Computation Schemes for Splitting Fields of Polynomials

Sébastien Orange (1) , Guénaël Renault (2) , Kazuhiro Yokoyama (3)

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre
2 SALSA - Solvers for Algebraic Systems and Applications
3 Department of Mathematics [Rikkyo]

In this article, we present new results about the computation of a general shape of a triangular basis generating the splitting ideal of an irreducible polynomial given with the permutation representation of its Galois group G. We provide some theoretical results and a new general algorithm based on the study of the non redundant bases of permutation groups. These new results deeply increase the efficiency of the computation of the splitting field of a polynomial.

Domaines: Informatique [cs]; Calcul formel [cs.SC]

Sébastien Orange, Guénaël Renault, Kazuhiro Yokoyama. Computation Schemes for Splitting Fields of Polynomials. ISSAC '09: the 2009 international symposium on Symbolic and algebraic computation, Jul 2009, Seoul, South Korea. pp.279-286, ⟨10.1145/1576702.1576741⟩. ⟨hal-01294703⟩