Implement ProductSet.__iter__ using product_cantor

Closes sympy/sympy#10497
diofant · Jan 30, 2016 · cab56f4 · cab56f4
1 parent 7b01884
commit cab56f4
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diff --git a/sympy/sets/sets.py b/sympy/sets/sets.py
@@ -624,8 +624,9 @@ def is_iterable(self):
         return all(set.is_iterable for set in self.sets)
 
     def __iter__(self):
+        from sympy.utilities.iterables import product_cantor
         if self.is_iterable:
-            return itertools.product(*self.sets)
+            return product_cantor(*self.sets)
         else:
             raise TypeError("Not all constituent sets are iterable")
 

diff --git a/sympy/sets/tests/test_fancysets.py b/sympy/sets/tests/test_fancysets.py
@@ -262,3 +262,9 @@ def test_ImageSet_simplification():
     assert imageset(Lambda(n, sin(n)),
                     imageset(Lambda(m, tan(m)), S.Integers)) == \
             imageset(Lambda(m, sin(tan(m))), S.Integers)
+
+
+def test_issue_10497():
+    # __iter__ for infinite product set
+    assert (list(itertools.islice(iter(S.Integers**2), 7)) ==
+            [(0, 0), (1, 0), (1, 1), (-1, 1), (-1, -1), (2, -1), (2, 2)])