GAP Manual: 51.2. CompositionMaps

CompositionMaps( paramap2, paramap1 )
CompositionMaps( paramap2, paramap1, class )

For parametrized maps paramap1 and paramap2 where paramap[i] is a bound position or a set of bound positions in paramap2, CompositionMaps( paramap2, paramap1 ) is a parametrized map with image CompositionMaps( paramap2, paramap1, class ) at position class.

If paramap1[ class ] is unique, we have [ CompositionMaps( paramap2, paramap1, class ) = paramap2[ paramap1[ class ] ], ] otherwise it is the union of paramap2[i] for i in paramap1[ class ].

    gap> map1:= [ 1, [ 2, 3, 4 ], [ 4, 5 ], 1 ];;
    gap> map2:= [ [ 1, 2 ], 2, 2, 3, 3 ];;
    gap> CompositionMaps( map2, map1 ); CompositionMaps( map1, map2 );
    [ [ 1, 2 ], [ 2, 3 ], 3, [ 1, 2 ] ]
    [ [ 1, 2, 3, 4 ], [ 2, 3, 4 ], [ 2, 3, 4 ], [ 4, 5 ], [ 4, 5 ] ]

Note: If you want to get indirections of characters which contain unknowns (see chapter Unknowns) instead of sets of possible values, use Indirected Indirected.