Error in `examples/challenges-by-frank-luebeck/example6.g.gz`: no method found for `CharacteristicPolynomialMatrixNC`

[fingolfin]

This is another issue in the GAP library related to matrices; in this case it seems there are troubles computing the char poly of a matrix over a "large" field, GF(2^16).

Reproducer:

$ gap -b examples/challenges-by-frank-luebeck/example6.g.gz
# Read matrix group "example6" over GF(65536) in dimension 67.
gap> ri:=RecognizeGroup(example6); time;
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `CharacteristicPolynomialMatrixNC' on 3 arguments
* [1] CharacteristicPolynomialMatrixNC( DefaultFieldOfMatrix( mat ), mat, 1 )
    @ /Users/mhorn/Projekte/GAP/gap/lib/matrix.gi:758
  [2] CharacteristicPolynomial( r )
    @ /Users/mhorn/Projekte/GAP/repos/pkg/gap-packages/recog/gap/projective/sl.gi:150
  [3] RECOG.SLn_godown( list )
    @ /Users/mhorn/Projekte/GAP/repos/pkg/gap-packages/recog/gap/projective/sl.gi:188
  [4] RECOG.SLn_constructppd2( g, d, q )
    @ /Users/mhorn/Projekte/GAP/repos/pkg/gap-packages/recog/gap/projective/sl.gi:369
  [5] RECOG.SLn_constructsl2( sld, d, q )
    @ /Users/mhorn/Projekte/GAP/repos/pkg/gap-packages/recog/gap/projective/sl.gi:47
  [6] RECOG.FindStdGens_SL( gm )
    @ /Users/mhorn/Projekte/GAP/repos/pkg/gap-packages/recog/gap/projective/classicalnatu\
ral.gi:934
  [7] f( ri )
    @ /Users/mhorn/Projekte/GAP/repos/pkg/gap-packages/recog/gap/base/methods.gi:117
  [8] CallRecogMethod( db[i].method, ri )
    @ /Users/mhorn/Projekte/GAP/repos/pkg/gap-packages/recog/gap/base/methsel.gi:89
  [9] CallMethods( allmethods, 10, ri )
    @ /Users/mhorn/Projekte/GAP/repos/pkg/gap-packages/recog/gap/base/recognition.gi:511
 [10] RecogniseGeneric( Group( List( GeneratorsOfGroup( H ), function ( x )
          return ImageElm( Homom( ri ), x );
      end ) ), methodsforimage( ri ), depthString, InitialDataForImageRecogNode( ri ) )
    @ /Users/mhorn/Projekte/GAP/repos/pkg/gap-packages/recog/gap/base/recognition.gi:594
 [11] RecogniseGeneric( G, FindHomDbMatrix, "", rec(
     ) )
    @ /Users/mhorn/Projekte/GAP/repos/pkg/gap-packages/recog/gap/base/recognition.gi:112
<function "RecogniseGroup">( <arguments> )
 called from read-eval loop at *stdin*:1
type 'quit;' to quit to outer loop

Presumably this is less an issue in recog, and more one in GAP. If so, we should be able to extract a standalone reproducer.

Or maybe it is an issue in recog after all. We'll see.