Deterministically Computing Reduction Numbers of Polynomial Ideals

2014/04/07 by Hashemi, Amir, Schweinfurter, Michael, Seiler, Werner M.
#13P10 and 68W30 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/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.

Related

• Reduced ideals from the reduction algorithm
• An upper bound on the reduction number of an ideal
• Existence and Construction of a Gröbner Basis for a Polynomial Ideal
• Constructive characterization of the reduction numbers
• Reduction numbers and initial ideals