23:44
@martin: Are you still on this, or is the current state of solution "good enough"? Here's where I'm at: Method of "flash" mentioned earlier is a mixed bag. Sometimes blindingly fast (as in handily beats CoefficientRules for getting all distinct), sometimes a dog, slower than current getCoeff. I kind of expected that from the method, but... bummer.
@martin: However, I've made the "a-ha!" on the earlier truncated products idea. The basic idea is to get coeffs. for each of the terms (where each (a^x+b^x...)^z is a "term"), and then use those to get the ultimate result. Now, even though CoefficientRules is fairly fast on individual simple terms like that (it probably has some magic sauce internally), I tested step 1 of this idea (getting those coeff. sets) on...
a nine term set with internal powers ranging from 1 to 9 and external powers ranging from 1 to 10 with a few duplicates thrown in. Using CoefficientRules took nearly five minutes on the netbook. New step took... 0 seconds (below timer resolution). I gave up trying bigger tests to get timings, CR just takes too long.
So, assuming I can come up with a reasonably efficient step 2 (I think I can), this could be good. But, if you're "done", will relegate to spare-spare-time thinking. Let me know...
