Computations involving symbolic powers

TL;DR

This paper introduces a Macaulay2 software package designed to facilitate the computation of symbolic powers of ideals, addressing longstanding open questions and aiding in the study of their properties.

Contribution

The paper presents a new computational tool for symbolic powers, enabling researchers to explore equality and containment problems more effectively.

Findings

Software successfully computes symbolic powers of ideals.

Enables investigation of equality and containment problems.

Facilitates research on open questions in symbolic power theory.

Abstract

Symbolic powers are a classical commutative algebra topic that relates to primary decomposition, consisting, in some circumstances, of the functions that vanish up to a certain order on a given variety. However, these are notoriously difficult to compute, and there are seemingly simple questions related to symbolic powers that remain open even over polynomial rings. In this paper, we describe a Macaulay2 software package that allows for computations of symbolic powers of ideals and which can be used to study the equality and containment problems, among others.