since we are very unexperienced in the use of GAP we would
like to know how to deal with the following problem:
We are given a finitly presented group G (we know how to encode
this in GAP) and want GAP to replace each generator by a product
of two new symbols (a representation of G) thus giving us a
new set of relators.
This can be done using functions on Associative Words;
Then we would like GAP to give us the
Fox-derivatives of this set of new relators.
You can define your Fox derivatives as elements of
a FreeMagmaRing (e.g. FreeMagmaRing(Integers,FreeGroup(2))).
You would have to explicitly program computing the terms in
the derivative via abovementioned Subword, etc.
Unfortunately, finitely presented algebras functionality is still
almost absent in GAP, so you won't be able to do much with these