Comment #4 on issue 3837 by [email protected]: RootOf.free_symbols gives wrong result
http://code.google.com/p/sympy/issues/detail?id=3837

RootOf.free_symbols uses the poly method to get the underlying polynomial. If a PurePoly is returned, it will give the null set for free symbols (if it is univariate). Using sol above:

sol[0]
RootOf(x**3 + 4*x + 1, 0)
_.poly
Poly(x**3 + 4*x + 1, x, domain='ZZ')


vs

RootOf(y**3 +5*y + 1, 0)
RootOf(y**3 + 5*y + 1, 0)
_.poly
PurePoly(y**3 + 5*y + 1, y, domain='ZZ')

So the question is "Why does poly give a PurePoly in one case but not the other?"

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