Ticket #3913: sage-trac3913.patch

a/sage/rings/number_field/class_group.py

@@ -148 +148 @@
-    """
-    def __init__(self, ideal, class_group):
-        """
-A fractional ideal class
+Returns the ideal class of this fractional ideal
-        """
-        self.__ideal = ideal
-        MultiplicativeGroupElement.__init__(self, class_group)
@@ -171 +171 @@
-        return self.parent()((self.__ideal * other.__ideal).reduce_equiv())
-
-    def is_principal(self):
+        """
+        Returns True iff this ideal class is the trivial (principal) class
+
+        EXAMPLE:
+        sage: K.<w>=QuadraticField(-23)
+        sage: OK=K.ring_of_integers()
+        sage: C=OK.class_group()
+        sage: P2a,P2b=[P for P,e in (2*OK).factor()]
+        sage: c=C(P2a)
+        sage: c.is_principal()    
+        False
+        sage: (c^2).is_principal()
+        False
+        sage: (c^3).is_principal()
+        True
+        """
-        return self.__ideal.is_principal()
-
-    def reduce(self):
@@ -190 +206 @@
-        """
-        return self.parent()(self.__ideal.reduce_equiv())
-
-
-
-
-
+
+
+
-
+        EXAMPLE:
+            sage: K.<w>=QuadraticField(-23)
+            sage: OK=K.ring_of_integers()
+            sage: C=OK.class_group()
+            sage: h=C.order(); h
+            3
+            sage: P2a,P2b=[P for P,e in (2*OK).factor()]
+            sage: c=C(P2a); c
+            Fractional ideal class (2, 1/2*w - 1/2)
+            sage: c.order()
+            3
+
+            sage: k.<a> = NumberField(x^2 + 20072); G = k.class_group(); G
+            Class group of order 76 with structure C38 x C2 of Number Field in a with defining polynomial x^2 + 20072
+            sage: [c.order() for c in G.gens()]
+            [38, 2]
+
+        """
+        try:
+            return self.__multiplicative_order
+        except AttributeError:
+            from sage.groups.generic import order_from_multiple
+            self.__multiplicative_order = order_from_multiple(self,self.parent().order(),operation='*')
+            return self.__multiplicative_order
+
+    multiplicative_order = order
+    
-    def ideal(self):
-        """
-        Return a representative ideal in this ideal class.
+
+        EXAMPLE:
+        sage: K.<w>=QuadraticField(-23)
+        sage: OK=K.ring_of_integers()
+        sage: C=OK.class_group()
+        sage: P2a,P2b=[P for P,e in (2*OK).factor()]
+        sage: c=C(P2a); c
+        Fractional ideal class (2, 1/2*w - 1/2)
+        sage: c.ideal()
+        Fractional ideal (2, 1/2*w - 1/2)
-        """
-        return self.__ideal
-
@@ -205 +257 @@
-        """
-        Return generators for a representative ideal in this
-        ideal class.
+
+        EXAMPLE:
+        sage: K.<w>=QuadraticField(-23)
+        sage: OK=K.ring_of_integers()
+        sage: C=OK.class_group()
+        sage: P2a,P2b=[P for P,e in (2*OK).factor()]
+        sage: c=C(P2a); c
+        Fractional ideal class (2, 1/2*w - 1/2)
+        sage: c.gens()
+        (2, 1/2*w - 1/2)
-        """
-        return self.ideal().gens()