Size of coefficients of lexicographical Groöbner bases: The zero-dimensional, radical and bivariate case

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

2 Citations (Scopus)

Abstract

This work is limited to the zero-dimensional, radical, and bivariate case. A lexicographical Gröbner basis can be simply viewed as Lagrange interpolation polynomials. In the same way the Chinese remaindering theorem generalizes Lagrange interpolation, we show how a triangular decomposition is linked to a specific Gröbner basis (not the reduced one). A bound on the size of the coefficients of this specific Gröbner basis is proved using height theory, then a bound is deduced for the reduced Gröbner basis. Besides, the link revealed between the Gröbner basis and the triangular decomposition gives straightforwardly a numerical estimate to help finding a lucky prime in the context of modular methods.

Original languageEnglish
Title of host publicationISSAC 2009 - Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation
Pages119-126
Number of pages8
DOIs
Publication statusPublished - 2009 Dec 1
Externally publishedYes
Event2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009 - Seoul, Korea, Republic of
Duration: 2009 Jul 282009 Jul 31

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC

Conference

Conference2009 International Symposium on Symbolic and Algebraic Computation, ISSAC 2009
CountryKorea, Republic of
CitySeoul
Period09/7/2809/7/31

Keywords

  • Gröbner bases
  • Space complexity
  • Triangular sets

ASJC Scopus subject areas

  • Mathematics(all)

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