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Dear GAP forum,

I'm sure I'm missing something, but I can't understand the difference

between:

a) IsBinaryRelation( R ); ^^^ b) IsSymmetricBinaryRelation( rel ). ^^^^^

For example, if I write:

gap> A := Domain([1,2,3,4]);;

gap> elems := [Tuple([1,1]),Tuple([2,2]),Tuple([3,3]),Tuple([4,4]),

Tuple([1,3]),Tuple([3,1]),Tuple([2,4]),Tuple([4,2])];;

gap> R := GeneralMappingByElements(A, A, elems);

<general mapping: <object> -> <object> >

gap> IsTotal(R);

true

gap> IsBinaryRelation(R);

true

gap> IsSymmetricBinaryRelation(R);

Error no method found for operation IsSymmetricBinaryRelation with 1

argument

etc.

How many arguments does "rel" mean? (Other argument sets, such as "A, A,

elems", "R, elems", "elems", etc. don't work either.)

If I write:

gap> R := EquivalenceRelationByPartition(A, [[1,3],[2,4]]);

<equivalence relation on <object> >

gap> IsSymmetricBinaryRelation(R); # one argument!

true

it works. But if I assign an equivalence relation to R, I already know

that it is a symmetric, reflexive and transitive relation!

Please, could anybody tell me what I'm missing?

Thanks

Sergio

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