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2015-02-20 21:58:34 -0500 commented answer Number field containing real/imaginary part of algebraic number

This is insightful, but the other solution is ultimately much shorter.

2015-02-20 21:57:32 -0500 commented answer Number field containing real/imaginary part of algebraic number

Thanks so much, I got it to work with: QQbar.polynomial_root(number_field.defining_polynomial(), CIF(number_field.gen_embedding())

2015-02-13 12:47:13 -0500 asked a question Number field containing real/imaginary part of algebraic number

I have a number field N with an embedding into C (e.g., NumberField(x^3+3, 'z', 0.7+1.2j)). I would like the smallest number field N' that contains all Re(z) and Im(z) for z in N. I would also like a mapping from x in N to (Re(x), Im(x) in N'xN' - or at least know what Re(z) and Im(z) is in N' for the generator z of N.

What is a good way of doing this?

I was thinking along the lines of N.composite_fields(NumberField(N.defining_polynomial, 'z', embedding=ComplexField()(N.gen_embedding()).conjugate()),both_maps=True). But I ran into http://trac.sagemath.org/ticket/14164 with this occasionally. Is there a better way of doing it?

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