The above worksheet contains some computations I needed for a paper I am writing for the next issue of Maple Transactions. The computations are within reach of hand computation (which is why I know the right answers). I wanted Maple to be able to do them, however.
I couldn't make Maple do anything but verify that I was right (this is useful, I will admit). But can anyone find any artful ways to simplify or solve any of those steps? I suspect that this is quite hard in general, but with these things involving phi = (1+sqrt(5))/2 it's likely that others would find some "art" useful. By the way, phi is not built-in to Maple, as far as I know. Any more votes for including it?
There is an undocumented feature reported here that is useful: asympt works with "leadterm" and this turns out to be necessary. I forget how I found out that leadterm works with asympt. It's not in ?asympt, though I think that it should be.