View source for Xcas

{{Short description|Computer algebra system}}
{{Use dmy dates|date=August 2019|cs1-dates=y}}
{{Use list-defined references|date=October 2022}}
{{Infobox software
| name = Xcas
| logo=Xcas icon 2.png
| logo caption=
| screenshot = Xcas 1.5 running on windows 10.png
| screenshot alt = Xcas 1.5 running on windows 10, ploting function and calculating the derivative of the cubed function.
| caption = Xcas 1.5 running on Windows 10
| developer = {{ill|Bernard Parisse|fr}}
| released = {{Start date and age|2000|df=yes}}
| latest_release_version = {{LSR/wikidata}}
| programming language = [[C++]]
| operating_system = [[Microsoft Windows|Windows]], [[macOS]], [[Linux]], [[FreeBSD]], [[Android (operating system)|Android]], [[iOS]]
| genre = [[Computer algebra system]] (CAS)
| license = [[GNU]] [[GNU General Public License|GPL]]
| website = {{URL|https://xcas.univ-grenoble-alpes.fr/en.html}}
}}
[[File:Xcas brøk ny.png|alt=calculate fractions without common denominator|thumb|Figure 1. Xcas calculates fractions without common denominator.]]
[[File:Xcas løser ligning, beregner differentialkvotient og stamfunktion mm.png|thumb|Figure 2. Xcas can solve equations, calculate derivatives, antiderivatives and more.]]
[[File:Nyere forsøg Xcas løser differentialligninger algebraisk.png|thumb|Figure 3. Xcas can solve differential equations.]]
'''Xcas''' is a user interface to '''Giac''', which is an [[Open-source software|open source]]<ref name="R1"/> [[Computer Algebra System|computer algebra system]] (CAS) for [[Microsoft Windows|Windows]], [[macOS]] and [[Linux]] among many other platforms. Xcas is written in [[C++]].<ref name="R2"/> Giac can be used directly inside software written in C++.

Xcas has compatibility modes with many popular algebra systems like [[WolframAlpha]],<ref name="Tõnisson 2017"/> [[Wolfram Mathematica|Mathematica]],<ref name="R3"/> [[Maple (software)|Maple]],<ref name="R4"/> or [[MuPAD]]. Users can use Giac/Xcas to develop formal algorithms or use it in other software. Giac is used in [[SageMath]]<ref name="Tõnisson 2017"/> for calculus operations. Among other things, Xcas can solve [[differential equation]]s (Figure 3) and draw [[Graph of a function|graph]]s. There is a forum for questions about Xcas.<ref name="R5"/>

[[CmathOOoCAS]], an [[OpenOffice.org]] plugin which allows formal calculation in [[OpenOffice.org#Components|Calc]] spreadsheet and [[OpenOffice.org#Components|Writer]] word processing, uses Giac to perform calculations.<ref name="R6"/>

