CAFE : Computer algebra and functional equations (project-team)

About the project : Project-Team site Activity report Videos and photos Research reports Theses Theme : Sym Symbolic systems Sophia Antipolis - Méditerranée research center

CAFE has been dissolved on 12/31/2006

Project-Team Presentation

Our goal is to develop new computer algebra methods for solving functional equations, i.e. equations where the unknowns represent functions rather than numerical values, and to further the use of such methods in engineering by producing the programs and tools necessary to apply them to industrial problems. The functional equations that we study more particularly are differential, difference and q-difference equations.

Research themes

• Algebraic algorithms: we are studying efficient algorithms, based on differential algebra (differential ideal theory and differential Galois theory) as well as their generalisations to difference equations and further to more general equations. We also study the automatic handling of non-generic cases when the equations contain parameters.
• Mathematical databases: we are developping a deductive database of mathematical formulas, that allows the natural storage of non-algorithmic knowledge for computer algebra. This creates numerous problems at the edge of computer algebra, rewriting and automatic reasoning.
• Special-purpose computer algebra libraries: we are implementing our methods in special-purpose stand-alone libraries that are callable from various computer algebra systems.
• Sofware components: we are developping the necessary tools and protocols for using databases and dedicated libraries as software components inside a larger scientific computing environment.

International and industrial relations

• International research projects: we participated in the OpenMath project (ESPRIT Multimedia Standards 24.969), the CATHODE-2 (ESPRIT WG 24.490) and ``Math'' (W3C) working groups, and the Lyapunov Institute project Direct Computer Algebra Methods for Exact Solutions of Systems of Linear Functional Equations. We are now active participants in the OpenMath Thematic Network (IST-2000-28719), in a new Lyapunov Institute project, in a french-chinese PRA project, and in two PAI projects (one with england and one with slovenia).
• Industrial contacts: we are in contact with the development teams of the main computer algebra systems (NAG, SciFace, WMI, WRI) and with the editor Springer-Verlag.
• Academic collaborations: we are maintaining active collaborations with several computer algebra teams: GAGE (Ecole Polytechnique), LACO (Limoges), ETH (Switzerland), RIACA (Holland), ORCCA (Ontario, Canada), the University of Kent (UK), the Academia Sinica (China), the computer center of the russian academy of sciences (Moscow) and the University of Ljubljana (Slovénia).

Scientific leader

Evelyne HUBERT
+33 4 92 38 71 78
Evelyne.Hubert@inria.fr
Secretary : +33 4 92 38 77 90