QQbar should accept number field elements with embeddings

[robertwb]

One should be able to do

sage: K.<a> = NumberField(x^3-x+1, embedding=-1.32)
sage: QQbar(a)
-1.324717957244746?

Followup to #4621

CC: @videlec

Component: number theory

Reviewer: Peter Bruin

Issue created by migration from https://trac.sagemath.org/ticket/7960

[videlec]

comment:5

cc'ing me.

The function sage.rings.number_field.number_field_morphisms.create_embedding_from_approx should really be smarter. This is related to what I am currently doing in #17830.

[mezzarobba]

comment:6

Fixed in #13041.

[pjbruin]

comment:8

The requested example now works. It would be even nicer to also have a coercion map from K to QQbar, but currently we do not have this:

sage: K.<a> = NumberField(x^3 - x + 1, embedding=-1.32)
sage: QQbar(a)
-1.324717957244746?
sage: QQbar.coerce_map_from(K) is None
True

[pjbruin]

Reviewer: Peter Bruin

[pjbruin]

comment:9

Replying to @pjbruin:

It would be even nicer to also have a coercion map from K to QQbar

OK, there is already a ticket for this: #5355. Positive review for this one.

[embray]

comment:10

Presuming these are all correctly reviewed as either duplicate, invalid, or wontfix.

[slel]

comment:11

Just fixing the example in the ticket description so anyone can check this now works.