1. Computing inhomogeneous Gröbner bases
- Author
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Bigatti, A.M., Caboara, M., and Robbiano, L.
- Subjects
- *
GROBNER bases , *ALGORITHMS , *POLYNOMIALS , *MATHEMATICAL analysis , *NUMERICAL analysis , *ALGEBRA , *APPROXIMATION theory - 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]
- Published
- 2011
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