Vol. 11, No. 1, 2021

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

Luca Amata and Marilena Crupi

Vol. 11 (2021), 71–81
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 g1,,gr such that deg(g1) deg(g2) deg(gr). 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 FM, with M a graded submodule of F. Moreover, if HFM is the Hilbert function of a graded E-module FM, some routines are able to compute the unique lexicograhic submodule L of F such that HFM = HFL.

Keywords
exterior algebra, monomial modules, Hilbert functions, algorithms
Mathematical Subject Classification
Primary: 13A02, 15A75, 68W30
Supplementary material

Monomial modules over exterior algebras

Milestones
Received: 16 June 2020
Revised: 5 May 2021
Accepted: 3 June 2021
Published: 14 July 2021
Authors
Luca Amata
Department of Mathematics and Computer Sciences, Physical and Earth Sciences
University of Messina
Messina
Italy
Marilena Crupi
Department of Mathematics and Computer Sciences, Physical and Earth Sciences
University of Messina
Messina
Italy