On Sun, Mar 28, 2010 at 12:35 PM, Owen <[email protected]> wrote:
> sage: n=(1+sqrt(5))/2;n
> 1/2*sqrt(5) + 1/2
> sage: N(n)
> 1.61803398874989
>
> Is there some way I can ask for the eigenvalues (or any other roots)
> in such a format?

You can see that

sage: ((1+sqrt(5))/2).parent()
Symbolic Ring

So, if you make your matrix over the Symbolic Ring (SR), then you get:

sage: sage: m=matrix(SR, 2,2,[0,1,1,1]);m
[0 1]
[1 1]
sage: m.eigenvalues()
[-1/2*sqrt(5) + 1/2, 1/2*sqrt(5) + 1/2]

There should be some way to get if from [-0.618033988749895?,
1.618033988749895?] which really store exact values, but I'm not sure
off the top of my head.

--Mike

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