NormalBaseNumberField( F )
NormalBaseNumberField( F, x )
returns a list of cyclotomics which form a normal base of the number
field F (see Number Field Records), i.e. a vector space base of the
field F over its subfield F.field which is closed under the action
of the Galois group F.galoisGroup of the field extension.
The normal base is computed as described in~Art68: Let Phi denote the polynomial of a field extension L/L^{prime}, Phi^{prime} its derivative and alpha one of its roots; then for all except finitely many elements z in L^{prime}, the conjugates of frac{Phi(z)}{(z-alpha)cdotPhi^{prime}(alpha)} form a normal base of L/L^{prime}.
When NormalBaseNumberField( F ) is called, z is chosen as integer,
starting with 1, NormalBaseNumberField( F, x ) starts with z=<x>,
increasing by one, until a normal base is found.
gap> NormalBaseNumberField( CF( 5 ) );
[ -E(5), -E(5)^2, -E(5)^3, -E(5)^4 ]
gap> NormalBaseNumberField( CF( 8 ) );
[ 1/4-2*E(8)-E(8)^2-1/2*E(8)^3, 1/4-1/2*E(8)+E(8)^2-2*E(8)^3,
1/4+2*E(8)-E(8)^2+1/2*E(8)^3, 1/4+1/2*E(8)+E(8)^2+2*E(8)^3 ]
GAP 3.4.4