ExteriorIdeals: a package for computing monomial ideals in an exterior algebra
type: Item
instance of: scholarly article
title: ExteriorIdeals: a package for computing monomial ideals in an exterior algebra
zbMATH Open document ID: 1409.13001
author: Luca Amata
author: Marilena Crupi
published in: The Journal of Software for Algebra and Geometry
publication date: 2019-01-08T00:00:00Z
review text: This paper introduces ExteriorIdeals Macualay2 package, a package for working with ideals over exterior algebra. More precisely, let $K$ be a field. Given the exterior algebra $E$ of a $n$-dimensional $K$-vector space V, this package allows us: \begin{itemize} \item[--] to check if a given monomial ideal $I$ in $E$ is stable, strongly stable or lex and to produce stable or strongly stable ideals containing $I$; \item[--] to verify whether an (n+1)-tuple $h=(h_0,h_1,\dots,h_n)$ of non negative integers is the Hilbert function of a graded $K$-algebra of the form $E/I$ ; this commands is based on the constructive proof of the Kruskal-Katona theorem; \item[--] to obtain, given a graded ideal I, the unique lex ideal $I^{lex}$ with the same Hilbert functions as I; and so on. \end{itemize} One can find all functions and commands on the following website: \url{https://faculty.math.illinois.edu/Macaulay2/doc/Macaulay2-1.13/share/doc/Macaulay2/ExteriorIdeals/html/index.html}.
reviewed by: Gema Maria Diaz Toca
Mathematics Subject Classification ID: 13A02
Mathematics Subject Classification ID: 13-04
Mathematics Subject Classification ID: 15A75
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 6998254
zbMATH Keywords: exterior algebra
zbMATH Keywords: monomial ideals
zbMATH Keywords: Hilbert functions
zbMATH Keywords: combinatorial commutative algebra
zbMATH Keywords: software
describes a project that uses: Macaulay2
MaRDI profile type: Publication
full work available at URL: jsag.2018.8.71
OpenAlex ID: W2893628010
cites work: Gotzmann theorems for exterior algebras and combinatorics
cites work: Resolutions of monomial ideals and cohomology over exterior algebras
cites work: Q4274969
cites work: Q5298638
cites work: Bounding Betti numbers of monomial ideals in the exterior algebra
cites work: Upper bounds for the betti numbers of graded ideals of a given length in the exterior algebra
cites work: Classes of Graded Ideals with Given Data in the Exterior Algebra
cites work: Hyperplane arrangement cohomology and monomials in the exterior algebra
cites work: Extremal properties of Hilbert functions
cites work: Monomial Ideals
cites work: Free resolutions of lex-ideals over a Koszul toric ring
cites work: Hilbert functions and Betti numbers of homogeneous ideals in an exterior algebra
cites work: Piecewise lexsegment ideals in exterior algebras
Wikidata QID: Q129203005
DOI: 10.2140/JSAG.2018.8.71
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description: scientific article; zbMATH DE number 6998254