Comment #12 on issue 3068 by smi...@gmail.com: incorrect sign calculated
http://code.google.com/p/sympy/issues/detail?id=3068
Although changes have been committed that allow SymPy to return the sign if
it thinks that it can be computed, there is still an error somewhere. The
following XFAIL test was added because the computed sign should always by 1
regardless of x, but it is not (it ends up being -1).
```
@XFAIL
def test_issue_3068X():
eps = pi**-1500
big = pi**1000
one = cos(x)**2 + sin(x)**2
e = big*one - big + eps
assert sign(simplify(e)) == 1
for xi in (111, 11, 1, S(1)/10):
assert sign(e.subs(x, xi)) == 1
example for q = e.subs(x, 1)
q
pi**(-1500) - pi**1000*(cos(1)**2 + sin(1)**2) + pi**1000
sign(q)
-1
q.is_positive
q.is_negative
q.is_zero
```
Somewhere SymPy gets the idea that the sign can be computed, but sign()
should agree with the assumption system which says (for the above) that it
can't decide, and since sign got it wrong it should be determined where
this faulty determination is being made.
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