|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 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.
|Keywords||Buchberger algorithm, Gröbner bases, critical pair, S-polynomial|
|Editor||A. Cohen, X. Gao and N. Takayama|
|Conferencename||First International Congress on Mathematical Software 2002 (Beijing/China)|