On the bit-size of non-radical triangular sets

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish
Title of host publicationMathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings
EditorsIlias S. Kotsireas, Johannes Blomer, Dimitris E. Simos, Temur Kutsia
PublisherSpringer Verlag
Pages264-269
Number of pages6
ISBN (Print)9783319724522
DOIs
Publication statusPublished - 2017 Jan 1
Externally publishedYes
Event7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017 - Vienna, Austria
Duration: 2017 Nov 152017 Nov 17

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10693 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2017
CountryAustria
CityVienna
Period17/11/1517/11/17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Dahan, X. (2017). On the bit-size of non-radical triangular sets. In I. S. Kotsireas, J. Blomer, D. E. Simos, & T. Kutsia (Eds.), Mathematical Aspects of Computer and Information Sciences - 7th International Conference, MACIS 2017, Proceedings (pp. 264-269). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10693 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-72453-9_19