TITLE: Computations with conetypes of hyperbolic groups
QUESTION [5 upvotes]: I'd like to know if there exists (and, in this case, where I can find it) some computer program/programming language/any kind of software that can find explicitly the conetypes of a hyperbolic group on which I am working (a presentation of which is known).

REPLY [9 votes]: My KBMAG package can compute a finite state automaton that accepts the language of geodesic words in a hyperbolic group, and I think the states of that automaton correspond exactly to the conetypes.
It is not particularly easy to use. If you write down the presentation of the group you are interested in, then I can try out the computation for you.