LIP6 1997/014: Rapport de Recherche
LIP6 /
LIP6 research
reports
4 pages - Septembre/September 1997 -
French document.
PostScript : 35 Ko /Kb
Contact : par mail / e-mail
Thème/Team: Calcul Formel
Titre français : Construction de l'idéal des relations entre les racines d'un polynôme
Titre anglais : Computation of the ideal of the relations between the roots of a univariate polynomial
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 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.
Key-words : computer algebra, Galois theorie, ideal fixed by a group, minimal polynomial
Publications internes LIP6 1997 / LIP6 research reports 1997