Thanks, Dima.
On Tuesday, September 25, 2012 10:08:13 AM UTC-7, Dima Pasechnik wrote:
>
> So this is a bug...
Maybe more like: my mistake. I had my print versions of the complex/real
algebraic numbers mixed up.
Here is the essence of how these (exact) eigenvalues are computed for
rational matrices (not just adjacency matrices of graphs). It would be a
definite improvement to recognize symmetric matrices (through a keyword or
an optional check) and then create these roots in AA rather than QQbar.
sage: G = graphs.GridGraph([3,2])
sage: p = G.am().fcp(); p
(x - 1) * (x + 1) * (x^2 - 2*x - 1) * (x^2 + 2*x - 1)
sage: f = p[2][0]; f
x^2 - 2*x - 1
sage: evs = f.root_field('t').gen(0).galois_conjugates(QQbar); evs
[-0.4142135623730951?, 2.414213562373095?]
sage: evs[0].parent()
Algebraic Field
sage: evs = f.root_field('t').gen(0).galois_conjugates(AA)
sage: evs[0].parent()
Algebraic Real Field
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