>
>
> (1) As in your first construction but replace each field constructed
> after the forst with the corresponding absolute field.
>
>
I have tried this but got something like:
F0.<foo0>= NumberField(x^2 - 2)
F1.<foo1>= F0.extension( polygen(F0)^2 - 5 )
L= F1.absolute_field("bar")
L(foo0)
...
TypeError: No compatible natural embeddings found for Number Field in bar with
defining polynomial x^4 - 14*x^2 + 9 and Number Field in foo0 with defining
polynomial x^2 - 2
So I cannot recover my square roots as elements of the field. I guess I could
ask for the roots of X^2 - 2 over L.
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