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Janet-Like Monomial Division

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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

In this paper we introduce a new type of monomial division called Janet-like, since its properties are similar to those of Janet division. We show that the former division improves the latter one. This means that a Janet divisor is always a Janet-like divisor but the converse is generally not true. Though Janet-like division is not involutive, it preserves all algorithmic merits of Janet division, including Noetherianity, continuity and constructivity. Due to superiority of Janet-like division over Janet division, the algorithm for constructing Gröbner bases based on the new division is more efficient than its Janet division counterpart.

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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 Monomial Division. 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_15

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  • DOI: https://doi.org/10.1007/11555964_15

  • 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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