Matrix powers when the base domain is Rationals

[cdwensley]

Came across this while working on #6339.
If m1 := Matrix( Integers, [ [1,1], [0,1] ] ); then m1^2 is calculated correctly.
But if m1 := Matrix( Rationals, [ [1,1], [0,1] ] ); then m1^2 throws an error.

[cdwensley]

And here is another apparent problem:

gap> m1 := Matrix( Integers, [ [1,1], [2,2], [3,3], [4,4], [5,5] ] );;
gap> v1 := ZeroVector( 2, m1 );;
gap> m1[5] := v1;; Unpack( m1 );  ## this works OK
[ [ 1, 1 ], [ 2, 2 ], [ 3, 3 ], [ 4, 4 ], [ 0, 0 ] ]
gap> m2 := Matrix( [ [7,7], [8,8], [9,9] ], m1 );;
gap> m1{ [1..3] } := m2;
Error, List Assignments: <rhss> must be a dense list (not a positional object)
Stack trace:
not in any function at *stdin*:114
type 'quit;' to quit to outer loop

[fingolfin]

Thanks for the report, @cdwensley !

I can reproduce this: the following input

m1 := Matrix( Integers, [ [1,1], [0,1] ] );
m1^2;
m1 := Matrix( Rationals, [ [1,1], [0,1] ] ); 
m1^2;

leads to this output

gap> m1 := Matrix( Integers, [ [1,1], [0,1] ] );
<2x2-matrix over Integers>
gap> m1^2;
<2x2-matrix over Integers>
gap> m1 := Matrix( Rationals, [ [1,1], [0,1] ] );
<2x2-matrix over Rationals>
gap> m1^2;
Error, no method found! For debugging hints type ?Recovery from NoMethodFound
Error, no 1st choice method found for `Enumerator' on 1 arguments
*[1] Enumerator( C )
   @ /Users/mhorn/Projekte/GAP/gap/lib/coll.gi:849
 [2] for a in id do
    r := addb( b, a );
    if r = true then
        repeat
            Add( t, a );
            a := a * m;
            r := addb( b, a );
        until r <> true;
    fi;
od;
   @ /Users/mhorn/Projekte/GAP/gap/lib/matrix.gi:4699
 [3] trafo( mat )
   @ /Users/mhorn/Projekte/GAP/gap/lib/matrix.gi:4737
<function "POW_MAT_INT">( <arguments> )
 called from read-eval loop at *stdin*:4
type 'quit;' to quit to outer loop
brk>

So it looks like it might be a bug in POW_MAT_INT ? (CC @frankluebeck)
Or maybe just a matter of adjusting POW_MAT_INT to be "safe" for MatrixObj, by using the appropriate new row transformation primitives? (CC @ThomasBreuer)

For the record, this is not a recent regression; I can reproduce this error back in GAP 4.11.1, but it is not there in GAP 4.10.2. But that's because back then, we did not (yet) dispatch to POW_MAT_INT:

gap> Display(ApplicableMethod(POW, [m1,2]));
function ( obj, gmp )
    <<kernel code from src/integer.c:POW_OBJ_INT>>
end