Dear Forum,

I'm using version 4b5, and here's the problem I'm having:

gap> x:=Indeterminate(Rationals,"x");
x
gap> a:=AlgebraicExtension(Rationals,x^4-2*x^2+9);
<field in characteristic 0>
gap> RootOfDefiningPolynomial(a);
Error no method found for operation RootOfDefiningPolynomial at
[...]

As far as I can see from the source code, this function is implemented
so far for the finite fields only.
This is easy to see by doing grep in <GAP-source-path>/gap4b5/lib/ :

$ fgrep " RootOfDefiningPolynomial" *
ffe.gi:#M RootOfDefiningPolynomial( <F> ) . . . . . . . for standard finite fields
ffe.gi:InstallMethod( RootOfDefiningPolynomial,
ffe.gi: return RootOfDefiningPolynomial( F );
field.gd:#A RootOfDefiningPolynomial( <F> )

(note that only the 1st line of the fgrep output is relevant in this case).

As there is nothing w.r.t. "Polynomial" in
<GAP-source-path>/gap4b5/src/, we can safely conclude that
we haven't overlooked some other definition...

Hope this helps,
Dmitrii

PS. Should this actually be moved to the gap4 list ?