Etude des relations algébriques entre les racines d'un polynôme d'une variable

Annick Valibouze 1
1 CALFOR - Calcul formel
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : Galois theory allows us to deal with effective computation in algebraic extensions of fields. In this aim, the present paper is devoted to an inductive construction of a generating system for the ideal of relations among the roots of a univariate polynomial over a field. The idea is to define new ideals between the ideal of symmetric relations and the ideal of relations and to give a correspondence between these ideals and finite sets of permutations. The fundamental tools of this construction are multivariate polynomials called minimal polynomials associated to our ideals. These polynomials characterize the considered ideals and allow to construct a generating system for them.
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Submitted on : Tuesday, May 5, 2015 - 1:41:49 PM
Last modification on : Friday, November 15, 2019 - 11:34:05 AM

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  • HAL Id : hal-01148792, version 1

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Annick Valibouze. Etude des relations algébriques entre les racines d'un polynôme d'une variable. Bulletin of the Belgian Mathematical Society - Simon Stevin, Belgian Mathematical Society, 1999, 6 (4), pp.507-535. ⟨hal-01148792⟩

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