Computing multiplicity sequences
Justin Chen, Youngsu Kim, Jonathan Monta\~no
TL;DR
The paper introduces the MultiplicitySequence package for Macaulay2, which computes the multiplicity sequence of graded ideals and related invariants using two different strategies, enhancing computational algebra tools.
Contribution
It presents new computational methods and implementations for calculating multiplicity sequences and invariants of monomial ideals in Macaulay2.
Findings
Effective algorithms for multiplicity sequence computation
Implementation of two strategies: bivariate Hilbert polynomial and general elements
Enhanced tools for studying graded ideals and monomial invariants
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 implemented for computing multiplicity sequences: one via the bivariate Hilbert polynomial, and the other via the technique of general elements.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Algebraic Geometry and Number Theory