Xcas
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Xcas
Xcas does solve differential equations

Developer(s) Bernard Parisse 2000; 21 years ago 1.5.0-85 / 12 December 2019 sourceforge.net/p/xcas/code/HEAD/tree/ C++ Windows, macOS, Linux, FreeBSD Computer algebra system GNU GPL www-fourier.ujf-grenoble.fr/~parisse/giac.html

Xcas is a user interface to Giac, which is a free,[1]open source[2] basic Computer Algebra System (CAS)[3] for Microsoft Windows, Apple macOS, Linux, and FreeBSD;[4] Xcas is written in C++.[5] Giac can be used directly inside software written in C++.

Giac has a compatibility mode with WolframAlpha,[6]Mathematica, Maple,[7]MuPAD, Matlab, Yacas, SageMath, Qcas, ExpressionsinBar (64 bit app for macOS)[8][9] and Magma, CPMP-Tools, WordMat (addon to Microsoft Word)[10] software and TI-89, TI-92, Voyage 200 and TI-Nspire calculators.[11] Users can use Giac/Xcas as well as a free software compatible with Maple to develop formal algorithms or use it in other software. Xcas is used in SageMath for calculus operations. Among other things Xcas can solve equations and draw graphs. There is a forum for questions about Xcas.[12]

CmathOOoCAS, an OpenOffice.org plugin which allows formal calculation in Calc spreadsheet and Writer word processing, uses Xcas to perform calculations.

## Features

Here is a brief overview of what Xcas is able to do:[13]

## Some Xcas commands

• propfrac(42/15) = 2 + 4/5
• Calculate square root = sqrt(4) = 2
• Draw a vertical line in coordinate system: line(${\displaystyle x}$ =1) = the vertical line ${\displaystyle x}$=1
• Draw graph: plot(function)
• Calculate average: mean([3, 4, 2]) = 3
• Calculate variance: variance([3, 4, 2]) = 2/3
• Calculate standard deviation: stddev([3, 4, 2]) = sqrt(2/3)
• Calculate determinant of a matrix: det([[1,2], [3,4]]) = -2
• Calculate local extrema of a function: extrema(-2*cos(${\displaystyle x}$)-cos(${\displaystyle x}$)^2,${\displaystyle x}$) = [0], [pi]
• Calculate cross product of two vectors: cross([1, 2, 3], [4, 3, 2]) = [-5, 10, -5]
• Calculate permutations: nPr
• Calculate combinations: nCr
• Solve equation: solve(equation,${\displaystyle x}$)
• Factoring Polynomial: factor(polynomial,${\displaystyle x}$) or cfactor(polynomial,${\displaystyle x}$)
• Differentiation of function: diff(function,${\displaystyle x}$)
• Calculate integral aka antiderivative: int(function,${\displaystyle x}$)
• Calculate definite integral aka area under curve: int(function,${\displaystyle x}$,lowerlimit,upperlimit)
• Calculate definite integral aka solid of revolution - finding volume by rotation (around the ${\displaystyle x}$ axis): int(pi*function^2,${\displaystyle x}$,lowerlimit,upperlimit)
• Calculate definite integral aka Solid of Revolution - finding volume by rotation (around the ${\displaystyle y}$ axis) for a decreasing function: int(2*pi*${\displaystyle x}$*function,${\displaystyle x}$,lowerlimit,upperlimit)
• Separation of variables: split((${\displaystyle x}$+1)*(${\displaystyle y}$-2),[${\displaystyle x}$,${\displaystyle y}$]) = [${\displaystyle x}$+1,${\displaystyle y}$-2]
• desolve differential equation (right side of Differential Equation written as ${\displaystyle y'}$or ${\displaystyle y''}$): desolve(differential equation,${\displaystyle y}$)

or read more commands and features here: http://www-fourier.ujf-grenoble.fr/~parisse/giac/cascmd_en.pdf

## History

Xcas and Giac are open-source projects [23] developed by Bernard Parisse[24] et al. at the Joseph Fourier University of Grenoble (Isère), France, since 2000.[5] Xcas and Giac are based on experiences gained with Parisse's former project Erable.[25] In 2013 the mathematical software Xcas was also integrated into GeoGebra's CAS view.[26] Since 2013 there are videos showing how Xcas works.[23][27]

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 1.4.9 engine under a dual-license scheme.

## References

1. ^ "Berkeley Madonna alternatives". getalternative.net. Retrieved .
2. ^ "COMPARISON OF OPEN SOURCE SOFTWARES IN MATHEMATICS EDUCATION". Konuralp Journal of Mathematics. 2019-05-02. Retrieved .
3. ^ "Computer algebra in gravity research". University of Mons. 2019-05-05. Retrieved .
4. ^ "Freeware and Open Source Software Tools for Distance Learning in Mathematics". University of Mons. 2019-05-05. Retrieved .
5. ^ a b "Development of a user-friendly and open-source multibody framework with the help of symbolic tools". University of Mons. 2019-05-05. Retrieved .
6. ^
7. ^ "xcas - Computer Algebra System - console and graphical calculator". reposcope.com. Retrieved .
8. ^ "ExpressionsinBar". www.alelvisoftware.com. Retrieved .
9. ^
10. ^ "WordMat". Microsoft WordMat. Retrieved .
11. ^ https://swmath.org/software/6662
12. ^ "Le forum de XCAS - Page d'accueil". xcas.univ-grenoble-alpes.fr. Retrieved .
13. ^ "MATHEMATICS EDUCATION AS A SCIENCE AND A PROFESSION" (PDF). Josip Juraj Strossmayer University of Osijek. 2019-05-02. Retrieved .
16. ^ "Using Xcas in Calculus Curricula: a Plan of Lectures and Laboratory Projects" (PDF). Computational and Applied Mathematics Journal. 2019-11-15. Retrieved .
17. ^ Halkos, George E.; Tsilika, Kyriaki D. (2011). "Xcas as a Programming Environment for Stability Conditions for a Class of Differential Equation Models in Economics". American Institute of Physics Conference Series. 1389 (1): 1769. Bibcode:2011AIPC.1389.1769H. doi:10.1063/1.3636951.
18. ^
19. ^ "Computeralgebra-Rundbrief Nr. 62: Fachgruppe Computeralgebra" (PDF). (Gesellschaft fuer Informatik e.V. 2019-05-02. Retrieved . (in German)
20. ^ "Xcas for Windows". logitheque. 2016-06-09. Retrieved .
21. ^ "Symbolic Algebra Everywhere". Joey Bernard. 2015-12-15. Retrieved .
22. ^ https://www.scribd.com/document/363002275/Xcas-Calcul-Formel-Lycee
24. ^
25. ^ "Computer algebra in gravity research". University of Mons. 2019-05-05. Retrieved .
26. ^ "Xcas". SemanticScholar. 2016-06-09. Retrieved .
27. ^