An algorithm for computing the Hilbert--Samuel multiplicities and reductions of zero-dimensional ideals of Cohen--Macaulay local rings

Takafumi Shibuta; Shinichi Tajima

An algorithm for computing the Hilbert--Samuel multiplicities and reductions of zero-dimensional ideals of Cohen--Macaulay local rings

Commutative Algebra 2019-07-09 v2

Authors: Takafumi Shibuta , Shinichi Tajima

Abstract

In this paper, we present an algorithm for computing the minimal reductions of $\mathfrak{m}$ -primary ideals of Cohen--Macaulay local rings. Using this algorithm, we are able to compute the Hilbert--Samuel multiplicities and solve the membership problem for the integral closure of $\mathfrak{m}$ -primary ideals.

Keywords

Hilbert--Samuel multiplicity minimal reductions Cohen--Macaulay local rings zero-dimensional ideals integral closure

Cite

@article{arxiv.1710.01435,
  title  = {An algorithm for computing the Hilbert--Samuel multiplicities and reductions of zero-dimensional ideals of Cohen--Macaulay local rings},
  author = {Takafumi Shibuta and Shinichi Tajima},
  journal= {arXiv preprint arXiv:1710.01435},
  year   = {2019}
}

Comments

12 pages, Accepted for publication in Journal of Symbolic Computation

An algorithm for computing the Hilbert--Samuel multiplicities and reductions of zero-dimensional ideals of Cohen--Macaulay local rings

Abstract

Keywords

Cite

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