42.2 IsMapping

IsMapping( map )

IsMapping returns true if the general mapping map is single valued and false otherwise. Signals an error if map is not a general mapping.

    gap> g := Group( (1,2,3,4), (2,4), (5,6,7) );;  g.name := "g";;
    gap> p4 := MappingByFunction( g, g, x -> x^4 );
    MappingByFunction( g, g, function ( x )
        return x ^ 4;
    end )
    gap> IsMapping( p4 );
    true
    gap> IsMapping( InverseMapping( p4 ) );
    false    # note that the inverse mapping is multi valued
    gap> p5 := MappingByFunction( g, g, x -> x^5 );
    MappingByFunction( g, g, function ( x )
        return x ^ 5;
    end )
    gap> IsMapping( p5 );
    true
    gap> IsMapping( InverseMapping( p5 ) );
    true    # 'p5' is a bijection 

IsMapping first tests if the flag map.isMapping is bound. If the flag is bound, it returns its value. Otherwise it calls map.operations.IsMapping( map ), remembers the returned value in map.isMapping, and returns it.

The default function called this way is MappingOps.IsMapping, which computes the sets of images of all the elements in the source of map, provided this is finite, and returns true if all those sets have size one. Look in the index under IsMapping to see for which mappings this function is overlaid.

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