real and imag of number field element do not respect embedding

[dkrenn]

sage: CC(QQ.extension(x^2 + 5*x + 12, 'alpha1').gen())

and

sage: SR(QQ.extension(x^2 + 5*x + 12, 'alpha1').gen())

throw exceptions as they should, but

sage: real(QQ.extension(x^2 + 5*x + 12, 'alpha1').gen())
-5/2
sage: imag(QQ.extension(x^2 + 5*x + 12, 'alpha1').gen())
1/2*sqrt23

return a result. Indeed the real part is independent of the embedding, so correct, but the imaginary part is depends in the embedding.

Component: number fields

Issue created by migration from https://trac.sagemath.org/ticket/26537