Excellent. It should be cross-referenced from the docstring to
complex_embeddings(), real_embeddings() and also possibly
embeddings().
I also notice that places() gives maps to RIF, CIF while
{real,complex}_embeddings give maps to RealField, ComplexField. I
don't have a feel for which is better since I have never used RIF and
CIF, but it might be better to be consistent.
John
2008/9/6 Craig Citro <[EMAIL PROTECTED]>:
>
>> * K.complex_embeddings() gives all the embeddings of K into CC (the
>> complex numbers).
>> You would need to eliminate one of ecah conjugate pair of embeddings.
>>
>> TODO: implement a flag to complex_embeddings() which only gives one of
>> each pair.
>>
>
> Actually, this code already exists:
>
> sage: x = polygen(QQ); K.<a> = NumberField(x^3-2)
> sage: K.places()
> [Ring morphism:
> From: Number Field in a with defining polynomial x^3 - 2
> To: Real Field with 106 bits of precision
> Defn: a |--> 1.259921049894873164767210607278,
> Ring morphism:
> From: Number Field in a with defining polynomial x^3 - 2
> To: Complex Field with 53 bits of precision
> Defn: a |--> -0.629960524947437 + 1.09112363597172*I]
>
> sage: K.places(prec=53)
> [Ring morphism:
> From: Number Field in a with defining polynomial x^3 - 2
> To: Real Double Field
> Defn: a |--> 1.25992104989,
> Ring morphism:
> From: Number Field in a with defining polynomial x^3 - 2
> To: Complex Double Field
> Defn: a |--> -0.629960524947 + 1.09112363597*I]
>
> It doesn't do anything remarkably clever, and makes the choice to
> always take the embedding with positive imaginary part. One could
> easily add a flag to make this more customizable ...
>
> -cc
>
> >
>
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