On Friday, October 26, 2018 at 9:07:58 AM UTC-7, Daniel Krenn wrote:
>
> What my troubles are, is that by using abs my computation gets inexact, 
> which I want to avoid at all cost. 
> (So I think I just have to treat CyclotomicFields etc. special) 
>
> Yes, that indicates you are probably more interested in a relative norm 
than in an absolute value, if exactness matters for you.

The right target to take values in would probably be (if K is a cyclotomic 
field):

 K.maximal_totally_real_subfield()

For arbitrary number fields with a complex embedding, the associated real 
field might not be a subfield (for that you need the corresponding complex 
conjugation to be an element of the automorphism group over Q).

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