  Let 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.
