Frobenius normal form does not work with this matrix

[GalaxyCo]

B := [ [ Z(11)^5, 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11),
       0*Z(11), 0*Z(11) ], [ 0*Z(11), Z(11)^5, 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11),
      0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11) ], [ 0*Z(11), 0*Z(11), Z(11)^5, 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11),
       0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11) ],
  [ 0*Z(11), 0*Z(11), 0*Z(11), Z(11)^5, 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11),
       0*Z(11), 0*Z(11) ], [ 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), Z(11^2)^30, 0*Z(11), 0*Z(11), 0*Z(11), Z(11)^5,
       0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11) ],
  [ 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), Z(11^2)^29, 0*Z(11), 0*Z(11), 0*Z(11), Z(11^2)^119, 0*Z(11), 0*Z(11),
      0*Z(11), 0*Z(11) ], [ 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), Z(11)^5, 0*Z(11), 0*Z(11), 0*Z(11),
       0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11) ], [ 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), Z(11)^5,
      0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11) ],
  [ 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), Z(11^2)^27, 0*Z(11), 0*Z(11), 0*Z(11), Z(11^2)^30, 0*Z(11), 0*Z(11), 0*Z(11),
       0*Z(11), 0*Z(11) ], [ 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), Z(11^2)^86, 0*Z(11), 0*Z(11), 0*Z(11),
       Z(11^2)^29, 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11) ],
  [ 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), Z(11)^5, 0*Z(11),
       0*Z(11), 0*Z(11) ], [ 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11),
      0*Z(11), Z(11)^5, 0*Z(11), 0*Z(11) ], [ 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11),
       0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), Z(11)^5, 0*Z(11) ],
  [ 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11), 0*Z(11),
       0*Z(11), Z(11)^5 ] ];

Called FrobeniusNormalForm(B);

Produces error

Error, Vector is locked over current field at /home/peter/gap/gap-4.15.1/lib/vecmat.gi:1252 called from
ConvertToVectorRepNC( v, q ) at /home/peter/gap/gap-4.15.1/lib/mat8bit.gi:401 called from
ConvertToMatrixRep( arg[1] ) at /home/peter/gap/gap-4.15.1/lib/mat8bit.gi:418 called from
ConvertToMatrixRepNC( orbit ); at /home/peter/.gap/pkg/nofoma/gap/nofoma.gi:149 called from
SpinMatVector1( A, idm[j], sp[1], sp[2], sp[4], sp[5] ) at /home/peter/.gap/pkg/nofoma/gap/nofoma.gi:181 called from
CyclicChainMat( A ) at /home/peter/.gap/pkg/nofoma/gap/nofoma.gi:252 called from
...  at *stdin*:42
you can 'quit;' to quit to outer loop, or
you can 'return;' to continue

[fingolfin]

The problem is that the code uses ConvertToMatrixRepNC to liberally and without a prescribed field size. Here the input matrix is over a field with 121 elements, but some matrices that are created during the computation probably are already defined over a field with 11 elements.

Ideally the target field (or field size) is passed to ConvertToMatrixRepNC... and perhaps use ConvertToMatrixRep .

And if fields are larger than 256, better don't use these functions at all sigh.

You can probably also talk to @ThomasBreuer in Aachen in person if you want to know more.