Algebraic Computation of resolvents without extraneous powers

Philippe Aubry (1) , Annick Valibouze (2, 1)

1 APR - Algorithmes, Programmes et Résolution
2 LSTA - Laboratoire de Statistique Théorique et Appliquée

This paper presents an algorithm for computing algebraically relative resolvents which enhances an existing algorithm by avoiding the accumulation of superfluous powers in the intermediate computations. The superfluous power generated at each step is predetermined over a certain quotient ring. As a byproduct, an efficient algorithm for extracting an n-th root of an univariate polynomial is obtained.

Keywords: Galois group; galoisian ideal; triangular ideal; splitting field; resolvent; minimal polynomial

Domains: Symbolic Computation [cs.SC]

Philippe Aubry, Annick Valibouze. Algebraic Computation of resolvents without extraneous powers. European Journal of Combinatorics, 2012, 33 (7), pp.1369-1385. ⟨10.1016/j.ejc.2012.03.003⟩. ⟨hal-00624447⟩