Title  Minimal sets of critical pairs 
Author(s)  Massimo Caboara, Martin Kreuzer, Lorenzo Robbiano 
Type  Article in Conference Proceedings 
Abstract  In 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 nonminimal 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. 
Keywords  Buchberger algorithm, Gröbner bases, critical pair, Spolynomial 
Length  15 
File 

Language  English 
Pages  390404 
Publisher  World Scientific 
Address  Singapore 
Year  2002 
Editor  A. Cohen, X. Gao and N. Takayama 
Edition  0 
Translation 
No 
Refereed 
Yes 
Book  Mathematical Software 
Conferencename  First International Congress on Mathematical Software 2002 (Beijing/China) 