Presentation

I'm working in Grenoble since 1992. My initial research domain was mathematical physics. I started programming small programs on HP48 calculators, it became later popular and my colleague Renée De Graeve contacted HP. I worked with HP one year on the HP49G CAS (the same CAS was later available on the HP40G, 40GS, 49G+ and 50G).
In year 2000, I started with Renée a free computer algebra system programmed in C++, named Giac/Xcas, Giac is the computing kernel, Xcas is one of its interfaces I maintain myself. Giac can be used in several contexts: from embedded systems in calculators (minimal requirements: 2Mo of ROM and 128K of RAM) to big computations of Groebner basis on servers with 80 threads in parallel. It is used by projects like Geogebra, the HP Prime calculator CAS, the PocketCAS software for iPhone/iPad/Mac, also ported to other calculator manufacturers, like the Casio Prizm family or the TI Nspire CX and CX2. It is used internally by the Goodnotes app to check some maths while student are training for tests. It is available as a standard package on most Linux distributions, and is also a standard package for SageMath.

Computer algebra system

Giac/xcas, a free computer algebra system

Giac/Xcas is a free computer algebra system for Windows, Mac OS X and Linux/Unix (license GPL3). It has a compatibility mode for maple, mupad and the TI89. It is available as a standalone program (graphic or text interfaces) or as a C++ library. It's name is derived from GiNaC and means Giac Is A Computer algebra system.

• Download xcas
• Xcas reference card,
• Test giac offline (download once), like a calc Smartcas (N. Pujol)
• Create interactive HTML pages (with Giac CAS computing kernel) with simple modifications in your LaTeX source files: latex+hevea+giac
• Discuss xcas on the forum.
• Some documentation is available in English PDF or Espanol on-line . The complete documentation is available in French.
• For more information on the Giac/xcas project, visit its homepage

CAS e-prints

• Certifying a probabilistic parallel modular algorithm for rational univariate representation (2021) Arxiv
• Computing huge Groebner basis like cyclic10 over Q with Giac (2019) Arxiv
• Compiling LATEX to computer algebra-enabled HTML5 (2017) Arxiv
• Sparse multivariate factorization by mean of a few bivariate factorizations (2016) Arxiv
• A probabilistic and deterministic modular algorithm for computing Groebner basis over Q (2013) Arxiv, some ideas are already in N.Idrees/ G.Pfister/ S. Steidel: Parallelization of Modular Algorithms, Journal of Symbolic Computation 46 (2011) 672-684
• Jordan Normal and Rational Normal Form Algorithms, in collaboration with M. Vaughan (2004): Arxiv PDF, LaTeX, maple/xcas source.
• A correct proof of the heuristic GCD algorithm (2002): Arxiv PDF, LaTeX.

HP Prime

Giac/Xcas is the native CAS of the HP Prime calculator and Android, iOS, Windows/Mac applications emulating the HP Prime. Press the CAS key and try Xcas commands, most of them work unchanged Documentation by Renée De Graeve, translated by J.M. Lecointre.

Old HP Calculators

I'm the main author of the CAS of the HP49G, HP40G, HP49G+ and HP48GII calculators. I have also developped in 2005 an interactive and analytic geometry module.

HP CAS documentation

HP49G, HP49G+, HP48GII, HP50G documentation

CAS documentation for all ROM versions PDF or LaTeX, by Renée De Graeve , translated by Ivan Cibrario Bertolotti

HP40G/GS CAS documentation

• HP40GS : CAS in Equationwriter and HOME, including symbolic matrix instructions not available in HP manual: PDF, LaTeX, available under the FDL license.
• HP40G : translation of the original CAS manual made by Mark Howell for HP: DOC, Postscript,

HP49G CAS source code

The source code of my contribution to the HP49G CAS is released under the LGPL license of the Free Software Foundation. If you want to modify the CAS on your calculator, please get the file casrelease.zip, unzip it, and follow the instructions in the file CASrelease/README. Warning, the file casrelease.zip is not released under the LGPL license and may not be redistributed as is. The files subject to the LGPL license are all the files contained in the CASrelease/ROM/CAS and CASrelease/ROM/CAS2 directories except files containing ALG48 code, namely CAS/berle.s*, CAS/binary.s*, CAS/distdiv.s*, CAS/error.s*, CAS/errors.s*, CAS/grobner.s*, CAS/mkpoly.s*, CAS/pfctr.s*, CAS/prime.s*, CAS/qarth.s*, CAS/root.s*, CAS/smod.s*, CAS/util.s*, CAS/zckconv.s*, CAS/zcmp.s*, CAS/znext.s*, CAS/zpush.s*, CAS/zsutil.s*, CAS/ztests.s*, CAS2/asmgamma.s*, CAS2/asmpsi.s*, CAS2/numgamma.s*, CAS2/numpsi.s*, CAS2/qpi.s*, CAS2/symgamma.s*, CAS2/sympsi.s*, CAS2/util.s*, CAS2/zfact.s*

