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.
GAP 3.4.4