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
Country/TerritoryKorea, 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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