I am interested in the growth rate of some finitely generated (infinite, non-abelian) discrete groups. Knowing very little about geometric group theory, I am wondering if I can plug them into sage and have it output estimate the (word) growth rate somehow.
I know theoretically I could write a program to do this, but since the naive algorithm I have in mind would take forever to run to any reasonable length (there are exponentially many words that need to be reduced...) I wondering if there are slicker methods out there.
Or perhaps I am being too naive - can the true growth rate of an arbitrary group take a long time to appear? (For the easy groups I can think of now, the growth rate is immediately apparent...)