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Efficient Computation of Algebraic Local Cohomology Classes and Change of Ordering for Zero-Dimensional Standard Bases

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Computer Algebra in Scientific Computing (CASC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9301))

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Abstract

A new effective algorithm for computing a set of algebraic local cohomology classes is presented. The key ingredient of the proposed algorithm is to utilize a standard basis. As the application, an algorithm is given for the conversion of a standard basis of a zero-dimensional ideal with respect to any given local ordering into a standard basis with respect to any other local ordering, in the formal power series ring. The new algorithm always outputs a reduced standard basis.

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Author information

Authors and Affiliations

  1. Institute of Socio-Arts and Sciences, Tokushima University, 1-1 Minamijosanjima, Tokushima, Japan

    Katsusuke Nabeshima

  2. Graduate School of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennoudai, Tsukuba, 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. Laboratory of Information Technologies, Joint Institute of Nuclear Research, Dubna, Russia

    Vladimir P. Gerdt

  2. Institute for Mathematics, Universität Kassel, Kassel, Germany

    Wolfram Koepf

  3. Institut für Mathematik, Universität Kassel, Kassel, Hessen, Germany

    Werner M. Seiler

  4. Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2015 Springer International Publishing Switzerland

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Nabeshima, K., Tajima, S. (2015). Efficient Computation of Algebraic Local Cohomology Classes and Change of Ordering for Zero-Dimensional Standard Bases. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2015. Lecture Notes in Computer Science(), vol 9301. Springer, Cham. https://doi.org/10.1007/978-3-319-24021-3_25

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  • DOI: https://doi.org/10.1007/978-3-319-24021-3_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24020-6

  • Online ISBN: 978-3-319-24021-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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