Varying methods exist for computing a presentation of a finitely generated commutative cancellative monoid. We use an algorithm of Contejean and Devie [An efficient incremental algorithm for solving systems of linear diophantine equations, Inform. and Comput. 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.
Chapman, S.T., García-Sánchez, P.A., Llena, D., & Rosales, J.C. (2006). Presentations of finitely generated cancellative commutative monoids and nonnegative solutions of systems of linear equations. Discrete Applied Mathematics, 154(14), 1947-1959. doi:10.1016/j.dam.2006.03.013
Discrete Applied Mathematics