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

TL;DR

This paper introduces stdPairs.spyx, a SageMath library for computing standard pairs and related algebraic structures of monomial ideals over non-normal affine semigroup rings, expanding computational tools in algebraic geometry.

Contribution

The paper presents a new SageMath library that extends existing tools to handle monomial ideals over non-normal affine semigroup rings, including algorithms and compatibility features.

Findings

Provides algorithms for standard pairs over non-normal affine semigroup rings.

Includes methods for associated primes, multiplicities, and primary decomposition.

Ensures compatibility with Macaulay2 and Normaliz.

Abstract

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.