Hi!

On Nov 26, 1:51 am, Alex Raichev <[EMAIL PROTECTED]> wrote:
> sage: F.<a>= NumberField(x^2-2)
> sage: a^2
> 2
> sage: a^2 in QQ
> True
> sage: a^2 in QQbar
> False
> sage: 2 in QQbar
> True

A related observation:
 sage: F.<a>=NumberField(x^2-2)
 sage: QQ.is_subring(F)
 True
 sage: F.is_subring(QQbar)
 False

Cheers,
    Simon

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