I want to construct the field $K=Q[i,w]$ where $w=\sqrt[4]{2}$ and define a field homomorphism such as $w\mapsto iw$, $i\mapsto -i$. I'd like to do
K.<w,I> = NumberField([x^4-2,x^2+1])
H = End(K)
H([I*w,-I])
but it doesn't work because $K$ is considered to be the relative field $(Q[i])[w]$. I know I could work with the absolute field
K_abs.<theta> = K.absolute_field()
but I'd really like to define the morphism in terms of $w,i$. Is it possible?
