Multigraded Hilbert functions and Buchberger algorithm

Abstract

In this paper we continue the work done in [GMRT]. Namely we describe an algorithm which allows to drive the classical Buchberger Algorithm by meansof multigrade Hilbert-Poincar6 series. The re-suIt is that in the multigrade caseone can kill many more useless critical pairs. Besides, the new algorithm, called MGHDriven, is intrinsically parallelizable and it is now implemented in ~~(see [cNR]).