  In this paper we present a novel project-and-lift approach to compute the set
of minimal generators of the semigroup $(\Lambda\cap\R^n_+,+)$ for lattices
$\Lambda\subseteq\Z^n$. This problem class includes the computation of Hilbert
bases of cones $\{z:Az=0,z\in\R^n_+\}$ for integer matrices $A$. A similar
approach can be used to compute only the extreme rays of such cones. Finally,
some combinatorial applications and computational experience are presented.
