Vol. 9, No. 1, 2019

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Calculations involving symbolic powers

Ben Drabkin, Eloísa Grifo, Alexandra Seceleanu and Branden Stone

Vol. 9 (2019), 71–80
Abstract

Symbolic powers is 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.

Keywords
symbolic powers, Macaulay2
Mathematical Subject Classification 2010
Primary: 13P99
Secondary: 13A15, 13C99
Supplementary material

For calculations involving symbolic powers

Milestones
Received: 5 December 2017
Revised: 2 February 2019
Accepted: 20 May 2019
Published: 16 October 2019
Authors
Ben Drabkin
Department of Mathematics
University of Nebraska
Lincoln, NE
United States
Eloísa Grifo
Department of Mathematics
University of Michigan
Ann Arbor, MI
United States
Alexandra Seceleanu
Department of Mathematics
University of Nebraska
Lincoln, NE
United States
Branden Stone
Mathematics Department
Hamilton College
Clinton, NY
United States