Trac #30602: Partitions_n.__iter__ creates partitions with int (inste…

…ad of Integer) parts

Several iterators over partitions return partitions whose parts are of
type `int` instead of `Integer`:
{{{
sage: type(Partitions(3)[0][0])
<class 'int'>
sage: type(Partitions(3, length=3)[0][0])
<class 'int'>

sage: type(Partitions(3, max_part=3)[0][0])
<class 'sage.rings.integer.Integer'>
}}}

URL: https://trac.sagemath.org/30602
Reported by: mantepse
Ticket author(s): Mike Hansen
Reviewer(s): Travis Scrimshaw

src/sage/combinat/partition.py

@@ -6655,9 +6655,15 @@ def __iter__(self):
 
             sage: [x for x in Partitions(4)]
             [[4], [3, 1], [2, 2], [2, 1, 1], [1, 1, 1, 1]]
+
+        TESTS::
+
+            sage: all(isinstance(i, Integer) for p in Partitions(4) for i in p)
+            True
+
         """
         for p in ZS1_iterator(self.n):
-            yield self.element_class(self, p)
+            yield self.element_class(self, [Integer(i) for i in p])
 
     def subset(self, **kwargs):
         r"""
@@ -6787,10 +6793,17 @@ def __iter__(self):
             ....:      == number_of_partitions_length(n, k)
             ....:      for n in range(9) for k in range(n+2) )
             True
+
+        TESTS::
+
+            sage: partitions = Partitions(9, length=3)
+            sage: all(isinstance(i, Integer) for p in partitions for i in p)
+            True
+
         """
         for p in ZS1_iterator_nk(self.n - self.k, self.k):
-            v = [i + 1 for i in p]
-            adds = [1] * (self.k - len(v))
+            v = [Integer(i + 1) for i in p]
+            adds = [Integer(1)] * (self.k - len(v))
             yield self.element_class(self, v + adds)
 
     def cardinality(self, algorithm='hybrid'):