Certification algébrique pour le calcul de la résolvante de Lagrange

Algebraic certification of numerical algorithms computing Lagrange resolvents

Ines Abdeljaoued-Tej (1) , Faiçal Bouazizi (2, 3) , Annick Valibouze (4, 5)

1 LR11IPT09 - Laboratoire de Bioinformatique, biomathématiques, biostatistiques (BIMS)
2 Département de Mathematiques [Sfax]
3 APR - Algorithmes, Programmes et Résolution
4 APR - Algorithmes, Programmes et Résolution
5 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

In this article, we introduce two new methods to calculate Lagrange's resolvents. The first one, based on Lagrange's algorithm, enables to calculate algebraically the resolvent and the second one is numeric with algebraic certification.

Mots clés: Lagrange resolvent; minimal polynomial; galoisian ideal; Galois group; triangular ideal

Domaines: Calcul formel [cs.SC]; Analyse numérique [cs.NA]

Ines Abdeljaoued-Tej, Faiçal Bouazizi, Annick Valibouze. Algebraic certification of numerical algorithms computing Lagrange resolvents. Journal of Algebra and Its Applications, 2018, 17 (1), pp.1850007. ⟨10.1142/S021949881850007X⟩. ⟨hal-00483257⟩