==Features==
Here is a brief overview of what Xcas is able to do:<ref name="R7"/><ref>Read more commands and features [http://www-fourier.ujf-grenoble.fr/~parisse/giac/cascmd_en.pdf here].</ref>
* Xcas has the ability of a scientific calculator that provides [[show input]] and writes [[pretty print]]
* Xcas also works as a [[spreadsheet]];<ref name="reference-card"/>
* [[computer algebra]];
* [[2D geometry]] in the plane;<ref name="Gandit2009"/>
* 3D geometry in space;<ref name="Gandit2009"/>
* [[spreadsheet]];<ref name="reference-card"/>
* [[statistics]];
* [[regression analysis|regression]] (exponential, linear, logarithmic, logistic, polynomial, power)
* programming;<ref name="R8"/>
* solve [[equation]]s even with [[Complex number|complex]] roots (Figure 2);
* solving [[trigonometric]] equations 
* solve [[differential equation]]s<ref name="R9"/><ref name="R10"/> (Figure 3);
* draw [[Graph of a function|graphs]];
* calculate [[Differential calculus|differential]] (or [[derivative]]) of [[Function (mathematics)|functions]] (Figure 2);
* calculate [[antiderivative]] of [[Function (mathematics)|functions]] (Figure 2);
* calculate [[area]] and [[integral]] [[calculus]];
* [[linear algebra]]<ref name="R11"/>
Example Xcas commands:
* produce mixed fractions: <code>propfrac(42/15)</code> gives 2 + {{sfrac|4|5}}
* calculate square root: <code>sqrt(4)</code> = 2
* draw a vertical line in coordinate system: <code>line(x=1)</code> draws the vertical line <math>x=1</math> in the output window
* draw graph: <code>plot(function)</code> (for example, <code>plot(3 * x^2 - 5)</code> produces a plot of {{math|1=''y'' = 3''x''<sup>2</sup> − 5}}
* calculate average: <code>mean([3, 4, 2])</code> is 3
* calculate [[variance]]: <code>variance([3, 4, 2])</code> is {{sfrac|2|3}}
* calculate [[standard deviation]]: <code>stddev([3, 4, 2])</code> is {{sfrac|{{radic|6}}|3}}
* calculate [[determinant]] of a [[Matrix (mathematics)|matrix]]: {{code|det([[1,2], [3,4]])}} is {{val|-2}}
* calculate local extrema of a function: <code>extrema(-2*cos(x)-cos(x)^2,x)</code> is [0, π]
* calculate [[cross product]] of two [[Vector (mathematics and physics)|vector]]s: <code>cross([1, 2, 3], [4, 3, 2])</code> is {{math|[-5, 10, -5]}}
* calculate [[permutation]]s: <code>nPr()</code>
* calculate [[combination]]s: <code>nCr()</code>
* solve [[equation]]: <code>solve(equation,x)</code>
* factoring polynomials: <code>factor(polynomial,x)</code> or <code>cfactor(polynomial,x)</code>
* differentiation of function: <code>diff(function,x)</code>
* calculate indefinite integrals/antiderivatives: <code>int(function,x)</code>
* calculate definite integrals/area under the curve of a function: <code>int(function,x,lowerlimit,upperlimit)</code>
** calculate definite integral (also called [[solid of revolution]]) - finding volume by rotation (around the ''x''-axis): <code>int(pi*function^2,x,lowerlimit,upperlimit)</code>
** calculate definite integral (also called solid of revolution) - finding volume by rotation (around the ''y''-axis) for a decreasing function: <code>int(2*pi*x*function,x,lowerlimit,upperlimit)</code>
* [[separation of variables]]: <code>split((x+1)*(y-2),[x,y])</code> produces {{tmath|[x+1,y-2]}}
* desolve [[differential equation]] (the derivatives are written as y{{prime}} or y{{pprime}}): <code>desolve(differential equation,y)</code>

==Supported operating systems==
* [[Microsoft]] [[Microsoft Windows|Windows]]<ref name="R12"/>
* [[Apple Inc.|Apple]] [[macOS]]<ref name=":0"/>
* [[Linux]]/[[Unix]]<ref name="R13"/><ref name="R14"/>
* [[FreeBSD]]<ref name=":2"/>
* [[Android (operating system)|Android]]<ref name=":1"/>
* [[iOS]] (paid version)
* [https://www-fourier.univ-grenoble-alpes.fr/~parisse/xcasen.html Online]<ref name="R15"/>

==History==
Xcas and Giac are [[open-source software|open-source]] projects developed and written by {{ill|Bernard Parisse|fr}} and Renée De Graeve at the former [[Joseph Fourier University]] of [[Grenoble]] (now the [[Grenoble Alpes University]]),<ref name="R16"/> [[France]] since 2000.<ref name="University of Mons"/> Xcas and Giac are based on experiences gained with Parisse's former project [[Erable]].<ref name="R17"/>
[[Pocket CAS]] and [[CAS Calc P11]] utilize Giac.

The system was also chosen by [[Hewlett-Packard]] as the CAS for their [[HP Prime]] calculator, which utilizes the Giac/Xcas 1.5.0 engine under a dual-license scheme.

In 2013, the mathematical software Xcas was also integrated into [[GeoGebra]]'s CAS view.<ref name="R18"/>

== Use in education ==
Since 2015, Xcas is used in the [[French education system]].<ref name="R19"/><ref name="R20"/><ref name="R21"/><ref name="R22"/> Xcas is also<ref name="Module 2 - Introduction"/> used in [[Germany|German]]<ref name="Halkos"/> [[universities]],<ref name="R23"/><ref name="R24"/> and in [[Spain]] and [[Mexico]].<ref name="R25"/> It is also used at the [[University of North Carolina Wilmington]]<ref name="R26"/> and the [[University of New Mexico]].<ref name="R27"/> Xcas is used in particular for learning algebra.<ref name="R28"/>

