I am trying to compute the Galois group $\mathrm{Gal}(L/k)$ where $L/k$ is a Galois extension of number fields. $k$ is not necessarily $\mathbb{Q}$.
k = NumberField(x^2 + 1, 'i', embedding = I)
F = k.extension(x^4 - 17, 'a', embedding = 17^(1/4))
F.<a> = F.absolute_field()
G = F.galois_group()
k_gal = []
for g in G:
if g(i) == i:
k_gal.append(g)
Gal_F_k = G.subgroup(k_gal)
But Sage returns a TypeError.
TypeError: a fails to convert into the map's domain Number Field in a with defining polynomial x^8 + 4*x^6 - 28*x^4 + 208*x^2 + 256, but a `pushforward` method is not properly implemented
How could I fix my code?
