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05679820 Colin, Antoine Giusti, Marc Efficient computation of square-free Lagrange resolvents. Suzuki, Masakazu (ed.) et al., The joint conference of ASCM 2009 and MACIS 2009. 9th international conference on Asian symposium on computer mathematics and 3rd international conference on mathematical aspects of computer and information sciences, Fukuoka, Japan, December 14--17, 2009. Selected papers. Fukuoka: Kyushu University, Faculty of Mathematics. COE Lecture Note 22, 348-351 (2009). 2009 Fukuoka: Kyushu University, Faculty of Mathematics EN Cohen-Macaulay algebra square-free resolvents Summary: If $H$ is a finite subgroup of the general linear group $\bold{GL}_n(k)$, we propose a general frame to compute efficiently in the invariant algebra $k[X_1,\dots,X_n]^H$. The classical Noether normalization of this Cohen-Macaulay algebra takes a natural form when expressed with adequate data structures, based on evaluation rather than writing. This allows to compute more efficiently its multiplication tensor. As an illustration we give a fast symbolic algorithm to compute the coefficients of the Lagrange resolvent associated to the given subgroup $H$, either generically or specialized. We show also how to find square-free resolvents with better theoretical complexity (polynomial in the index of the group after a precomputation depending only on $H$). This relies on a geometric link between the discriminant of the natural Noether projection and two other discriminants related to fundamental invariants.