Computing inhomogeneous Gröbner bases

In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Gröbner 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 self-saturating Buchberger’s Algorithm, and the main result is described in Theorem 21. 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.