Trac #17493: bind SymPy's ComplexInfinity

{{{
sage: import sympy
sage: SR(sympy.factorial(-2))
------------------------------------------------------------------------
---
...
AttributeError: 'ComplexInfinity' object has no attribute '_sage_'
}}}

URL: http://trac.sagemath.org/17493
Reported by: rws
Ticket author(s): Ralf Stephan
Reviewer(s): Karl-Dieter Crisman, Marc Mezzarobba

src/sage/rings/infinity.py

@@ -551,6 +551,12 @@ def __init__(self):
 
             sage: sage.rings.infinity.UnsignedInfinityRing_class() is sage.rings.infinity.UnsignedInfinityRing_class() is UnsignedInfinityRing
             True
+        
+        Sage can understand SymPy's complex infinity (:trac:`17493`)::
+        
+            sage: import sympy
+            sage: SR(sympy.zoo)
+            Infinity
         """
         ParentWithGens.__init__(self, self, names=('oo',), normalize=False)
 
@@ -901,6 +907,23 @@ def _mul_(self, other):
             return self
         raise ValueError("unsigned oo times smaller number not defined")
 
+    def _sympy_(self):
+        """
+        Converts ``unsigned_infinity`` to sympy ``zoo``.
+
+        EXAMPLE::
+
+            sage: import sympy
+            sage: sympy.sympify(unsigned_infinity)
+            zoo
+            sage: gamma(-3)._sympy_() is sympy.factorial(-2)
+            True
+            sage: gamma(-3) is sympy.factorial(-2)._sage_()
+            True
+        """
+        import sympy
+        return sympy.zoo
+
 
 unsigned_infinity = UnsignedInfinityRing.gen(0)
 less_than_infinity = UnsignedInfinityRing.less_than_infinity()