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Habilitation à diriger des recherches

Algorithmes pour l'étude des solutions réelles des systèmes polynomiaux

Fabrice Rouillier 1 
1 SALSA - Solvers for Algebraic Systems and Applications
LIP6 - Laboratoire d'Informatique de Paris 6, Inria Paris-Rocquencourt
Abstract : This presentation summarizes a set of general methods for solving systems of polynomial equations (with or without inequalities), mainly centered on the study of their real roots; The main subject is the “resolution” of systems with an arbitrary number of solutions (finite or infinite), depending or not on parameters. Since the field is vast, one constrains it by imposing it that the algorithms are exact or certified or, in other words, that the results are never ambiguous from the user’s point of view (number or structure of the solutions, numerical approximations when it makes sense, real character of the solutions, etc.). The exposed work was carried out with two principal objectives: to progress in the development of useful effective methods in real geometry, but especially to propose some credible alternatives to the standard tools for scientific computations, with the objective of answering to some open problems (or considered difficult) in various applications. This assessment of several years of work is, in particular, the occasion to show the specific efforts which seem to be necessary to obtain convincing results (efficient implementations, cost of the certification/exactness, balance between theoretical and practical efficiency, etc.) and is articulated around some selected applications which justify the main theoretical, algorithmic but also technical choices.
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Habilitation à diriger des recherches
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Submitted on : Friday, January 13, 2017 - 4:05:14 PM
Last modification on : Friday, February 4, 2022 - 3:13:42 AM
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  • HAL Id : tel-01435142, version 1


Fabrice Rouillier. Algorithmes pour l'étude des solutions réelles des systèmes polynomiaux. Calcul formel [cs.SC]. Université Pierre & Marie Curie - Paris 6, 2007. ⟨tel-01435142⟩



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