Abstract

Let $K$ be a field, $E$ the exterior algebra of a finite-dimensional $K$-vector space, and $F$ a finitely generated graded free $E$-module with homogeneous basis $g_1,\dots ,g_r$ such that $deg\left(g_1\right)\le deg\left(g_2\right)\le \cdots \le deg\left(g_r\right)$. We present a Macaulay2 package to manage some classes of monomial submodules of $F$. The package is an extension of our ExteriorIdeals package on monomial ideals (J. of Software for Alg. and Geom. 8:7 (2018), 71–79), and contains some algorithms for computing stable, strongly stable and lexicograhic $E$-submodules of $F$. This package also includes some methods to check whether a sequence of nonnegative integers is the Hilbert function of a graded $E$-module of the form $F∕M$, with $M$ a graded submodule of $F$. Moreover, if $H_{F∕M}$ is the Hilbert function of a graded $E$-module $F∕M$, some routines are able to compute the unique lexicograhic submodule $L$ of $F$ such that $H_{F∕M}=H_{F∕L}$.

Keywords

Mathematical Subject Classification

Supplementary material

Monomial modules over exterior algebras

Milestones

Authors