Fix Derangements(0) to return 1 and yield the empty permutation (Fix #39734)

Author: TinaJin0228

src/sage/combinat/derangements.py

@@ -281,6 +281,9 @@ def __iter__(self):
             sage: D = Derangements([1,1,2,2,2])
             sage: D.list()
             []
+            sage: D = Derangements(0)
+            sage: D.list()
+            [[]]
         """
         if self.__multi:
             for p in Permutations(self._set):
@@ -309,7 +312,10 @@ def _iter_der(self, n):
              [3, 4, 1, 2],
              [2, 1, 4, 3]]
         """
-        if n <= 1:
+        if n == 0:
+            yield []
+            return 
+        elif n == 1:
             return
         elif n == 2:
             yield [2, 1]
@@ -359,7 +365,9 @@ def _count_der(self, n):
             sage: D._count_der(5)
             44
         """
-        if n <= 1:
+        if n == 0:
+            return Integer(1)
+        if n == 1:
             return Integer(0)
         if n == 2:
             return Integer(1)
@@ -415,6 +423,9 @@ def cardinality(self):
             sage: D = Derangements([1,1,2,2,2])
             sage: D.cardinality()
             0
+            sage: D = Derangements(0)
+            sage: D.cardinality()
+            1
         """
         if self.__multi:
             sL = set(self._set)