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Dear Gap Forum,

On Thu, 16 Sep 1999, Sergio Polini wrote:

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!

trueit 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?

You are missing nothing. What you are asking GAP to do isn't implemented

yet.

The property IsSymmetricBinaryRelation is defined only for

EquivalenceRelation. That is, there is no code that determines this

property for arbitrary binary relations in Rel 4.1. This property is set

to be true for those objects for which it is known to be true i.e.

equivalence relations. Hence the error message apprears for binary

relations but not for equivalence relations.

The only good new here is that the next release will probably contain an

implementation to determine this property for binary relations (along

with the reflexive, transitive properties).

Regards,

Robert

.......................................................................

Robert F. Morse

Associate Professor of Computer Science

University of Evansville

1800 Lincoln Ave

Evansville, IN 47722

Phone: (812) 479-2994

e-mail: rfmorse@evansville.edu

http://www.evansville.edu/~rm43

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