Ticket #3810: sage-3810-combined.patch

sage/groups/abelian_gps/abelian_group.py

@@ -775 +775 @@
             pass
         if not(self.is_finite()):
            raise NotImplementedError, "Group must be finite"
-        if self.order()==1:
-            L = [AbelianGroupElement(self, 1)]
-        else:
-            L = [AbelianGroupElement(self, t) for t in mrange(self.invariants())]
+        self.__list = list(self.__iter__())
+        return list(self.__list)
+#         if self.order()==1:
+#             L = [AbelianGroupElement(self, 1)]
+#         else:
+#             L = [AbelianGroupElement(self, t) for t in mrange(self.invariants())]
         self.__list = L
         return list(L)
      
@@ -790 +792 @@
             sage: G = AbelianGroup([2,3], names = "ab")
             sage: [a for a in G]
             [1, b, b^2, a, a*b, a*b^2]
+            sage: L = list(G); L
+            [1, b, b^2, a, a*b, a*b^2]
+
+            The returned list is a reference; mutating it does not allow the
+            user to (accidentally?) alter the computed generators:
+
+            sage: L[0] = 0
+            sage: list(G)
+            [1, b, b^2, a, a*b, a*b^2]
+            sage: G = AbelianGroup([1], names="a")
+            sage: list(G)
+            [1]
+            sage: G = AbelianGroup([])
+            sage: G.list()
+            [1]
+            sage: list(G)
+            [1]
         """
-        for g in self.list():
-            yield g
-
+        invs = self.invariants()
+        if len(invs)==0:
+            yield AbelianGroupElement(self, [])
+        for t in mrange(invs):
+            yield AbelianGroupElement(self, t)
 
 class AbelianGroup_subgroup(AbelianGroup_class):
     """

sage/groups/abelian_gps/abelian_group.py

@@ -777 +777 @@
            raise NotImplementedError, "Group must be finite"
         self.__list = list(self.__iter__())
         return list(self.__list)
-#         if self.order()==1:
-#             L = [AbelianGroupElement(self, 1)]
-#         else:
-#             L = [AbelianGroupElement(self, t) for t in mrange(self.invariants())]
-        self.__list = L
-        return list(L)
      
     def __iter__(self):
         """

sage/rings/number_field/class_group.py

@@ -104 +104 @@
         if i < 0 or i >= len(self.__gens):
             raise IndexError
         return self.__gens[i]
+
+    def __iter__(self):
+        r"""
+        Return an iterator of all ideal classes in this class group.
+
+        EXAMPLES:
+            sage: K.<a> = NumberField(x^4 + 23)
+            sage: G = K.class_group()
+            sage: G
+            Class group of order 3 with structure C3 of Number Field in a with defining polynomial x^4 + 23
+            sage: list(G)
+            [Trivial principal fractional ideal class, Fractional ideal class (2, 1/2*a^2 + a - 1/2), Fractional ideal class (2, 1/2*a^2 + 1/2)]
+            sage: G.list()
+            [Trivial principal fractional ideal class, Fractional ideal class (2, 1/2*a^2 + a - 1/2), Fractional ideal class (2, 1/2*a^2 + 1/2)]
+
+        TESTS:
+            sage: K.<a> = NumberField(x^2 + 1)
+            sage: G = K.class_group()
+            sage: G
+            Class group of order 1 with structure  of Number Field in a with defining polynomial x^2 + 1
+            sage: list(G)
+            [Trivial principal fractional ideal class]
+            sage: G.list()
+            [Trivial principal fractional ideal class]
+
+            sage: C = NumberField(x^2 + x + 23899, 'a').class_group(); C
+            Class group of order 68 with structure C34 x C2 of Number Field in a with defining polynomial x^2 + x + 23899
+            sage: len(list(C.__iter__()))
+            68
+        """
+        from sage.misc.mrange import mrange
+        invs = self.invariants()
+        T = mrange(invs)
+        g = self.gens()
+        for t in T:
+            I = self(1)
+            for i, j in enumerate(t):
+                I *= g[i]**j
+            yield I
+        if not T:
+            yield self(1)
 
     def _repr_(self):
         """