The standard coherence criterion for lower previsions is expressed using an
infinite number of linear constraints. For lower previsions that are essentially
defined on some finite set of gambles on a finite possibility space, we present
a reformulation of this criterion that only uses a finite number of constraints.
Any such lower prevision is coherent if it lies within the convex polytope
defined by these constraints. The vertices of this polytope are the extreme
coherent lower previsions for the given set of gambles. Our reformulation makes
it possible to compute them. We show how this is done and illustrate the
procedure and its results.