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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