I'd like to have the result of a sage calculation somehow remain as an
irrational fraction.  Specifically, here I'm calculating the
eigenvalues of the matrix who's powers generate the fibonacci numbers:
sage: m=matrix(2,2,[0,1,1,1]);m
[0 1]
[1 1]
sage: m.eigenvalues ()
[-0.618033988749895?, 1.618033988749895?]

I'd LOVE to be able to somehow get the more meaningful value of which
contains the 1+/-sqrt(5) form:

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?

[This is pretty noob, I realize, but I tried several searches, and
even found golden-ratio, but couldn't figure out how to achieve the
desired result of not evaluating irrationals]

Thanks!  Sage rocks!

   -- Owen

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