LIP6 2006/002

• Reports «Un nouvel outil pour calculer les groupes et idéaux de Galois et factoriser les polynômes dans des extensions algébriques»
• S. Orange, G. Renault, A. Valibouze
• 127 pages - 02/22/2005 - document en - http://www.lip6.fr/lip6/reports/2006/lip6-2006-002.pdf 908 Ko
• Contact Jean-Charles.Faugere (at) nulllip6.fr
• TeamSPIRAL
In this paper, we study some relations between univariate polynomials and their Galois group. There are presented in the form of tables, called "splitting tables". We show how these tables occur in factorizations over algebraic extensions, in the determination of Galois groups, in the computation of roots field and in computation of polynomials with given Galois group and coefficients in a number field.