  We describe a rigorous computer algorithm for attempting to construct an
explicit, discretized metric for which a complex polynomial map is expansive on
a given neighborhood of its Julia set. We show construction of such a metric
proves the map is hyperbolic. We also examine the question of whether the
algorithm can be improved, and the related question of how to build a metric as
close to euclidean as possible. Finally, we give several examples generated
with our implementation of this algorithm.
