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An Algorithm for Computing Standard Bases by Change of Ordering via Algebraic Local Cohomology

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Mathematical Software – ICMS 2014 (ICMS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8592))

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Abstract

An algorithm is introduced for transforming a standard basis of a zero-dimensional ideal, in the formal power series ring, into another standard basis with respect to any given local ordering. The key ingredient of the proposed algorithm is an efficient method for solving membership problems for Jacobi ideals in local rings, that utilizes the Grothendieck local duality theorem. Namely, a new algorithm for computing a standard basis of a given zero-dimensional ideal with respect to any given local ordering, is derived by using algebraic local cohomology. Its implementation is introduced, too.

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References

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Author information

Authors and Affiliations

  1. Institute of Socio-Arts and Sciences, The University of Tokushima, 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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Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Box 8205, 27695, Raleigh, NC, USA

    Hoon Hong

  2. Courant Institute, Dept. of Computer Science, New York Institute, 251 Mercer Street, 10012, New York, NY, USA

    Chee Yap

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Nabeshima, K., Tajima, S. (2014). An Algorithm for Computing Standard Bases by Change of Ordering via Algebraic Local Cohomology. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_63

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  • DOI: https://doi.org/10.1007/978-3-662-44199-2_63

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44198-5

  • Online ISBN: 978-3-662-44199-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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