Vol. 11, No. 1, 2021

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Standard pairs of monomial ideals over nonnormal affine semigroups in SageMath

Byeongsu Yu

Vol. 11 (2021), 129–142

We present StdPairs, a SageMath library to compute standard pairs of a monomial ideal over a pointed (nonnormal) affine semigroup ring. Moreover, StdPairs 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 Matusevich and Yu (2020). We also provide methods that allow the outputs from this library to be compatible with the Normaliz package of Macaulay2 and SageMath.

affine semigroups, standard pairs, monomial ideals, semigroup rings
Mathematical Subject Classification
Primary: 13F65, 68W30, 90C90
Secondary: 13P25, 20M25
Supplementary material

SageMath library for standard pairs of monomial ideals computations

Received: 22 October 2020
Revised: 12 July 2021
Accepted: 10 August 2021
Published: 20 February 2022
Byeongsu Yu
Department of Mathematics
Texas A&M University
College Station, TX
United States