Mathematics in Computer Science

, Volume 13, Issue 1–2, pp 205–216 | Cite as

An Algorithm for Computing Grothendieck Local Residues I: Shape Basis Case

  • Katsuyoshi OharaEmail author
  • Shinichi Tajima


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.


Local residues Local cohomology Holonomic system Computer algebra 

Mathematics Subject Classification

Primary 32A27 Secondary 13N10 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsKanazawa UniversityKanazawaJapan
  2. 2.Graduate School of Science and TechnologyNiigata UniversityNiigataJapan

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