[MONOiD]

2.19 IsEquivalence

IsEquivalence( rel )

IsEquivalence returns true if the binary relation rel is an equivalence relation and false otherwise. 

    gap> IsEquivalence( Relation( [ [ ], [ 1 ], [ 1, 2 ] ] ) );
    false
    gap> IsEquivalence( Relation( [ [ 1 ], [ 2, 3 ], [ 2, 3 ] ] ) );
    true
A relation rel is an equivalence relation if rel is reflexive, symmetric, and transitive, i.e., if rel is a symmetric preorder (see IsPreOrder). (See also EquivalenceClasses.)

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Version 2.4 (May 1998)
[MONOiD]