HP49/50 Interative Geometry

To be used in conjunction with the CASrelease above. This application is released under the GPL license (for dual-licensing contact the author):

• ROM files for 49G/G+/50G. These ROMs provide also a small spreadsheet.
• Documentation in English
• To get it from source, copy the files geo.s and cas2user.s in CASrelease/ROM/CAS2/
• In CASrelease/ROM/CAS2/sload.nn add the line
  REL geo.o
  after the line REL bank64.o
• You can also add ROMPTR xGEO at line 617 in CAS2/interf.s
• Do a make in the CASrelease/ROM directory
• Reflash your calc. It is a good idea to reflash the whole system unless you have previously flashed the 49 with casrelease. Otherwise erasing bank 7 and reflashing it is sufficient.

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Mathematical physics

Publications

• Liens entre les résonances pour l'opérateur de Dirac et de Schrodinger, Equations Dériv. Partielles, St. Jean-De-Monts, vol 12, 1990.
• Résonances pour l'opérateur de Dirac, PhD thèsis, Orsay, 1992
• Résonances pour l'opérateur de Dirac-II, Helvetica Physica Acta, vol 65 (1992), pp. 1077-1118
• Approximation des valeurs propres de certaines perturbations singulières et application à l'opérateur de Dirac, in collaboration with A. Mohamed, Annales de l'Institut Henri Poincaré- Physique Théorique, vol. 56 (3), pp. 235-277, 1992
• Asymptotique de la Largeur de la Première Bande de l'Opérateur de Dirac avec Potentiel Périodique, in collaboration with A. Mohamed et Outassourt Helvetica Physica Acta, vol. 66, 1993, pp. 192-215
  Erratum vol. 68, 1995, pp. 187-188
• Comparaison entre la décroissance de fonctions propres de l'opérateur de Dirac et de Klein-Gordon. Application à l'étude de l'effet tunnel, in collaboration with Bernard Helffer, Annales de l'Institut Henri Poincaré- Physique Théorique, vol. 60 (2), pp. 147-187, 1994
• Équilibre instable en régime semi-classique I , in collaboration with Yves Colin de Verdière, Communications in Partial Differential Eq uations, vol. 19 (9-10), pp. 1535-1563, 1994, PDF
• Équilibre instable en régime semi-classique II , in collaboration with Yves Colin de Verdière, Annales de l'Institut Henri Poincaré- Physique Théorique, vol 61 (3), pp. 347-367, 1994 PDF
• Effet d'Aharonov-Bohm sur un état borné de l'opérateur de Dirac, Asymptotic Analysis, vol. 10, pp. 199-224, 1995.
• Singular Bohr-Sommerfeld rules (III) , in collaboration with Yves Colin de Verdière, Communication Math. Phys., vol. 205, pp. 459-500, 1999 Postscript
• Construction BKW pour l'opérateur de Dirac. Cas d'un potentiel périodique. in collaboration with A. Mohamed, Annales de l'Institut Henri Poincaré- Physique Théorique, vol.70 (4), pp. 341-367, 1999, online HTML , postscript ou HTML archive
• Semi-classical study of the origin of quantized Hall conductance in periodic potentials, in collaboration with Frédéric Faure, Journal of Mathematical Physics, vol. 41 (1), pp. 62-75, 2000

Preprint

Construction BKW en fonds de puits, cas particuliers (Dirac, Schrodinger avec champ magnétique) : PDF format or LaTeX source

Lecture notes

Cours de gémétrie différentielle et symplectique , course of the Ecole d'été sur les D-modules (Institut Fourier, Grenoble, June 1995), available as on-line HTML, postscript or tar-gzipped html
Introduction à l'opérateur de Dirac lecture given at the Groupe de travail quantique à (Grenoble, March 1997), available as on-line HTML , postscript or tar-gzipped html Note that other documents are available from my French homepage.