== χCAS ==
There is a port of Giac/Xcas for [[Casio graphic calculators|Casio graphing calculators]] fx-CG10, fx-CG20, fx-CG50, fx-9750GIII and fx-9860GIII, called [https://www-fourier.ujf-grenoble.fr/~parisse/casio/khicasioen.html χCAS (KhiCAS)]. These calculators do not have their own [[computer algebra system]]. It is also available for [[TI-Nspire series|TI Nspire CX, CX-II]], and [[NumWorks|Numworks N0110]]<ref>{{Cite web|url=https://www-fourier.ujf-grenoble.fr/~parisse/install_en|title=Installing Xcas}}</ref>

==See also==
{{Portal|Mathematics|Free and open-source software}}
* [[Comparison of computer algebra systems]]
* [[WolframAlpha]]

==References==
{{Reflist|refs=
<ref name="R1">{{Cite web|url=https://pari.math.u-bordeaux.fr/Events/PARI2016/talks/Parisse.pdf|title=Giac/Xcas and Pari/GP}}</ref>
<ref name="R2">{{Cite web |title=Elsevier Enhanced Reader |url=https://reader.elsevier.com/reader/sd/pii/S2095034915302142?token=BE1FC741327E0877498CD798CFA7B4FBC7930B3B1AAC9B95F3BCC54C4AD39121EBA4DA737B4F42F988AF2ACBE0B0D1CB&originRegion=eu-west-1&originCreation=20220608080827 |access-date=2022-06-08 |website=reader.elsevier.com |language=en}}</ref>
<ref name="Tõnisson 2017">{{cite thesis |last1=Tõnisson |first1=Eno |title=Differences between expected answers and the answers offered by computer algebra systems to school mathematics equations |date=9 November 2017 |hdl=10062/58398 |hdl-access=free }}</ref>
<ref name="R3">{{Cite web|title=Computer Algebra in Education|url=https://math.unm.edu/~aca/ACA/2017/education.html|access-date=2022-01-03|website=math.unm.edu}}</ref>
<ref name="R4">{{Cite web|url=https://reposcope.com/package/xcas|title=xcas - Computer Algebra System - console and graphical calculator|website=reposcope.com|language=en|access-date=2020-04-12}}</ref>
<ref name="R5">{{Cite web|url=https://xcas.univ-grenoble-alpes.fr/forum/|title=Le forum de XCAS - Page d'accueil|website=xcas.univ-grenoble-alpes.fr|access-date=2020-04-12}}</ref>
<ref name="R6">{{Cite web|url=https://www-fourier.ujf-grenoble.fr/~parisse/giac/tutoriel_en.pdf|title=An introduction to the Xcas interface}}</ref>
<ref name="R7">{{cite news|title=MATHEMATICS EDUCATION AS A SCIENCE AND A PROFESSION|url=https://files.eric.ed.gov/fulltext/ED577935.pdf#page=201|access-date=2017-10-05|publisher=Josip Juraj Strossmayer University of Osijek|date=2019-05-02}}</ref>
<ref name="reference-card">{{Cite web|url=https://www.yumpu.com/en/document/read/21966726/xcas-reference-card|title = Xcas reference card}}</ref>
<ref name="Gandit2009">{{cite conference |first1=Michèle |last1=Gandit |title=Experimenting and proof in mathematics with XCAS |editor1-last=Bardini |editor1-first=C. |editor2-last=Fortin |editor2-first=P. |editor3-last=Oldknow |editor3-first=A. |editor4-last=Vagost |editor4-first=D. |conference=Proceedings of the 9th International Conference on Technology in Mathematics Teaching |date=2009 |location=Metz, France |citeseerx=10.1.1.580.4878 }}</ref>
<ref name="R8">{{cite journal |last1=Halkos |first1=George E. |last2=Tsilika |first2=Kyriaki D. |title=Using Xcas in Calculus Curricula: a Plan of Lectures and Laboratory Projects |journal=Computational and Applied Mathematics Journal |date=2015 |volume=1 |issue=3 |url=http://www.aascit.org/journal/archive2?journalId=928&paperId=1966 |s2cid=58451849 }}</ref>
