On Nov 26, 2008, at 3:30 AM, Simon King wrote:
>
> Dear Michael,
>
> On Nov 26, 11:34 am, mabshoff <[EMAIL PROTECTED]
> dortmund.de> wrote:
>> please open a ticket. I would guess as you did that those two
>> related.
>
> Done, it is # 4621.
>
> By the way, the above problem appears even more directly:
> sage: F.<a>= NumberField(x^2-2)
> sage: 2 in QQbar
> True
> sage: F(2) in QQbar
> False
>
> Although F has no canonical embedding into QQbar, my understanding is
> that there is a hopefully unique maximal subfield of F that does have
> a canonical embedding into QQbar.
Into the mathematical \bar{Q}, yet. Sage's QQbar is \bar{Q} with a
choice of embedding into \C, and as F does not have a (chosen)
embedding into \C it doesn't have a chosen embedding into QQbar.
> If this is correct, there could be a
> method F.max_subfield_coercing_into(QQbar), and since F(2) is in that
> subfield, one has a reason to expect `F(2) in QQbar` to be True.
One *does* expect F(2) to be in QQbar, the same that one expects the
rational number 4/2 to be in ZZ, so I agree that the above is a bug.
- Robert
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