On Thu, Jan 21, 1999 at 06:28:12PM +0100, Dmitrii Pasechnik wrote:
> 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

Thanks for the response. Actually x^4-2*x^2+9 is a Galois Field, its
Galois closure group is C_2 x C_2. I wonder what's included in GAP's
definition of *standard finite fields*.

I'll double check at the GAP4 mailing list.

Igor