(-x).is_extended_positive fails for extended_real and infinite

[oscarbenjamin]

When an expression is only known to be extended_real and infinite its sign is unknown so is_extended_positive should give None but

In [1]: x = Symbol('x', infinite=True, extended_real=True)                                                                        

In [2]: print(x.is_extended_positive)                                                                                             
None

In [3]: print((-x).is_extended_positive)                                                                                          
True

The obvious fix is

diff --git a/sympy/core/mul.py b/sympy/core/mul.py
index da2a8b18e7..ea0df52dfc 100644
--- a/sympy/core/mul.py
+++ b/sympy/core/mul.py
@@ -1401,12 +1401,12 @@ def _eval_pos_neg(self, sign):
                 saw_NON = True
             elif t.is_extended_nonnegative:
                 saw_NON = True
-            elif t.is_positive is False:
+            elif t.is_extended_positive is False:
                 sign = -sign
                 if saw_NOT:
                     return
                 saw_NOT = True
-            elif t.is_negative is False:
+            elif t.is_extended_negative is False:
                 if saw_NOT:
                     return
                 saw_NOT = True

Which gives

In [3]: print((-x).is_extended_positive)                                                                                          
None

However it also leads to test failures in other places where positive=False is used:

$ pytest sympy/core/ -n4

...
============================================================ FAILURES ============================================================
_________________________________________________ test_symbol_falsepositive_mul __________________________________________________
[gw1] darwin -- Python 3.5.7 /Users/enojb/current/sympy/35venv/bin/python3.5

    def test_symbol_falsepositive_mul():
        # To test pull request 9379
        # Explicit handling of arg.is_positive=False was added to Mul._eval_is_positive
        x = 2*Symbol('x', positive=False)
>       assert x.is_positive is False  # This was None before
E       assert None is False
E        +  where None = 2*x.is_positive

sympy/core/tests/test_assumptions.py:460: AssertionError
_________________________________________________ test_neg_symbol_falsepositive __________________________________________________
[gw1] darwin -- Python 3.5.7 /Users/enojb/current/sympy/35venv/bin/python3.5

    def test_neg_symbol_falsepositive():
        x = -Symbol('x', positive=False)
        assert x.is_positive is None
        assert x.is_nonpositive is None
>       assert x.is_negative is False
E       assert None is False
E        +  where None = -x.is_negative

sympy/core/tests/test_assumptions.py:472: AssertionError
_________________________________________________ test_neg_symbol_falsenegative __________________________________________________
[gw1] darwin -- Python 3.5.7 /Users/enojb/current/sympy/35venv/bin/python3.5

    def test_neg_symbol_falsenegative():
        # To test pull request 9379
        # Explicit handling of arg.is_negative=False was added to Mul._eval_is_positive
        x = -Symbol('x', negative=False)
>       assert x.is_positive is False  # This was None before
E       assert None is False
E        +  where None = -x.is_positive

sympy/core/tests/test_assumptions.py:482: AssertionError
                                                         DO *NOT* COMMIT!                                                         
================================= 3 failed, 1696 passed, 65 skipped, 41 xfailed in 60.70 seconds =================================

The fix for that is probably to add Mul._eval_is_positive (and Mul._eval_is_negative) as well as Mul._eval_is_extended_positive. However this should be done intelligently to avoid duplicating the _eval_pos_neg routine. Maybe just:

def _eval_is_positive(self):
    if self._eval_is_finite() is False:
        return False
    return self._eval_pos_neg(1)

It should be checked that this doesn't lead to any slowdown though.

[oscarbenjamin]

In #17535 I've added some comments about this and an XFAIL test.