Hilbert functions and the Buchberger algorithm

Abstract

In this paper we show how to use the knowledge of the Hilbert-Poincaré series of an ideal I to speed up the Buchberger algorithm for the computation of a Gröbner basis. The algorithm is useful in the change of ordering and in the validation of modular computations, also with tangent cone orderings; speeds the direct computation of a Gröbner basis if the ideal is a complete intersection, e.g. in the computation of cartesian from parametric equations, can validate or disprove a conjecture that an ideal is a complete intersection, and is marginally useful also when the conjecture is false. A large set of experiments is reported. © 1996 Academic Press Limited.