42.13 PreImagesRepresentative

PreImagesRepresentative( map, img )

PreImagesRepresentative returns an representative of the set of preimages of img under map, i.e., a single element elm, such that img in Images( map, elm ) (see Images).

    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> PreImagesRepresentative( p4, (5,6,7) );
    (5,6,7)
    gap> p5 := MappingByFunction( g, g, x -> x^5 );
    MappingByFunction( g, g, function ( x )
        return x ^ 5;
    end )
    gap> PreImagesRepresentative( p5, (2,4)(5,6,7) );
    (2,4)(5,7,6) 

PreImagesRepresentative calls
map.operations.PreImagesRepresentative( map, img ) and returns this value.

The default function called this way is MappingOps.PreImagesRepresentative, which calls PreImages( map, img ) and returns the first element in this set. Look in the index under PreImagesRepresentative to see for which mappings this function is overlaid.

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