id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
12715 Number field embeddings should go via AA and QQbar davidloeffler davidloeffler "Sage has a very nice module for the fields of algebraic numbers and algebraic real numbers (defined internally by a number field element and a choice of embedding).
This is almost tautologically the right target for real/complex embeddings of number fields, but at the moment it is *impossible* to create such embeddings -- the target is silently changed to the real/complex ""lazy"" fields in {{{ sage.rings.real_lazy }}}, which do not (and should not) coerce to AA / QQbar.
{{{
sage: K. = NumberField(x^3 - x - 1, embedding = AA(1))
sage: K.coerce_embedding()
Generic morphism:
From: Number Field in a with defining polynomial x^3 - x - 1
To: Real Lazy Field
Defn: a -> 1.324717957244746?
sage: AA.has_coerce_map_from(K)
}}}
The above code should clearly return an embedding into AA; and more generally any embedding into any real field should be automagically refined to one into AA (not into RLF)" defect new major sage-6.4 number fields qqbar coercion N/A