Something is Seriously odd in the World of Composition of Mappings

[stevelinton]

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Observed behaviour

gap> phi := IdentityMapping(SymmetricGroup([1..5]));
IdentityMapping( Sym( [ 1 .. 5 ] ) )
gap> psi := IdentityMapping(SymmetricGroup([1,2,3,4,6]));
IdentityMapping( Sym( [ 1, 2, 3, 4, 6 ] ) )
gap> CompositionMapping(phi,psi);
CompositionMapping( IdentityMapping( Sym( [ 1 .. 5 ] ) ), IdentityMapping( Sym( [ 1, 2, 3, 4, 6 ] ) ) )
gap> Source(last);
Sym( [ 1, 2, 3, 4, 6 ] )
gap> alpha := CompositionMapping(phi,psi);
CompositionMapping( IdentityMapping( Sym( [ 1 .. 5 ] ) ), IdentityMapping( Sym( [ 1, 2, 3, 4, 6 ] ) ) )
gap> Source(alpha);
Sym( [ 1, 2, 3, 4, 6 ] )
gap> Range(alpha);
Sym( [ 1 .. 5 ] )
gap> ImagesSource(alpha);
Group([ (1,2,3,4,6), (1,2) ])
gap> PreImagesRange(alpha);
Group([ (1,2,3,4,5), (1,2) ])
gap> ImagesRepresentative(alpha,(1,2,3,4,5));
(1,2,3,4,5)
gap> 

Expected behaviour

alpha should be the identity mapping on the INTERSECTION of Sym([1..5]) and Sym([1,2,3,4,6])
In fact it seems to be a fairly inconsistent object.

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master branch.

So something pretty odd is going on here. For z := CompositionMapping(x,y) the manual doesn't seem to tell us either (a) what the requirements for Source(x) and Range(y) are?
(b) What Source(z) and Range(z) should be. Once we know that, we can fix the methods.

I haven't explored non-identity mappings yet.

[stevelinton]

Digging into the manual, I see I should really have used Images rather than ImagesRepresentative but the result is still odd:

gap> Images(alpha,(1,2,3,4,6));
RightCoset(Group(()),(1,2,3,4,6))
gap> Range(alpha);             
Sym( [ 1 .. 5 ] )

So the Images are outside the Range, even though the input is inside the Source

[stevelinton]

More oddness:

gap> g := Subgroup(s,[(1,2,3,4,5),(1,2)]);
Group([ (1,2,3,4,5), (1,2) ])
gap> h := Subgroup(s,[(1,2,3,4,6),(1,2)]);
Group([ (1,2,3,4,6), (1,2) ])
gap> k := Subgroup(s,[(1,2,3,4,7),(1,2)]);   
Group([ (1,2,3,4,7), (1,2) ])
gap> alpha := GroupHomomorphismByImages(g,h);
[ (1,2,3,4,5), (1,2) ] -> [ (1,2,3,4,6), (1,2) ]
gap> beta := GroupHomomorphismByImages(h,k); 
[ (1,2,3,4,6), (1,2) ] -> [ (1,2,3,4,7), (1,2) ]
gap> CompositionMapping(beta,alpha);
[ (1,2,3,4,5), (1,2) ] -> [ (1,2,3,4,7), (1,2) ]
gap> CompositionMapping(beta,beta); 
Error, List Element: <list>[7] must have an assigned value in
  img := opr( img, S.transimages[bimg[1]] ); at /Users/sal/GIT/gap/lib/ghomperm.gi:108 called from 
ImageSiftedBaseImage( S, OnTuples( BaseStabChain( S ), elm ), S.idimage, OnRight 
 ) at /Users/sal/GIT/gap/lib/ghomperm.gi:1008 called from
ImagesRepresentative( hom1, g ) at /Users/sal/GIT/gap/lib/ghomperm.gi:1047 called from
func( C[i] ) at /Users/sal/GIT/gap/lib/coll.gi:665 called from
List( S.labelimages, function ( g )
      return ImagesRepresentative( hom1, g );
  end ) at /Users/sal/GIT/gap/lib/ghomperm.gi:1047 called from
CompositionMapping2( nxt, com ) at /Users/sal/GIT/gap/lib/mapping.gi:398 called from
...  at *stdin*:8
you can 'return;' after assigning a value
brk> 

Arguably this should give an error abotu the sources and ranges (or be a restricted mapping), but this is clearly wrong. As is

gap> l := ClosureGroup(h,k);       
Group([ (1,2,3,4,6), (1,2), (1,2,3,4,7) ])
gap> gamma := IdentityMapping(l);  
IdentityMapping( Group([ (1,2,3,4,6), (1,2), (1,2,3,4,7) ]) )
gap> delta := CompositionMapping(alpha,gamma);
CompositionMapping( [ (1,2,3,4,5), (1,2) ] -> [ (1,2,3,4,6), (1,2) ],
 IdentityMapping( Group([ (1,2,3,4,6), (1,2), (1,2,3,4,7) ]) ) )
gap> ImagesSource(delta);
Error, List Element: <list>[6] must have an assigned value in
  img := opr( img, S.transimages[bimg[1]] ); at /Users/sal/GIT/gap/lib/ghomperm.gi:108 called from 
ImageSiftedBaseImage( S, OnTuples( BaseStabChain( S ), elm ), S.idimage, OnRight 
 ) at /Users/sal/GIT/gap/lib/ghomperm.gi:1008 called from
ImagesRepresentative( com!.map2, im 
 ) at /Users/sal/GIT/gap/lib/mapprep.gi:287 called from
ImagesRepresentative( map, gen ) at /Users/sal/GIT/gap/lib/mapphomo.gi:278 called from
func( C[i] ) at /Users/sal/GIT/gap/lib/coll.gi:665 called from
List( GeneratorsOfMagmaWithInverses( elms ), function ( gen )
      return ImagesRepresentative( map, gen );
  end ) at /Users/sal/GIT/gap/lib/mapphomo.gi:278 called from
...  at *stdin*:27
you can 'return;' after assigning a value
brk> 
gap> Range(alpha);
Group([ (1,2,3,4,6), (1,2) ])
gap> Source(delta);
Group([ (1,2,3,4,6), (1,2), (1,2,3,4,7) ])
gap>