Generalized Integral Dependence Relations

Abstract

A generalization of integral dependence relations in a ring of convergent power series is studied in the context of symbolic computation. Based on the theory of Grothendieck local duality on residues, an effective algorithm is introduced for computing generalized integral dependence relations. It is shown that, with the aid of local cohomology, generalized integral dependence relations in the ring of convergent power series can be computed in a polynomial ring. An extension of the proposed method to parametric cases is also discussed.