Abstract:
In this paper we describe how an idea centered on the concept of
selfsaturation allows several improvements in the
computation of Groebner bases via Buchberger's Algorithm.
In a nutshell, the idea is to extend the advantages of computing with
homogeneous polynomials or vectors to the general case.
When the input data are not homogeneous, we use a technique
described in Section 2: the main tool is the procedure of a
selfsaturating Buchberger's Algorithm, and
the main result is described in Theorem 14.
Another strictly related topic is treated in
Section 3 where a mathematical foundation is given
to the sugar trick which is nowadays widely used in
most of the implementations of Buchberger's Algorithm.
A special emphasis is given in Section 4 to the case
of a single grading, and Section 5 exhibits
some timings and indicators showing the practical merits of our approach.
Keywords:
Groebner bases, Buchberger's Algorithm
MSC:
13, 68
