Computation schemes for splitting fields of polynomials

Authors:
Sébastien Orange;Guénaël Renault;Kazuhiro Yokoyama
Affiliations:
Université du Havre, Le Havre, France;INRIA, Paris Rocquencourt, Paris 06 University, Paris, France;Rikkyo University, Tokyo, Japan
Venue:
Proceedings of the 2009 international symposium on Symbolic and algebraic computation
Year:
2009

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Abstract

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.