Status: Accepted
Owner: robert.kern
Labels: Type-Defect Priority-Medium WrongResult

New issue 1263 by robert.kern: Invalid movement of roots across fractions
http://code.google.com/p/sympy/issues/detail?id=1263

These came up while implementing the Wester tests. Basically, sqrt(1/z) is
being treated as equal to 1/sqrt(z)m but they are not in the case where z
is on the negative real axis. For example, if z=-1, then sqrt(1/-1) ==
sqrt(-1) == I, but 1/sqrt(-1) == 1/I == -I.

@XFAIL
def test_K8():
     z = Symbol('z', complex=True)
     # WrongResult!
     assert simplify(sqrt(1/z) - 1/sqrt(z)) != 0
     z = symbols('z', complex=True, negative=False)
     assert simplify(sqrt(1/z) - 1/sqrt(z)) == 0

def test_K9():
     z = Symbol('z', real=True, positive=True)
     assert simplify(sqrt(1/z) - 1/sqrt(z)) == 0

@XFAIL
def test_K10():
     # WrongResult!
     z = Symbol('z', real=True, negative=True)
     assert simplify(sqrt(1/z) + 1/sqrt(z)) == 0


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