Vol. 8, No. 1, 2018

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ExteriorIdeals: a package for computing monomial ideals in an exterior algebra

Luca Amata and Marilena Crupi

Vol. 8 (2018), 71–79
DOI: 10.2140/jsag.2018.8.71
Abstract

Let K be a field, V a K-vector space with basis e1,,en, 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 (n+1)-tuple (1,h1,,hn) (h1 n = dimKV ) of nonnegative integers is the Hilbert function of a graded K-algebra of the form EI, with I a graded ideal of E, is given. In particular, if HEI is the Hilbert function of a graded K-algebra EI, the package is able to construct the unique lexsegment ideal Ilex such that HEI = HEIlex.

Keywords
exterior algebra, monomial ideals, Hilbert functions, algorithms
Mathematical Subject Classification 2010
Primary: 13A02, 15A75, 68W30
Supplementary material

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

Milestones
Received: 28 August 2017
Revised: 15 May 2018
Accepted: 24 June 2018
Published: 16 July 2018
Authors
Luca Amata
Department of Mathematics and Computer Sciences, Physics and Geological Sciences
University of Messina
Messina
Italy
Marilena Crupi
Department of Mathematics and Computer Sciences, Physics and Geological Sciences
University of Messina
Messina
Italy