Generalized Integral Dependence Relations

  • Katsusuke NabeshimaEmail author
  • Shinichi Tajima
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11989)


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.


Integral closure Standard basis Local cohomology 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Graduate School of Technology, Industrial and Social SciencesTokushima UniversityTokushimaJapan
  2. 2.Graduate School of Science and TechnologyNiigata UniversityNishi-ku, NiigataJapan

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