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Xcas
Computer algebra system From Wikipedia, the free encyclopedia
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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++.
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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]
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Features
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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 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)orcfactor(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)
- calculate definite integral (also called solid of revolution) - finding volume by rotation (around the x-axis):
- separation of variables:
split((x+1)*(y-2),[x,y])produces - desolve differential equation (the derivatives are written as y′ or y″):
desolve(differential equation,y)
![{\displaystyle [x+1,y-2]}](http://wikimedia.org/api/rest_v1/media/math/render/svg/3d9c503aafd0cd278c812fc7499a03942d7da55a)
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Supported operating systems
History
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]
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 is used in particular for learning algebra.[39]
χCAS
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]
See also
References
Further reading
External links
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