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On Connection Between Constructive Involutive Divisions and Monomial Orderings

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Computer Algebra in Scientific Computing (CASC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4194))

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Abstract

This work considers the basic issues of the theory of involutive divisions, namely, the property of constructivity which assures the existence of minimal involutive basis. The work deals with class of ≻ -divisions which possess many good properties of Janet division and can be considered as its analogs for orderings different from the lexicographic one. Various criteria of constructivity and non-constructivity are given in the paper for these divisions in terms of admissible monomial orderings ≻ . It is proven that Janet division has the advantage in the minimal involutive basis size of the class of ≻ -divisions for which x 1 ≻ x 2 ≻ ... ≻ x n holds. Also examples of new involutive divisions which can be better than Janet division in minimal involutive basis size for some ideals are given.

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Author information

Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University,  

    Alexander Semenov

Authors
  1. Alexander Semenov
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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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© 2006 Springer-Verlag Berlin Heidelberg

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Semenov, A. (2006). On Connection Between Constructive Involutive Divisions and Monomial Orderings. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2006. Lecture Notes in Computer Science, vol 4194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11870814_22

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  • DOI: https://doi.org/10.1007/11870814_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45182-2

  • Online ISBN: 978-3-540-45195-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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