Presentation of Xcas , the swiss knife for mathematics.

Abstract

• Xcas is an interface to perform computer algebra, function graphs, interactive geometry (2-d and 3-d), spreadsheet and statistics, programmation. It may be used as a replacement for high end graphic calculators for example on netbooks (for about the same price as a calculator but with much more performances).
• Giac is a free (GPL) C++ library, it is the computation kernel, it may be used inside other C++ programs.
• Giac/Xcas has a compatibility mode for people used to the Maple or Mupad CAS as well as for users of TI calculators (TI89, Voyage 200, TI Nspire CAS).
• Short history: The Giac/Xcas project began in year 2000, following the development of the CAS for HP calculators. It has now around 150,000 lines of C++ code (most written by B. Parisse), and around 300 pages of English documentation (most written by R. De Graeve). It has interfaces with php, latex, texmacs and soon java, playing the role of computation kernel. It also interfaces with PARI, CoCoA, NTL, GSL, GMP, MPFR. Current development directions include faster algorithms for the mostly used operations: multiplication, division, gcd of multivariate polynomials. Giac/Xcas was awarded the 3rd price at the Trophées du Libre 2007 in the scientific software category. The presentation of Giac/Xcas at the Trophées du Libre 2007 is available here.

Main features of Xcas

	CAS: arbitrary precision integer and floats, integer and polynomial arithmetic (gcd, extended gcd, factorisation, ...), simplification, equation solver, partial fraction decomposition, calculus (derivation, integration, limit, series expansion), linear algebra (vectors, matrices, row reduction to echelon form, eigenvalues and eigenvectors)...
	2-d geometry: point, segment, line, triangle, polygons, circles, conics, parametric curves, intersection, tangents... Dynamic geometry. All geometric instructions are programmable
	3-d geometry and graphs: point, segment, line, plan, triangle, polygons, circles, conics, parametric curves, surfaces, intersection, tangents... Dynamic geometry. All geometric instructions are programmable
	Spreadsheet : relative and absolute references, cells can contain formal objects (e.g 1/2, sin(x), ...), 1-d and 2-d statistics (mean, stddev, hgistogram, covariance, regressions, ...)
	Programmation : functions, local variables, tests, loops. Choice of syntax (C-like, Maple, Mupad, TI89). It is sometimes possible to run a Maple, MuPAD or TI89 without user intervention inside Xcas. Program editor. Interactive debugguer.
	Mixing different level types

Giac

Giac in console mode

LaTeX and Giac

• pgiac is a perl script that translate a .w file into a .tex file by running somme commands (lines beginning with a .g or sections beginning with .g: and ending with .end) with giac. The resulting .tex file will contain the answers of the computations and may be compiled using your prefered LaTeX distribution. By J.M. Sarlat, in French.
• tablor.sty is a LaTeX style file that automates the process of describing the variations of a function inside a LaTeX document. By Guillaume Connan, in French. Also available inside texmacs via the professor and tablor plugin by E. Corcelle.
• See also some examples of LaTeX and giac interaction by Yves Delhaye , Guillaume Connan or Alexandre Boisseau.

About Xcas

(Incomplete) documentation

• Xcas tutorial on-line or PDF.
• Reference guide on-line or PDF
• Giac info documentation

Thanks to

• Renée De Graeve for her interest, beta testing and documentation writing.
• Jean-Pierre Branchard (Giac on-line and exomaths), see his home site
• Carlos Enriqe Carleos Artime for doing the Debian packages and several fixes in the giac build process.
• Alkiviadis Akritas, Eugenia Kelepesi-Akritas, George Nasopoulos for the Greek localization.
• Jose Manrique Lopez de la Fuente for his interest, Spanish translation of the documentation and on-line help, info about the FLVW library, Giac/xcas advertising. Have a look at his SDA project English , Espanol
• Jean-Yves Avenard for the first Mac OS X port
• Dirk Eddelbuettel for including giac in his Quantian scientific linux-live CD.
• the GiNaC crew for their interest, particulary R. Kreckel and recently A. Sheplyakov for doing the hard and annoying work of autoconfiguration/automake of giac
• Mike Ady for tests and improvement suggestions especially for the Windows version.
• Joris van der Hoeven for texmacs and integration of the giac interface
• IREM de Grenoble for xcas testings in highschools, especially Michèle Gandit and her class (Grenoble), Christianne Serret and her class (Crest), and for the Mac OS X port.
• CETRIL who organizes the Trophee du libre awards, where Xcas obtained rank 3 in the Scientific software category in 2007.
• Bernard Ycart for the French Xcas beginner documentation
• Michael Eisermann, Dominique Spehner and all the students of the Université de Grenoble I following the "mat249" course who experimented xcas and helped fixing bugs.
• Emilien Kia and Andreas Thillosen for the wxcas interface and numerous suggestions for giac, including parallel execution and the sourceforge project.
• Guillaume Connan and his classes.
• Francois Boisson (Clef Agreg)
• Stéphane Lejoly for Mac testings (including a few hard crash).
• Frédéric Han for the FreeBSD port.
• Jean-Joel Bataille for testings, especially the alien-converted RPM package.
• Emmanuel Peyre (command open to open files on a Mac)
• Pierre Rochard for the first linux PPC port.
• All testers, especially (by alphabetic order) Frederic Faure, Bruno Patin, Juan Antonio Martinez Rojas, Nicolas Rosillo, ... sorry for those I forgot!