On Wednesday, 26 September 2012 00:54:44 UTC+8, Rob Beezer wrote:
>
> To summarize some of this discussion more carefully:
>
> Eigenvalues of a symmetric rational matrix should already land in the 
> algebraic field (AA), so there is no need to convert them.  Error messages 
> appear to come from QQbar, since much of the functionality of AA is 
> contained in the same module as QQbar.
>
> sage: G = graphs.GridGraph([2,3])
> sage: spec = G.spectrum(); spec
> [2.414213562373095?, 1, 0.4142135623730951?, -0.4142135623730951?, -1, 
> -2.414213562373095?]
> sage: spec[0].parent()
> Algebraic Field
>

they should, but they don't. Look:

sage: a=AA(1)
Algebraic Real Field
sage: b=QQbar(1)
sage: b.parent()
Algebraic Field

 So this is a bug...

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