I was expecting x^2 as the characteristic polynomial.  What's gone
wrong?

sage: type(m)
<type 'sage.matrix.matrix_rational_dense.Matrix_rational_dense'>
sage: m
[   0    0  1/4    0    0  1/4    0    0 -1/4    0    0 -1/4]
[ 1/4    0    0 -1/4    0    0  1/4    0    0 -1/4    0    0]
[   0  1/4    0    0 -1/4    0    0 -1/4    0    0  1/4    0]
[   0    0  1/4    0    0  1/4    0    0 -1/4    0    0 -1/4]
[-1/4    0    0  1/4    0    0 -1/4    0    0  1/4    0    0]
[   0 -1/4    0    0  1/4    0    0  1/4    0    0 -1/4    0]
[   0    0 -1/4    0    0 -1/4    0    0  1/4    0    0  1/4]
[ 1/4    0    0 -1/4    0    0  1/4    0    0 -1/4    0    0]
[   0 -1/4    0    0  1/4    0    0  1/4    0    0 -1/4    0]
[   0    0 -1/4    0    0 -1/4    0    0  1/4    0    0  1/4]
[-1/4    0    0  1/4    0    0 -1/4    0    0  1/4    0    0]
[   0  1/4    0    0 -1/4    0    0 -1/4    0    0  1/4    0]
sage: m.charpoly()
x^12
sage: m**2
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0]

Graham

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