In Sage, the eigenvalues and vectors (over a Rational matrix) returns
the answer in numerical format.
Is it possible to returns the answer in radical format ?
I am aware that I can use the Maxima eigenvectors function in Sage to
get the answer in radical format. It is better if I do need to depend
on Maxima. (Please see example below.)
sage: sageMatrix = matrix(QQ,[[1,4],[4,2]])
sage: sageMatrix
[1 4]
[4 2]
sage: sageMatrix.eigenvalues()
[-2.531128874149275?, 5.531128874149275?]
sage: sageMatrix.eigenvectors_right()
[(-2.531128874149275?, [(1, -0.8827822185373187?)], 1),
(5.531128874149275?, [(1, 1.132782218537319?)], 1)]
sage: maximaMatrix=maxima('matrix[[1,4],[2,4]]')
sage: maximaMatrix
matrix[[1,4],[2,4]]
sage: maximaMatrix.eigenvectors()
[[[-(sqrt(41)-5)/2,(sqrt(41)+5)/2],[1,1]],[1,-(sqrt(41)-3)/8],[1,(sqrt
(41)+3)/8]]
Thanks in advance for any assistance!
Shing
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