On 03/28/2010 02:50 PM, Mike Hansen wrote:
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.
sage: QQbar(-1/2*sqrt(5) + 1/2)
-0.618033988749895?
sage: a=QQbar(-1/2*sqrt(5) + 1/2)
sage: a
-0.618033988749895?
sage: a.minpoly()
x^2 - x - 1
sage: solve(SR(a.minpoly()),x)
[x == -1/2*sqrt(5) + 1/2, x == 1/2*sqrt(5) + 1/2]
On the other hand, I think it would fairly straightforward for QQbar
objects to print out quadratic roots (that it knows are quadratic roots)
in the above format (using the quadratic equation), instead of using the
interval notation. It'd probably one or two if-cases in the printing code.
Thanks,
Jason
--Mike
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