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Janet-Like Gröbner Bases

  • Conference paper
Computer Algebra in Scientific Computing (CASC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3718))

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Abstract

We define a new type of Gröbner bases called Janet-like, since their properties are similar to those for Janet bases. In particular, Janet-like bases also admit an explicit formula for the Hilbert function of polynomial ideals. Cardinality of a Janet-like basis never exceeds that of a Janet basis, but in many cases it is substantially less. Especially, Janet-like bases are much more compact than their Janet counterparts when reduced Gröbner bases have “sparce” leading monomials sets, e.g., for toric ideals. We present an algorithm for constructing Janet-like bases that is a slight modification of our Janet division algorithm. The former algorithm, by the reason of checking not more but often less number of nonmultiplicative prolongations, is more efficient than the latter one.

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Author information

Authors and Affiliations

  1. Laboratory of Information Technologies, Joint Institute for Nuclear Research, 141980, Dubna, Russia

    Vladimir P. Gerdt

  2. Department of Mathematics and Mechanics, Saratov University, 410071, Saratov, Russia

    Yuri A. Blinkov

Authors
  1. Vladimir P. Gerdt
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  2. Yuri A. Blinkov
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Technische Universität München, Boltzmannstr. 3, 85748, Garching, Germany

    Victor G. Ganzha  & Ernst W. Mayr  & 

  2. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2005 Springer-Verlag Berlin Heidelberg

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Gerdt, V.P., Blinkov, Y.A. (2005). Janet-Like Gröbner Bases. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2005. Lecture Notes in Computer Science, vol 3718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11555964_16

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  • DOI: https://doi.org/10.1007/11555964_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28966-1

  • Online ISBN: 978-3-540-32070-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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