Galois Groups and the Simplification of Polynomials

J.H. Davenport

IBP-Litp 1996/11: Rapport de Recherche Litp / Litp research reports
12 pages - Mars/March 1996 - Document en anglais.

PostScript : Ko /Kb

Titre / Title: Galois Groups and the Simplification of Polynomials

Résumé : Cet article décrit des interfaces entre la théorie des groupes de Galois et la facturation des polynomes.

Abstract : It is well-known that the theory of Galois groups is closely connected to the factorization of polynomials, but in practice the connection is not as strong as one would like. There are three areas in which one could wish for better interfaces than one currently has. Polynomial factorization does not make much use of Galois theory at the moment. Computational Galois Theory tends to restrict its attention to transitive groups, whereas some of the more interesting observations about polynomial simplification come from non-transitive groups. Computational Galois Theory tends to regard polynomial factorization as a solved question, whose results can be relied on in the determination of Galois groups, whereas in fact some of the polynomials that need to be factored are distinctly non-trivial.

Publications internes Litp 1996 / Litp research reports 1996