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Generalized Integral Dependence Relations

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Book cover Mathematical Aspects of Computer and Information Sciences (MACIS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11989))

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Abstract

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.

This work has been partly supported by JSPS Grant-in-Aid for Scientific Research (C) (18K03214 and 18K03320).

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Authors and Affiliations

  1. Graduate School of Technology, Industrial and Social Sciences, Tokushima University, 2-1, Minamijosanjima-cho, Tokushima, Japan

    Katsusuke Nabeshima

  2. Graduate School of Science and Technology, Niigata University, 8050, Ikarashi 2-no-cho, Nishi-ku, Niigata, Japan

    Shinichi Tajima

Authors
  1. Katsusuke Nabeshima
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  2. Shinichi Tajima
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Correspondence to Katsusuke Nabeshima .

Editor information

Editors and Affiliations

  1. AIT Austrian Institute of Technology, Vienna, Austria

    Daniel Slamanig

  2. IMJ-PRG, Sorbonne University, Paris, France

    Elias Tsigaridas

  3. Institute of Information Technologies, Gebze Technical University, Gebze, Turkey

    Zafeirakis Zafeirakopoulos

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Nabeshima, K., Tajima, S. (2020). Generalized Integral Dependence Relations. In: Slamanig, D., Tsigaridas, E., Zafeirakopoulos, Z. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science(), vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_6

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  • DOI: https://doi.org/10.1007/978-3-030-43120-4_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-43119-8

  • Online ISBN: 978-3-030-43120-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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