e present an algorithm that computes an unmixed-dimensional decomposition of a finitely generated perfect differential ideal I. Each I_I in the decomposition I = I_1 ∩ …∩ I_k is given by its characteristic set. This decomposition is a generalization of the differential case of Kalkbrener's deocmposition. We use a different approach. The basic operation in our algorithm is the computation of the inverse of an algebraic polynomial with respect to a finite set of algebraic polynoials.
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