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On the Bit-Size of Non-radical Triangular Sets

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Mathematical Aspects of Computer and Information Sciences (MACIS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10693))

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Abstract

We present upper bounds on the bit-size of coefficients of non-radical purely lexicographical Gröbner bases (triangular sets) in dimension zero. This extends a previous work [4], constrained to radical triangular sets; it follows the same technical steps, based on interpolation. However, key notion of height of varieties is not available for points with multiplicities; therefore the bounds obtained are thus less universal and depend on some input data. We also introduce a related family of non-monic polynomials that have smaller coefficients, and smaller bounds. It is not obvious to compute them from the initial triangular set though.

Work supported by the JSPS grant Wakate B No. 50567518.

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Author information

Authors and Affiliations

  1. Faculty of General Educational Research, Ochanomizu university, Tokyo, Japan

    Xavier Dahan

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  1. Xavier Dahan
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Correspondence to Xavier Dahan .

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Editors and Affiliations

  1. University of Paderborn, Paderborn, Germany

    Johannes Blömer

  2. Wilfrid Laurier University, Waterloo, Ontario, Canada

    Ilias S. Kotsireas

  3. Johannes Kepler University Linz, Linz, Austria

    Temur Kutsia

  4. SBA Research, Vienna, Austria

    Dimitris E. Simos

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Dahan, X. (2017). On the Bit-Size of Non-radical Triangular Sets. In: Blömer, J., Kotsireas, I., Kutsia, T., Simos, D. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2017. Lecture Notes in Computer Science(), vol 10693. Springer, Cham. https://doi.org/10.1007/978-3-319-72453-9_19

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  • DOI: https://doi.org/10.1007/978-3-319-72453-9_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-72452-2

  • Online ISBN: 978-3-319-72453-9

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