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SPIRAL Team has been restructured

SPIRAL : Research projects


Our research activity focuses on Polynomial System Solving, interactions between Symbolic and Numerical algorithms and Random generation.

Solving Polynomial Systems

Solving polynomial systems is the main research thematic which is developped is our team. Our goal is to provide efficient implementations designed for real-life applications or teaching. This thematic is widely investigated including problems about arithmetics, Galois theory or the study of polynomial systems with coefficients in \"exotic\" ground fields.

SALSA Project

Scientific Leader : Fabrice Rouillier

SALSA means \"Software for ALgebraic Systems and Applications\". This project is joint with INRIA (Research unity Rocquencourt) whose aim is the design and the implmentation of certified algorithms solving polynomial systems. Among the application fields where some results have already been obtained, one can point out simulation, control and diagnostic of parallel manipulators, error correcting codes, cryptography, image compression and biophysics.

Chinese-SALSA Team

Chinese-SALSA is an associated team including members of the SALSA Project and reasearchers of the Chinese Academy of Sciences and the universities of Beihang and Peking. Our goals is to share knowledge and expertise on Grobner bases and triangular sets, to develop new methods for solving polynomial systems of equations and inequalities and develop the valorization of our works by solving significative applications in cryptography, automatic deduction, robotics...


SYNUS Action

Scientific Leader : Fabienne Jezequel

The two teams of the Scientific Computing department in LIP6 (PEQUAN and SPIRAL) are implied in a joint work involving both symbolical and numerical algorithms. This novel work is important for scientific computing. Symbolical computations provide accurate solutions but may be slow, whereas numerical algorithms, using a finite precision arithmetic, are usually faster but compute approximate results. Our aim is to decrease run time in formal algorithms by performing numerical computations when finite precision is appropriate. The work consists in determining in formal algorithms developed by the SPIRAL team which parts are numerically stable and provide satisfying results with a finite precision arithmetic. The study of the numerical quality of the codes can be carried out using the CADNA library developed in the PEQUAN team.

Random Generation Action

Scientific Leader : Michèle Soria

Random generation of structures defined by recursive specifications is a fruitful research field, from the algorithmic viewpoint and from the application fields viewpoints which include bio-informatics and software engineering.

The Boltzmann model, coming from analytic combinatorics appears to be particularly efficient to generate combinatorial objects specified by strong constraints which are modelled in terms of graphs or grammars. The 'Random Generation' Action aims at developping these methods to generate automatically and systematically tests for software verification.