> < ^ From:

> < ^ Subject:

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.

> < [top]