Abstract

Let $K$ be a field, $V$ a $K$-vector space with basis $e_1,\dots ,e_n$, and $E$ the exterior algebra of $V$. We introduce a Macaulay2 package that allows one to deal with classes of monomial ideals in $E$. More precisely, we implement in Macaulay2 some algorithms in order to easily compute stable, strongly stable and lexsegment ideals in $E$. Moreover, an algorithm to check whether an $\left(n+1\right)$-tuple $\left(1,h_1,\dots ,h_n\right)$ ($h_1\le n={dim}_{K}V$) of nonnegative integers is the Hilbert function of a graded $K$-algebra of the form $E∕I$, with $I$ a graded ideal of $E$, is given. In particular, if $H_{E∕I}$ is the Hilbert function of a graded $K$-algebra $E∕I$, the package is able to construct the unique lexsegment ideal $I^{lex}$ such that $H_{E∕I}=H_{E∕I^{lex}}$.

Keywords

Mathematical Subject Classification 2010

Supplementary material

ExteriorIdeals.m2 - Macaulay2 package for computing monomial ideals in an exterior algebra

Milestones

Authors