Xcas

Xcas, the swiss knife for mathematics
Developer(s)	Bernard Parisse [fr]
Initial release	2000; 24 years ago (2000)
Stable release	1.9.0.93[1]  (14 February 2024; 47 days ago (14 February 2024))
Repository	sourceforge.net/p/xcas/code/HEAD/tree/
Written in	C++
Operating system	Windows, macOS, Linux, FreeBSD, Android, iOS
Type	Computer algebra system (CAS)
License	GNU GPL
Website	xcas.univ-grenoble-alpes.fr/en.html

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 equations (Figure 3) and differential equations (Figure 4) 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]

Features

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 works also 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 aka solid of revolution - finding volume by rotation (around the x-axis): int(pi*function^2,x,lowerlimit,upperlimit)
  • Calculate definite integral aka 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)

Supported operating systems

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

History

Xcas and Giac are open-source projects developed and written by Bernard Parisse [fr] 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]

Use in education

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^[39] is used in particular for learning algebra.^[40]

χCAS

There is a port of Giac/Xcas for Casio graphing calculators: fx-CG10, fx-CG20, fx-CG50, fx-9750GIII, 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^[41]