Hi,

One can construct some finite field as an tower of extensions:
K.<x>=GF(3).extension(2)
L.<t>=K.extension(4)

The result seems to forget about K and L seems to be represented as 
L=GF(3)[t] and not L=K[t]=GF(3)[x,t]. 
In particular, is it a way to compute the norm of an element of L over K?
Also is it possible to obtain a basis of L/K?

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