<ref name="R9">{{cite journal |last1=Halkos |first1=George E. |last2=Tsilika |first2=Kyriaki D. |last3=Simos |first3=Theodore E. |last4=Psihoyios |first4=George |last5=Tsitouras |first5=Ch. |last6=Anastassi |first6=Zacharias |title=Xcas as a Programming Environment for Stability Conditions for a Class of Differential Equation Models in Economics |journal=Numerical Analysis and Applied Mathematics Icnaam 2011: International Conference on Numerical Analysis and Applied Mathematics |series=AIP Conference Proceedings |date=2011 |volume=1389 |issue=1 |pages=1769–1772 |doi=10.1063/1.3636951 |bibcode=2011AIPC.1389.1769H |doi-access=free }}</ref>
<ref name="R10">{{cite book |doi=10.1007/978-3-319-69242-5_6 |chapter=Integration and Differential Equations |title=Mathematics for Earth Science and Geography |series=Springer Textbooks in Earth Sciences, Geography and Environment |date=2019 |last1=Fleurant |first1=Cyril |last2=Bodin-Fleurant |first2=Sandrine |pages=145–177 |isbn=978-3-319-69241-8 |s2cid=189288194 }}</ref>
<ref name="R11">{{cite news|title=Computeralgebra-Rundbrief Nr. 62: Fachgruppe Computeralgebra |url=http://www.fachgruppe-computeralgebra.de/data/CA-Rundbrief/car62.pdf|access-date=2018-03-02|publisher=Gesellschaft für Informatik e.V.|date=2019-05-02}} (in German)</ref>
<ref name="R12">{{cite news|title=Xcas for Windows|url=https://www.logitheque.com/en/software/windows/education/maths-and-arithmetic/download/xcas_62297.htm|access-date=2018-12-05|publisher=logitheque|date=2016-06-09}}</ref>
<ref name=":0">{{Cite web |title=Installing Xcas |url=https://www-fourier.ujf-grenoble.fr/~parisse/install_en.html |access-date=2021-11-14 |website=www-fourier.ujf-grenoble.fr}}</ref>
<ref name="R13">{{cite news|title=Symbolic Algebra Everywhere|url=https://www.linuxjournal.com/content/symbolic-algebra-everywhere|access-date=2018-12-05|publisher=Joey Bernard|date=2015-12-15}}</ref>
<ref name="R14">{{Cite web|url=https://www.scribd.com/document/363002275/Xcas-Calcul-Formel-Lycee|title=Xcas Calcul Formel Lycee &#124; PDF &#124; Intégral &#124; Variable (Mathématiques)|website=Scribd}}</ref>
<ref name=":2">{{Cite web |title=Giac/Xcas, a free computer algebra system |url=https://www-fourier.ujf-grenoble.fr/~parisse/giac.html |access-date=2022-02-10 |website=www-fourier.ujf-grenoble.fr}}</ref>
<ref name=":1">{{Cite web|title=Xcas Pad – Apps i Google Play|url=https://play.google.com/store/apps/details?id=org.kde.necessitas.mucephi.android_xcas&hl=da&gl=US|access-date=2021-11-14|website=play.google.com|language=da}}</ref>
<ref name="R15">{{Cite web |title=Xcas en ligne |url=https://www.xcasenligne.fr/giac_online/demoGiacPhp.php |access-date=2022-03-18 |website=www.xcasenligne.fr}}</ref>
<ref name="R16">{{Cite web|title=Planète MATHS - Liste des ressources par niveau|url=http://www.ac-grenoble.fr/disciplines/maths/pages/PM/Affichage/FicheNiveau.php?niveau=9|access-date=2022-01-03|website=www.ac-grenoble.fr}}</ref>
<ref name="University of Mons">{{cite conference |last1=Fekih |first1=Lassaad Ben |last2=Verlinden |first2=Olivier |last3=Kouroussis |first3=Georges |date=2011 |title=Development of a user-friendly and open-source multibody framework with the help of symbolic tools |conference=4th International Congress Design and Modelling of Mechanical Systems |location=Sousse (Tunisia)}}</ref>
<ref name="R17">{{cite journal |last1=MacCallum |first1=Malcolm A. H. |title=Computer algebra in gravity research |journal=Living Reviews in Relativity |date=December 2018 |volume=21 |issue=1 |pages=6 |doi=10.1007/s41114-018-0015-6 |pmid=30174551 |pmc=6105178 |bibcode=2018LRR....21....6M }}</ref>
<ref name="R18">{{Cite web|title=Xcas {{!}} Semantic Scholar|url=https://www.semanticscholar.org/topic/Xcas/472762|access-date=2022-02-10|website=www.semanticscholar.org|language=en}}</ref>

