Degree bounds for Gröbner bases of low-dimensional polynomial ideals

Ernst W. Mayr, Stephan Ritscher

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

10 Scopus citations

Abstract

Let K[X] be a ring of multivariate polynomials with coefficients in a field K, and let f1,..., fs be polynomials with maximal total degree d which generate an ideal I of dimension r. Then, for every admissible ordering, the total degree of polynomials in a Gröbner basis for I is bounded by 2(1/2dn-r + d)2r. This is proved using the cone decompositions introduced by Dubé in [5]. Also, a lower bound of similar form is given.

Original languageEnglish
Title of host publicationProceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010
PublisherAssociation for Computing Machinery (ACM)
Pages21-27
Number of pages7
ISBN (Print)9781450301503
DOIs
StatePublished - 2010
Event2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010 - Munich, Germany
Duration: 25 Jul 201028 Jul 2010

Publication series

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

Conference

Conference2010 International Symposium on Symbolic and Algebraic Computation, ISSAC 2010
Country/TerritoryGermany
CityMunich
Period25/07/1028/07/10

Keywords

  • Bner basis
  • Complexity
  • Grö
  • Ideal dimension
  • Multivariate polynomial
  • Polynomial ideal

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