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arXiv · 1404.1721

Deterministically Computing Reduction Numbers of Polynomial Ideals

Amir Hashemi·Michael Schweinfurter·Werner M. Seiler
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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.

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Amir Hashemi, Michael Schweinfurter, Werner M. Seiler. 2014-06-13. Deterministically Computing Reduction Numbers of Polynomial Ideals. https://arxiv.org/abs/1404.1721

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