sage: OZ = lambda P: (ones_matrix(P.cardinality()) - P.lequal_matrix())
sage: set(min(OZ(P).eigenvalues()) for n in range(1, 7) for P in posets(n))
{-1, -1, 0}
sage: [type(x) for x in _]
[<class 'sage.rings.rational.Rational'>,
<class 'sage.rings.rational.Rational'>,
<class 'sage.rings.qqbar.AlgebraicNumber'>]
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