ExteriorIdeals: a package for computing monomial ideals in an exterior algebra
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}.
scientific article; zbMATH DE number 6998254