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TitleMinimal sets of critical pairs
Author(s) Massimo Caboara, Martin Kreuzer, Lorenzo Robbiano
TypeArticle in Conference Proceedings
AbstractIn the computation of a Gröbner basis using Buchberger's algorithm,
a key issue for improving the efficiency is to produce good techniques
for avoiding as many unnecessary critical pairs as possible.
A good solution would be to avoid all non-minimal critical pairs,
and hence to process only a minimal set of generators
of the module generated by the critical pairs. In this paper we
show how to obtain that desired solution while retaining the same
efficiency as with the classical implementation.
As a consequence, we get a new Optimized Buchberger Algorithm.
KeywordsBuchberger algorithm, Gröbner bases, critical pair, S-polynomial
Length15
File
LanguageEnglish
Pages390-404
PublisherWorld Scientific
AddressSingapore
Year2002
EditorA. Cohen, X. Gao and N. Takayama
Edition0
Translation No
Refereed Yes
BookMathematical Software
ConferencenameFirst International Congress on Mathematical Software 2002 (Beijing/China)
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