TITLE: Good Computer Package for Calculating Inverse of a Formal Power Series?
QUESTION [5 upvotes]: This might be a question people already asked or is obvious to experts, or is not appropriate for this forum, if so, I apologize. I am trying to calculate things like $z/(e^z-1)$, or find the inverse of $x=z+ 2z+5z^2+\cdots$, expand as power series. What is the best (or favorite) software package you use to do stuff like this?

REPLY [5 votes]: Okay, I've gathered the answers from the comments in alphabetical order.

flint has the fmpz_poly_revert_series command (A web search revealed a reference pdf, but no web page).  Some benchmarks seem to indicate that flint is unusually fast.
Maple has the reversion command.
Mathematica has the InverseSeries command.
Pari/GP has the serreverse function.
SAGE has the reversion command.