Computation of the ideal of the relations between the roots of a univariate polynomial

Construction de l'idéal des relations entre les racines d'un polynôme

Annick Valibouze (1)

1 CALFOR - Calcul formel

Galois theory allows us to deal with effective computation in algebraic extensions of fields. In this aim, the present paper is devoted to an effective inductive construction of an effective generator system for the ideal of relations between the roots of an 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 correspondance 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 characterise the considered ideals and allow to construct a generators system for them.

Cet article développe une vision effective de la théorie de Galois algébrique en apportant des propriétés inhérentes aux idéaux associés à un polynôme univarié.

Mots clés: computer algebra; Galois theorie; ideal fixed by a group; minimal polynomial

Mots clés: calcul formel; théorie de Galois algébrique; idéal fixe par un groupe; polynôme minimal

Domaines: Informatique [cs]

Annick Valibouze. Construction de l'idéal des relations entre les racines d'un polynôme. [Rapport de recherche] lip6.1997.014, LIP6. 1997. ⟨hal-02547598⟩