Merge branch 'public/10184' of git://trac.sagemath.org/sage into publ…

…ic/class_group_iter-10184

src/sage/rings/number_field/class_group.py

@@ -40,6 +40,7 @@
     sage: (O*(2, 1/2*a + 1/2))^3
     Fractional ideal (1/2*a - 3/2)
 """
+from six.moves import range
 
 from sage.groups.abelian_gps.values import AbelianGroupWithValues_class, AbelianGroupWithValuesElement
 from sage.groups.abelian_gps.abelian_group_element import AbelianGroupElement
@@ -555,17 +556,35 @@ def __iter__(self):
             sage: G.list()
             (Trivial principal fractional ideal class,)
         """
-        from sage.misc.mrange import mrange
-        orders = self.gens_orders()
-        T = mrange(orders)
-        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)
+        return self._iter_inner(self.one(), 0)
+
+    def _iter_inner(self, i0, k):
+        r"""
+        Yield all elements of the coset `i0 * \{h in H_k\}`, where
+        `H_k` is the subgroup of ``self`` generated by ``self.gens()[k:]``.
+
+        Each new element provided costs exactly one group operation, and is
+        not necessarily reduced.
+
+        EXAMPLES::
+
+            sage: x = ZZ['x'].gen()
+            sage: K.<v> = NumberField(x^4 + 90*x^2 + 45)
+            sage: OK = K.maximal_order()
+            sage: G = OK.class_group()
+            sage: iter = G._iter_inner(G.gen(0)^2,1)
+            sage: all(next(iter) in G for _ in range(4))
+            True
+        """
+        if k == self.ngens():
+            yield i0
+            return
+        I = i0
+        for _ in range(self.invariants()[k]):
+            for J in self._iter_inner(I, k + 1):
+                yield J
+            I *= self.gen(k)
+        return
 
     def _repr_(self):
         r"""