2.18 IsPartialOrder

IsPartialOrder( rel )

IsPartialOrder returns true if the binary relation rel is a partial order and false otherwise.

    gap> IsPartialOrder( Relation( [ [ 1 ], [ 1, 2 ], [ 1, 2, 3 ] ] ) );
    true
    gap> IsPartialOrder( Relation( [ [ 1, 2 ], [ 1, 2 ], [ 1, 2, 3 ] ] ) );
    false 

A relation rel is called a partial order if rel is reflexive, transitive and antisymmetric, i.e., if rel is an antisymmetric preorder (see IsPreOrder).

   
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