On an installation of Buchberger's algorithm
Journal of Symbolic Computation
“One sugar cube, please” or selection strategies in the Buchberger algorithm
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
Multigraded Hilbert functions and Buchberger algorithm
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Hilbert functions and the Buchberger algorithm
Journal of Symbolic Computation
The geobucket data structure for polynomials
Journal of Symbolic Computation
Journal of Symbolic Computation
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
A new efficient algorithm for computing Gröbner bases without reduction to zero (F5)
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
An analysis of inhomogeneous signature-based Gröbner basis computations
Journal of Symbolic Computation
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In this paper we describe how an idea centered on the concept of self-saturation allows several improvements in the computation of Grobner 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.