Paul Benjamin asked about computing the Green relations for semigroups
of partial 1-1 functions in gap.
As far as I know there is no such package, but there are several
softwares computing Green relations of semigroups of functions, none
of them in gap.
I can cite four such programs:
automat - developed by Hansel and Champarnaud in Paris, they published
a paper about it. Contact Georges Hansel <email@example.com> for more
tor - a program written by myself. It is in Turbo Pascal (it has
been translated to C with the help of a utility program).
Unfortunately, the program is written in Portuguese, the
documentation is VERY scarce and also in portuguese. In any case it
is available from me (AS IS).
amore - a system developed in Aachen and Kiel. Contact Wolfgang
Thomas <firstname.lastname@example.org> for more information.
automata - a Mathematica package developed by Klaus Stutner; the
package is available from mathsource.wri.com in the Applications/Complexity
directory, as item 0205-197 "Automata".
There is also a version of tor, called lim, which computes the Green
relations for semigroups of matrices over a particular finite