Hello. I have just acquired GAP, and apologize if
this question has been dealt with previously.

I need to compute structures on semigroups of
partial 1-1 functions, e.g., Green's relations.
GAP does not seem to have any of the relevant
things I need for this. Has anyone implemented
anything that would help, such as partial
functions?

If not, I'd like some feedback on my initial
ideas for implementing this. At first reading,
it appears that partial functions should be
implemented as lists with holes, and a new
domain type, something like "semigroups of
partial 1-1 functions" needs to be constructed
as a set of these lists, together with
operations that compose partial functions,
compute Green's relations, etc. I'll need to
build several new domains, such as "Brandt
semigroups" and "inverse semigroups".

Once the semigroup stuff is implemented, then
I can take advantage of GAP's group-theoretic
abilities, as I am computing symmetries of
various structures in Green's relations.

Thanks in advance,
Paul Benjamin