Merge branch 'u/kcrisman/ticket/17493' of git://trac.sagemath.org/sag…

…e into i17493

build/pkgs/sympy/patches/03_bind-zoo.patch

@@ -0,0 +1,16 @@
+diff --git a/sympy/core/numbers.py b/sympy/core/numbers.py
+--- a/sympy/core/numbers.py
++++ b/sympy/core/numbers.py
+@@ -2857,6 +2857,11 @@ def _eval_power(self, expt):
+                     return S.ComplexInfinity
+                 else:
+                     return S.Zero
++    
++    def _sage_(self):
++        import sage.all as sage
++        return sage.UnsignedInfinityRing.gen()
++
+
+ zoo = S.ComplexInfinity
+
+

src/sage/rings/infinity.py

@@ -553,6 +553,12 @@ 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)
 
@@ -903,6 +909,23 @@ 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()