2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68574Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z^d-graded injective resolution of M up to any desired cohomological degree. As an application, we derive an algorithm computing the local cohomology modules H^i_I(M) supported on any monomial (that is, Z^d-graded) ideal I. Since these local cohomology modules are neither finitely generated nor finitely cogenerated, part of this task is defining a finite data structure to encode them.22 pages, no figuresCommutative Algebra13P99, 13C11, 13D45, 14M25, 13D02text