.pdf

[34] Available software

[35] News (Webside ikke længere tilgængelig)

[36] TekVideo | Introduktion til mathematica

[37] ttp://entraproject.ruc.dk/wp-content/uploads/2016/03/deliv_1.2.pdf

[38] About Wolfram|Alpha: Making the World's Knowledge Computable

[autogeneret2-39] Wolfram|Alpha Examples: Equation Solving

[40] Wolfram|Alpha Widgets: "Triple Integral Calculator" - Free Mathematics Widget

[41] Top 20 Best Computer Algebra Systems for Linux in 2020

[42] Comparison of computer algebra systems

[43] "CPMP-Tools Software". Arkiveret fra originalen 12. januar 2020. Hentet 23. december 2020.

[44] ExpressionsinBar

[45] SolveODE Command - GeoGebra Manual

[46] GeoGebra Classic - GeoGebra

[47] teractive symbolic and numeric solution of ordinary differential equations - Maple Programming Help

[48] ttps://www.maplesoft.com/

[49] Wolfram|Alpha: Computational Intelligence

[50] Wolfram Mathematica: Modern Technical Computing

[51] MATLAB - MathWorks - MATLAB & Simulink

[52] Functions and Variables for Differential Equations (Maxima 5.44.0 Manual)

[53] Online Algebra Calculator | Maxima-online

[54] Solving ordinary differential equations — Sage 9.2 Reference Manual: Symbolic Calculus

[55] SageMath - Open-Source Mathematical Software System

[56] Singular

[57] "Singular". Arkiveret fra originalen 20. juli 2017. Hentet 23. december 2020.

[:10-58] "Differentialligninger - TI-nspire hjælp". Arkiveret fra originalen 23. oktober 2020. Hentet 20. december 2020.

[59] Download Your TI-Nspire™ CAS Student Software - Texas Instruments - US and Canada

[60] Undervisningmidler - Texas Instruments

[:9-61] TI-89 Online Simulator

[:8-62] TI-89 / TI-92+ / TI-V200 / TI-89T emulator (beta version 12-debrouxl)

[63] ttp://www-fourier.ujf-grenoble.fr/~parisse/giac/cascmd_en.pdf

[64] Giac/Xcas, a free computer algebra system

[65] Differential Equations — Yacas

[66] Yacas

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Mathematica

Platform	Windows (10),^[3] macOS, Linux, Raspbian, online service.^[4] All platforms support 64-bit implementations.^[5] (list)