Xcas

Xcas is a user interface to Giac, which is an open source^[2] computer algebra system (CAS) for Windows, macOS and Linux among many other platforms. Xcas is written in C++.^[3] Giac can be used directly inside software written in C++.

Xcas has compatibility modes with many popular algebra systems like WolframAlpha,^[4] Mathematica,^[5] Maple,^[6] or MuPAD. Users can use Giac/Xcas to develop formal algorithms or use it in other software. Giac is used in SageMath^[4] for calculus operations. Among other things, Xcas can solve differential equations (Figure 3) and draw graphs. There is a forum for questions about Xcas.^[7]

CmathOOoCAS, an OpenOffice.org plugin which allows formal calculation in Calc spreadsheet and Writer word processing, uses Giac to perform calculations.^[8]

Here is a brief overview of what Xcas is able to do:^[9][10]

• Xcas has the ability of a scientific calculator that provides show input and writes pretty print
• Xcas also works as a spreadsheet;^[11]
• computer algebra;
• 2D geometry in the plane;^[12]
• 3D geometry in space;^[12]
• spreadsheet;^[11]
• statistics;
• regression (exponential, linear, logarithmic, logistic, polynomial, power)
• programming;^[13]
• solve equations even with complex roots (Figure 2);
• solving trigonometric equations
• solve differential equations^[14][15] (Figure 3);
• draw graphs;
• calculate differential (or derivative) of functions (Figure 2);
• calculate antiderivative of functions (Figure 2);
• calculate area and integral calculus;
• linear algebra^[16]

Example Xcas commands:

• produce mixed fractions: propfrac(42/15) gives 2 + ⁠4/5⁠
• calculate square root: sqrt(4) = 2
• draw a vertical line in coordinate system: line(x=1) draws the vertical line ${\displaystyle x=1}$ in the output window
• draw graph: plot(function) (for example, plot(3 * x^2 - 5) produces a plot of y = 3x² − 5
• calculate average: mean([3, 4, 2]) is 3
• calculate variance: variance([3, 4, 2]) is ⁠2/3⁠
• calculate standard deviation: stddev([3, 4, 2]) is ⁠√6/3⁠
• calculate determinant of a matrix: det([[1,2], [3,4]]) is −2
• calculate local extrema of a function: extrema(-2*cos(x)-cos(x)^2,x) is [0, π]
• calculate cross product of two vectors: cross([1, 2, 3], [4, 3, 2]) is [-5, 10, -5]
• calculate permutations: nPr()
• calculate combinations: nCr()
• solve equation: solve(equation,x)
• factoring polynomials: factor(polynomial,x) or cfactor(polynomial,x)
• differentiation of function: diff(function,x)
• calculate indefinite integrals/antiderivatives: int(function,x)
• calculate definite integrals/area under the curve of a function: int(function,x,lowerlimit,upperlimit)
  • calculate definite integral (also called solid of revolution) - finding volume by rotation (around the x-axis): int(pi*function^2,x,lowerlimit,upperlimit)
  • calculate definite integral (also called solid of revolution) - finding volume by rotation (around the y-axis) for a decreasing function: int(2*pi*x*function,x,lowerlimit,upperlimit)
• separation of variables: split((x+1)*(y-2),[x,y]) produces ⁠${\displaystyle [x+1,y-2]}$⁠
• desolve differential equation (the derivatives are written as y′ or y″): desolve(differential equation,y)

• Microsoft Windows^[17]
• Apple macOS^[18]
• Linux/Unix^[19][20]
• FreeBSD^[21]
• Android^[22]
• iOS (paid version)
• Online^[23]

Xcas and Giac are open-source projects developed and written by Bernard Parisse and Renée De Graeve at the former Joseph Fourier University of Grenoble (now the Grenoble Alpes University),^[24] France since 2000.^[25] Xcas and Giac are based on experiences gained with Parisse's former project Erable.^[26] 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.^[27]

Since 2015, Xcas is used in the French education system.^{[28][29][30][31]} Xcas is also^[32] used in German^[33] universities,^[34][35] and in Spain and Mexico.^[36] It is also used at the University of North Carolina Wilmington^[37] and the University of New Mexico.^[38] Xcas is used in particular for learning algebra.^[39]

There is a port of Giac/Xcas for Casio graphing calculators fx-CG10, fx-CG20, fx-CG50, fx-9750GIII and fx-9860GIII, called χCAS (KhiCAS). These calculators do not have their own computer algebra system. It is also available for TI Nspire CX, CX-II, and Numworks N0110^[40]

• Comparison of computer algebra systems
• WolframAlpha

• De Graeve, Renée (2018-01-19) [2013]. "Symbolic computation and Mathematics with the calculator HP Prime" (PDF). Translated by Lecointre, Jean Michel. Retrieved 2018-01-22.
• Parisse, Bernard (2007): "Symbolic algebra and Mathematics with Xcas" (list of commands) (PDF). Retrieved 2022-06-08.
• Parisse, B., University of Grenoble (January, 2016) "Giac/Xcas and Pari/GP" (PDF). Retrieved 2022-06-08.
• Halkos, George (2015-04-25) [2014]. "Perspectives on integrating a computer algebra system into advanced calculus curricula" (PDF). Retrieved 2019-09-06.
• Verlinden, Olivier (2013): "Symbolic generation of the kinematics of multibody systems in EasyDyn: From MuPAD to Xcas/Giac.". Retrieved 2022-06-08.
• Commandes XCAS (French)
• Les principales fonctions de XCAS en calcul formel pour le lycée(French)
• Barnard Parisse: Mathématiques avec Xcas. (French)
• Les Maths et Mes Tics Archived 2022-07-02 at the Wayback Machine (French)
• Fabian Reimers (editor): "Computeralgebra-Rundbrief Nr. 62: Fachgruppe Computeralgebra" (PDF). (German)

• Official website
• Use Xcas online in your web browser