Standard pairs of monomial ideals over non-normal affine semigroups in SageMath

We present stdPairs.spyx, a SageMath library to compute standard pairs of a monomial ideal over a pointed (non-normal) affine semigroup ring. Moreover, stdPairs.spyx provides the associated prime ideals, the corresponding multiplicities, and an irredundant irreducible primary decomposition of a mono...

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Bibliographic Details
Published in:arXiv.org 2020-10
Main Author: Yu, Byeongsu
Format: Article
Language:English
Subjects:
Algorithms
Libraries
Polynomials
Rings (mathematics)
Online Access:Get full text
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Summary:We present stdPairs.spyx, a SageMath library to compute standard pairs of a monomial ideal over a pointed (non-normal) affine semigroup ring. Moreover, stdPairs.spyx provides the associated prime ideals, the corresponding multiplicities, and an irredundant irreducible primary decomposition of a monomial ideal. The library expands on the standardPairs function on Macaulay2 over polynomial rings, and is based on algorithms from arXiv:2005.10968v2 [math.AC]. We also provide methods that allow the outputs from this library to be compatible with the Normaliz package of Macaulay2 and SageMath.
ISSN:2331-8422
DOI:10.48550/arxiv.2010.08903