Computing the Lagrange resolvent by effectiveness of Galois Theorem

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

1 LIM - Laboratoire d'Ingénierie Mathématique
2 Département de Mathematiques [Sfax]
3 APR - Algorithmes, Programmes et Résolution
4 LSTA - Laboratoire de Statistique Théorique et Appliquée

In this article, we introduce a new method to calculate Lagrange resolvent. This technique is based on Lagrange's algorithm and it enables to calculate algebraically the resolvent. This algorithm is based on the fundamental theorem of symmetric functions:we generalize the effectivity of this theorem to any surgroup of the Galois's group of the polynomial.

Mots clés: Galois group; minimal polynomial; galoisian ideal; Groebner Basis; Groebner Basis.; Lagrange resolvents

Domaines: Calcul formel [cs.SC]

Ines Abdeljaoued, Faiçal Bouazizi, Annick Valibouze. Computing the Lagrange resolvent by effectiveness of Galois Theorem. 2010. ⟨hal-00602882⟩