ExteriorModules: a package for computing monomial modules over an exterior algebra

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, ...., g_r such that deg g_1 deg (g_2)≤ .....≤ deg(g_r). 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 .