Hi,
how can I define the prime sub-field of e in my example?

gap> Indeterminate(Rationals,"x");;
gap> p:=UnivariatePolynomial(Rationals,[5,0,-20,0,16],1);;
gap> e:=FieldExtension(Rationals,p);
gap> f:=PrimeField(e);
value property is already set the other way at
SetIsPrimeField( P, true );
<function>( <arguments> ) called from read-eval-loop
Entering break read-eval-print loop, you can 'quit;' to quit to outer loop,
or you can return to set it anyhow to continue
brk>