Using Galois ideals for computing relative resolvents

Philippe Aubry (1, 2) , Annick Valibouze (2, 3)

1 SPACES - Solving problems through algebraic computation and efficient software
2 CALFOR - Calcul formel
3 LSTA - Laboratoire de Statistique Théorique et Appliquée

In this paper we show that some ideals which occur in Galois theory are generated by triangular sets of polynomials. This geometric property seems important for the development of symbolic methods in Galois theory. It may and should be exploited in order to obtain more efficient algorithms, and it enables us to present a new algebraic method for computing relative resolvents which works with any polynomial invariant.

Mots clés: résolvante; idéal des relations; théorie de galois; idéal de galois; ideal of relations; galois theory; resolvent; galois ideal

Domaines: Autre [cs.OH]

Philippe Aubry, Annick Valibouze. Using Galois ideals for computing relative resolvents. Journal of Symbolic Computation, 2000, 30 (6), pp.635--651. ⟨10.1006/jsco.2000.0376⟩. ⟨inria-00099277⟩