Dear GAP-Forum,

Bruce Colletti wrote:

Subject: Equivalence Relations

Does GAP3.4.4 have a function that returns the cells that define a
user-specified equivalence relation?

For illustration, suppose S and A are respectively a subset and subgroup of
the group G. Let ~ be the equivalence relation on S defined by x ~ y iff x
and y are in the same right coset of A.

Does GAP have a dedicated function that allows one to define ~ and which
returns ~'s cells?

The GRAPE package deals with finite graphs with directed edges and
(possibly) loops, but no multiple edges. In other words, GRAPE deals
with relations on a finite set (the vertex-set). In GRAPE, G-graphs,
and hence G-invariant relations can be user-defined using the function
"Graph". The smallest equivalence relation containing a given symmetric,
irreflexive relation can be found using "ConnectedComponents", and
"QuotientGraph" can be put to use to find the smallest G-invariant
relation containing a given relation.

Help for these and other GRAPE functions can be found on-line in GAP.
Also, don't forget to 'RequirePackage("grape");'.

Regards, Leonard.