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Computing inhomogeneous Gröbner bases
- Source :
-
Journal of Symbolic Computation . May2011, Vol. 46 Issue 5, p498-510. 13p. - Publication Year :
- 2011
-
Abstract
- Abstract: 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 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. [Copyright &y& Elsevier]
Details
- Language :
- English
- ISSN :
- 07477171
- Volume :
- 46
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Journal of Symbolic Computation
- Publication Type :
- Academic Journal
- Accession number :
- 58756057
- Full Text :
- https://doi.org/10.1016/j.jsc.2010.10.002