Two identical spacegroups have different CocVecs.

[hongyi-zhao]

See my following testing:

gap> S1:=SpaceGroupOnLeftIT(3,229);
SpaceGroupOnLeftIT(3,229,'1')
gap> S2gen:=[ [ [ 0, 1, 0, -1 ], [ 0, 0, -1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 1 ] ], [ [ -1, 0, 0, -4 ], [ 0, 0, 1, -2 ], [ 0, -1, 0, 0 ], [ 0, 0, 0, 1 ] ], 
>   [ [ 1, 0, 0, 5/2 ], [ 0, 1, 0, -5/2 ], [ 0, 0, 1, 11/2 ], [ 0, 0, 0, 1 ] ] ];
[ [ [ 0, 1, 0, -1 ], [ 0, 0, -1, 1 ], [ 1, 0, 0, 1 ], [ 0, 0, 0, 1 ] ], [ [ -1, 0, 0, -4 ], [ 0, 0, 1, -2 ], [ 0, -1, 0, 0 ], [ 0, 0, 0, 1 ] ], 
  [ [ 1, 0, 0, 5/2 ], [ 0, 1, 0, -5/2 ], [ 0, 0, 1, 11/2 ], [ 0, 0, 0, 1 ] ] ]
gap> S2:=AffineCrystGroupOnLeft(S2gen);
<matrix group with 3 generators>
gap> S1=S2;
true
gap> CocVecs(S1);
[  ]
gap> CocVecs(S2);
[ [ 2, 0, 2 ], [ 0, 2, 2 ], [ 0, 0, 4 ] ]

Therefore, there seem to be some bugs in the algorithm implementation of CocVecs.

Regards,
Zhao