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TitleComputing inhomogeneous Gröbner bases
Author(s) Anna M. Bigatti, Massimo Caboara, Lorenzo Robbiano
TypeArticle in Journal
AbstractIn 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 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.
KeywordsGröbner bases, Buchberger’s Algorithm
URL http://www.sciencedirect.com/science/article/pii/S0747717110001719
JournalJournal of Symbolic Computation
Pages498 - 510
NoteGroebner Bases and Applications
Translation No
Refereed No