Converting a GF(9) matrix to a GF(3) matrix should be easier

[fingolfin]

I have an identity matrix over GF(9); I'd like to rewrite it to a GF(3) matrix; that is mathematically possible and sane. But surprisingly hard in GAP:

gap> m:=IdentityMat(1,GF(9));
[ [ Z(3)^0 ] ]
gap> ConvertToMatrixRep(m,3);
Error, ConvertToMatrixRep( <mat>, <q> ): not all entries of <mat> written over <q>
gap> Matrix(GF(3), m);
Error, ConvertToMatrixRep( <mat>, <q> ): not all entries of <mat> written over <q>
gap> ChangedBaseDomain(m, GF(3));
Error, ConvertToMatrixRep( <mat>, <q> ): not all entries of <mat> written over <q>
gap> Matrix(GF(3), List(m,List));  # works but is super inefficient
[ [ Z(3)^0 ] ]

Of course that wasn't a true compressed matrix, but rather a list of compressed vectors (well, one).

If we first convert to an actual compressed matrix, we fair slightly better (?), in that now ChangedBaseDomain works (yay), and ConvertToMatrixRep returns fail instead of raising an error (is that better or worse, though).

gap> ConvertToMatrixRep(m);
9
gap> m;
[ [ Z(3)^0 ] ]
gap> Is8BitMatrixRep(m);
true
gap> BaseDomain(m);
GF(3^2)
gap> ConvertToMatrixRep(m,3);
fail
gap> Matrix(GF(3), m);
Error, ConvertToMatrixRep( <mat>, <q> ): not all entries of <mat> written over <q>
gap> m2:=ChangedBaseDomain(m, GF(3));
[ [ Z(3)^0 ] ]
gap> Is8BitMatrixRep(m2);
true
gap> BaseDomain(m2);
GF(3)

[fingolfin]

BTW I think this is part of the "deeper issues" behind the recog regressed which is also discussed in issue #6389

[ThomasBreuer]

I think ImmutableMatrix would be an answer.

gap> m:= IdentityMat( 1, GF(9) );
[ [ Z(3)^0 ] ]
gap> m2:= ImmutableMatrix( GF(3), m );
[ [ Z(3)^0 ] ]
gap> Is8BitMatrixRep( m2 );
true

Of course, this does not help if one wants a mutable matrix over GF(3).

(I think that both Matrix(GF(3), m) and ChangedBaseDomain(m, GF(3)) should work.)

[fingolfin]

From a comment on another PR, but worth recording here as well: part of the issue is this:

gap> m:=IdentityMat(1,GF(9));
[ [ Z(3)^0 ] ]
gap> BaseDomain(m);
GF(3)
gap> BaseDomain(m[1]);
GF(3^2)

So BaseDomain on the entire matrix can disagree with it applied to its row(s).

[ThomasBreuer]

With the changes from #6396, the problem disappears:

gap> m:= IdentityMat( 1, GF(9) );
[ [ Z(3)^0 ] ]
gap> m1:= Matrix( GF(3), m );
[ [ Z(3)^0 ] ]
gap> m2:= ChangedBaseDomain( m, GF(3) );
[ [ Z(3)^0 ] ]
gap> Is8BitMatrixRep( m1 );  Q_VEC8BIT( m1[1] );
true
3
gap> Is8BitMatrixRep( m2 );  Q_VEC8BIT( m2[1] );
true
3