Field extension bug

[markuspf]

Observed behaviour

When creating a field extension over a field that is not a prime field:

    gap> f:= GF(4);;
    gap> x:= Indeterminate( f );;
    gap> g:= x^3 + x + 1;;
    gap> ext:= AlgebraicExtension( f, g );;
    gap> Length( Elements( ext ) );
    4096
    gap> Length( Set( Elements( ext ) ) );
    64

note that

gap> ext;
<algebra-with-one of dimension 6 over GF(2^2)>
gap> LeftActingDomain(ext);
GF(2^2)

but the extension defined above only has dimension 3 over GF(4). The Elements-Enumeration procedure assumes it gets a GF(4)-basis for ext, but it is actually getting a GF(2) basis.

Expected behaviour

Field extensions over field extensions should work more or less in general.

[markuspf]

The field extension code itself was written by @hulpke as far as I can tell. Maybe we can quickly talk about this when he is in St Andrews.

[olexandr-konovalov]

The fix is now submitted by @hulpke as a part of #877

[olexandr-konovalov]

The fix for this and also for one more bug was merged in #877