Singular

For the Newton-non-degenerate singularities many invariants are computable in terms of the Newton diagrams. Thus the natural way to check some guesses (and to look for counterexamples) is to go over all the Newton diagrams inside some Conv(x^N,y^N,z^N).

As the number of such diagrams grows exponentially, one needs some effective/fast algorithm. I wonder, what are the known algorithms? (if any) Is there something written in Singular?