Presentations of finitely generated cancellative commutative monoids and nonnegative solutions of systems of linear equations

Varying methods exist for computing a presentation of a finitely generated commutative cancellative monoid.We use an algorithm of Contejean andDevie [An efficient incremental algorithm for solving systems of linear diophantine equations, Inform. andComput. 113 (1994) 143–172] to show how these presentations can be obtained from the nonnegative integer solutions to a linear system of equations. We later introduce an alternate algorithm to show how such a presentation can be efficiently computed from an integer basis. © 2006 Elsevier B.V. All rights reserved.