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Computing multiplicity sequences

Justin Chen, Youngsu Kim and Jonathan Montaño

Vol. 14 (2024), 13–18
Abstract

The MultiplicitySequence package for Macaulay2 computes the multiplicity sequence of a graded ideal in a standard graded ring over a field, as well as several invariants of monomial ideals related to integral dependence. We discuss two strategies that were implemented for computing multiplicity sequences: one via the bivariate Hilbert polynomial, and the other via the technique of general elements.

Keywords
multiplicity sequence, j-multiplicity
Mathematical Subject Classification
Primary: 13H15
Secondary: 13-04
Supplementary material

This package computes the multiplicity sequence of an ideal $I$ in a standard graded equidimensional ring over a field.

Milestones
Received: 25 March 2021
Revised: 9 October 2023
Accepted: 31 October 2023
Published: 26 March 2024
Authors
Justin Chen
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Youngsu Kim
Department of Mathematics California State University
San Bernardino, CA
United States
Jonathan Montaño
School of Mathematical and Statistical Sciences
Arizona State University
Tempe, AZ
United States