Ticket #4528: krull.patch

sage/rings/number_field/order.py

@@ -290 +290 @@
         """
         return self.is_maximal()
     
-    
+    def krull_dimension(self):
+        """
+        Return the Krull dimension of this order, which is 1.
+
+        EXAMPLES:
+            sage: K.<a> = QuadraticField(5)
+            sage: OK = K.maximal_order()
+            sage: OK.krull_dimension()
+            1
+            sage: O2 = K.order(2*a)
+            sage: O2.krull_dimension()
+            1
+        """
+        return ZZ(1)
+
     def integral_closure(self):
         """
         Return the integral closure of this order.

sage/rings/ring.pyx

@@ -740 +740 @@
             False
         """
         return True
-    
+
     def krull_dimension(self):
         """
-        Return the Krull dimension if this commutative ring.
+        Return the Krull dimension of this commutative ring.
 
         The Krull dimension is the length of the longest ascending chain
         of prime ideals.
@@ -752 +752 @@
         \code{krull_dimension} is not implemented for generic commutative
         rings. Fields and PIDs, with Krull dimension equal to 0 and 1,
         respectively, have naive implementations of \code{krull_dimension}
+        Orders in number fields also have Krull dimension 1.
             sage: R = CommutativeRing(ZZ)
             sage: R.krull_dimension()
             Traceback (most recent call last):
@@ -765 +766 @@
             <type 'sage.rings.ring.CommutativeRing'>
             <class 'sage.rings.rational_field.RationalField'>
             <type 'sage.rings.integer_ring.IntegerRing_class'>
+
+            All orders in number fields have Krull dimension 1,
+            including non-maximal orders:            
+            sage: K.<i> = QuadraticField(-1)
+            sage: R = K.maximal_order(); R
+            Maximal Order in Number Field in i with defining polynomial x^2 + 1
+            sage: R.krull_dimension()
+            1
+            sage: R = K.order(2*i); R
+            Order in Number Field in i with defining polynomial x^2 + 1
+            sage: R.is_maximal()
+            False
+            sage: R.krull_dimension()
+            1
         """
         raise NotImplementedError
 
@@ -1019 +1034 @@
             sage: K = NumberField(x^2 + 1, 's')
             sage: OK = K.ring_of_integers()
             sage: OK.krull_dimension()
-            Traceback (most recent call last):
-            ...
-            NotImplementedError
+            1
 
         The following are not Dedekind domains but have
         a \code{krull_dimension} function.
@@ -1035 +1048 @@
             Multivariate Polynomial Ring in x, y, z over Integer Ring
             sage: U.krull_dimension()
             4
+
+            sage: K.<i> = QuadraticField(-1)
+            sage: R = K.order(2*i); R
+            Order in Number Field in i with defining polynomial x^2 + 1
+            sage: R.is_maximal()
+            False
+            sage: R.krull_dimension()
+            1
         """
         return 1