Nils Bruin wrote:
> If a field embeds into QQbar, then there should be an implied coercion
> into CC, though: QQbar as implemented in sage is a subfield of the
> field of complex numbers (as you can see from how the elements print).

Let me add that there are long-standing tickets (#5355, #12715) for 
making number field embeddings go into AA/QQbar instead of RR/CC. Quite 
a bit of progress has been made towards that goal, but we're not quite 
there yet.

-- 
Marc

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