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An Algorithm for Computing Grothendieck Local Residues II: General Case

Abstract

Grothendieck local residue is considered in the context of symbolic computation. An effective method based on the theory of holonomic D-modules is proposed for computing Grothendieck local residues. The key is the notion of Noether operator associated to a local cohomology class. The resulting algorithm and an implementation are described with illustrations.

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Correspondence to Katsuyoshi Ohara.

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This work has been partly supported by JSPS KAKENHI Grant Numbers JP17K05292, JP18K03320 and by the Research Institute for Mathematical Sciences, a Joint Usage/Research Center located in Kyoto University.

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Ohara, K., Tajima, S. An Algorithm for Computing Grothendieck Local Residues II: General Case. Math.Comput.Sci. (2020). https://doi.org/10.1007/s11786-019-00439-y

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Keywords

  • Local residues
  • Local cohomology
  • Holonomic D-modules
  • Noether operators

Mathematics Subject Classification

  • Primary 32A27
  • Secondary 13N10