Deterministically Computing Reduction Numbers of Polynomial Ideals
arXiv:1404.1721
Abstract
We discuss the problem of determining reduction number of a polynomial ideal I in n variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of I and requires computation in a polynomial ring with (n-dim(I))dim(I) parameters and n-dim(I) variables. The second one computes via a Grobner system the set of all reduction numbers of the ideal I and thus in particular also its big reduction number. However,it requires computations in a ring with n.dim(I) parameters and n variables.
This new version replaces the earlier version arXiv:1404.1721 and it has been accepted for publication in the proceedings of CASC 2014, Warsaw, Polnad