is 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 as a main tool the procedure of a self-saturating Buchberger's Algorithm. Another strictly related topic is treated later when 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 also given to the case of a single grading, and subsequently some timings and indicators showing the practical merits of our approach.
|Autori:||Bigatti A.M.; Caboara M; Robbiano L.|
|Titolo:||Computing inhomogeneous Groebner bases|
|Anno del prodotto:||2011|
|Digital Object Identifier (DOI):||10.1016/j.jsc.2010.10.002|
|Appare nelle tipologie:||1.1 Articolo in rivista|