<ref name="R19">{{Cite web|title=Liens mathématiques - Lycée Rosa Parks de Montgeron|url=http://www.lyc-rosaparks-montgeron.ac-versailles.fr/spip.php?article329|access-date=2022-01-03|website=www.lyc-rosaparks-montgeron.ac-versailles.fr}}</ref>
<ref name="R20">{{Cite web|title=M@ths en LIgne|url=https://membres-ljk.imag.fr/Bernard.Ycart/mel/|access-date=2022-01-03|website=membres-ljk.imag.fr}}</ref>
<ref name="R21">{{Cite web|title=Articles en ligne|url=https://www.epi.asso.fr/revue/articsom.htm|access-date=2022-01-03|website=www.epi.asso.fr}}</ref>
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<ref name="Module 2 - Introduction">{{Cite web |title=Module 2 - Introduction |url=https://www.didaktik.mathematik.uni-wuerzburg.de/edumatics/mod2/technology.html |access-date=2022-01-03 |website=www.didaktik.mathematik.uni-wuerzburg.de}}</ref>
<ref name="Halkos">{{Cite web |last1=Halkos |first1=George |last2=Tsilika |first2=Kyriaki |date=November 2014 |title=Perspectives on integrating a computer algebra system into advanced calculus curricula |url=https://mpra.ub.uni-muenchen.de/63898/ |access-date=2022-01-03 |website=mpra.ub.uni-muenchen.de |language=en}}</ref>
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<ref name="R26">{{Cite web|title=Xcas_session|url=http://people.uncw.edu/freezem/tools/webxcas/webxcas2.htm|access-date=2022-01-03|website=people.uncw.edu}}</ref>
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<ref name="R28">{{Cite web |title=THE DERIVE - NEWSLETTER #99 |url=http://www.austromath.at/dug/dnl99.pdf }}</ref>
}}

==Further reading==
* {{cite web |title=Symbolic computation and Mathematics with the calculator HP Prime |author-first=Renée |author-last=De Graeve |translator-first=Jean Michel |translator-last=Lecointre |date=2018-01-19 |orig-date=2013 |url=https://www-fourier.ujf-grenoble.fr/~parisse/hp-prime_cas.pdf |access-date=2018-01-22 }}
* Parisse, Bernard (2007): "[http://www-fourier.ujf-grenoble.fr/~parisse/giac/cascmd_en.pdf Symbolic algebra and Mathematics with Xcas]" (list of commands) (PDF). Retrieved 2022-06-08.
* Parisse, B., University of Grenoble (January, 2016) "[https://pari.math.u-bordeaux.fr/Events/PARI2016/talks/Parisse.pdf Giac/Xcas and Pari/GP]" (PDF). Retrieved 2022-06-08.
* {{cite web |title=Perspectives on integrating a computer algebra system into advanced calculus curricula |author-first=George |author-last=Halkos |date=2015-04-25 |orig-date=2014 |url=https://mpra.ub.uni-muenchen.de/63898/1/MPRA_paper_63898.pdf |access-date=2019-09-06}}
* Verlinden, Olivier (2013): "[https://www.sciencedirect.com/science/article/pii/S2095034915302142 Symbolic generation of the kinematics of multibody systems in EasyDyn: From MuPAD to Xcas/Giac].". Retrieved 2022-06-08.
* [http://www.mathsaulycee.sitew.com/fs/premiere_s/8uoow-xcas_commande_utile.pdf Commandes XCAS] (French)
* [http://briand-lyc.spip.ac-rouen.fr/IMG/pdf/xcas_fonctions.pdf Les principales fonctions de XCAS en calcul formel pour le lycée](French)
* Barnard Parisse: ''[https://www.apmep.fr/IMG/pdf/16-Xcas.pdf Mathématiques avec Xcas]''. (French)
*[https://visca.pagesperso-orange.fr/html/xcas.html Les Maths et Mes Tics] {{Webarchive|url=https://web.archive.org/web/20220702142837/https://visca.pagesperso-orange.fr/html/xcas.html |date=2022-07-02}} (French)
* Fabian Reimers (editor): "''[https://www.fachgruppe-computeralgebra.de/data/CA-Rundbrief/car62.pdf Computeralgebra-Rundbrief] Nr. 62'': ''Fachgruppe Computeralgebra''" (PDF). (German)

==External links==
* {{Official website|www-fourier.ujf-grenoble.fr/~parisse/giac.html}}
* [https://www-fourier.ujf-grenoble.fr/~parisse/xcasen.html Use Xcas online in your web browser]

{{Computer algebra systems}}

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[[Category:Computer algebra system software for Linux]]
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[[Category:Free software programmed in C++]]