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An algorithm for computing Grothendieck local residues. I: Shape basis case. (English) Zbl 07095839
Summary: Grothendieck local residue is considered in the context of symbolic computation. Basic ideas of our approach are the use of local cohomology, holonomic \(D\)-modules, and Noether operators. An effective method is introduced for computing Grothendieck local residues of rational \(n\)-forms under shape basis condition. Resulting algorithms that avoid the use of Gröbner bases on the Weyl algebra and an implementation are described. Some examples are also given for illustration.

32A27 Residues for several complex variables
13N10 Commutative rings of differential operators and their modules
Risa/Asir; OpenXM
Full Text: DOI
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