2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102179In this article, we present a new algorithm for computing a generating set of a lattice ideal. This algorithm is based on a project-and-lift approach and is implemented in 4ti2. We also include a computational comparison of several existing implementations to compute such generating sets.The manuscript has been rearranged and modified to improve presentation and readability of the project-and-lift algorithm to compute generating sets of lattice idealsCombinatoricsCommutative Algebratext