allow incomparable labels in SetPartition

src/sage/combinat/set_partition.py

@@ -73,7 +73,11 @@ def _repr_(self):
             sage: S([[1,3],[2,4]])
             {{1, 3}, {2, 4}}
         """
-        return '{' + ', '.join('{' + repr(sorted(x))[1:-1] + '}' for x in self) + '}'
+        try:
+            s = [sorted(x) for x in self]
+        except TypeError:
+            s = [sorted(x, key=str) for x in self]
+        return '{' + ', '.join('{' + repr(x)[1:-1] + '}' for x in s) + '}'
 
     def __hash__(self):
         """
@@ -532,7 +536,7 @@ def pre_conjugate(sp):
 
 
 class SetPartition(AbstractSetPartition,
-        metaclass=InheritComparisonClasscallMetaclass):
+                   metaclass=InheritComparisonClasscallMetaclass):
     r"""
     A partition of a set.
 
@@ -620,7 +624,11 @@ def __init__(self, parent, s, check=True):
             {}
         """
         self._latex_options = {}
-        ClonableArray.__init__(self, parent, sorted(map(frozenset, s), key=min), check=check)
+        try:
+            s = sorted(map(frozenset, s), key=min)
+        except TypeError:
+            s = sorted(map(frozenset, s), key=lambda b: min(str(b)))
+        ClonableArray.__init__(self, parent, s, check=check)
 
     def check(self):
         """
@@ -2821,7 +2829,11 @@ def __iter__(self):
             sage: SetPartitions(["a", "b"]).list()
             [{{'a', 'b'}}, {{'a'}, {'b'}}]
         """
-        for sp in set_partition_iterator(sorted(self._set)):
+        try:
+            s = sorted(self._set)
+        except TypeError:
+            s = sorted(self._set, key=str)
+        for sp in set_partition_iterator(s):
             yield self.element_class(self, sp, check=False)
 
     def base_set(self):
@@ -3179,7 +3191,11 @@ def __iter__(self):
             sage: SetPartitions(["a", "b", "c"], 2).list()
             [{{'a', 'c'}, {'b'}}, {{'a'}, {'b', 'c'}}, {{'a', 'b'}, {'c'}}]
         """
-        for sp in set_partition_iterator_blocks(sorted(self._set), self._k):
+        try:
+            s = sorted(self._set)
+        except TypeError:
+            s = sorted(self._set, key=str)
+        for sp in set_partition_iterator_blocks(s, self._k):
             yield self.element_class(self, sp, check=False)
 
     def __contains__(self, x):