English

Deterministically Computing Reduction Numbers of Polynomial Ideals

Commutative Algebra 2014-06-16 v2

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.

Keywords

Cite

@article{arxiv.1404.1721,
  title  = {Deterministically Computing Reduction Numbers of Polynomial Ideals},
  author = {Amir Hashemi and Michael Schweinfurter and Werner M. Seiler},
  journal= {arXiv preprint arXiv:1404.1721},
  year   = {2014}
}

Comments

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

R2 v1 2026-06-22T03:44:30.255Z