I encountered an issue which can be easily solved interactively but it may
give problems inside code:
sage: F = CyclotomicField(4, 'b')
sage: R = PolynomialRing(F, 'x, b')
sage: u, v = R.gens()
sage: f = v^2 - u
sage: f0 = f.subs({u:1})
sage: f1 = F[v](f0)
Related to this, I discovered number_field_elements_from_algebraics
which is useful to constuct a number field (abstract or embedded) in QQbar
from a finite set of algebraic numbers. There are several options but I saw
no way to change the name of the primitif element ('a') we may produce
errors as above.
It seems it is not difficult to add an optional keyword to choose this name.
Best, Enrique.
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