On Wed, 26 Aug 2009, john_perry_usm wrote:

>
> Just yesterday I bumped up against factoring univariate polynomials in
> QQbar (*not* CC). Being able to factor in QQbar would have a broad
> impact (or maybe not, but at least on one ticket I was studying), but
> I don't know about feasibility.
>
> regards
> john perry

It's already essentially implemented, just not exposed:

sage: f = QQbar['x'].random_element(7) - QQbar(2).sqrt()

sage: f
  -2*x^7 - x^4 - 2*x^3 + 2*x^2 - x - 2.414213562373095?

sage: f.roots()

[(-0.7171741662738754?, 1),
  (-0.8861392795468010? - 0.7421111421692789?*I, 1),
  (-0.8861392795468010? + 0.7421111421692789?*I, 1),
  (0.3910288165366135? - 1.040117802100559?*I, 1),
  (0.3910288165366135? + 1.040117802100559?*I, 1),
  (0.8536975461471252? - 0.5399456095037692?*I, 1),
  (0.8536975461471252? + 0.5399456095037692?*I, 1)]

- Robert

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