projective_space.py: Better test coverage and ensure maximal order

Author: guojing0

src/sage/schemes/projective/projective_space.py

@@ -1108,6 +1108,15 @@ def points_of_bounded_height(self, **kwds):
             sage: len(sorted(list(P.points_of_bounded_height(bound=2))))
             44
 
+        ::
+
+            sage: R.<x> = QQ[]
+            sage: K.<a> = NumberField(x^3 - 7)
+            sage: O = K.maximal_order()
+            sage: P.<z,w> = ProjectiveSpace(O, 1)
+            sage: len(sorted(list(P.points_of_bounded_height(bound=2))))
+            28
+
         ::
 
             sage: P.<w,z> = ProjectiveSpace(ZZ, 1)
@@ -1154,7 +1163,7 @@ def points_of_bounded_height(self, **kwds):
         elif R in NumberFields():
             # True for the rational field as well, so check is_RationalField first
             field_type = True
-        elif (R is ZZ) or isinstance(R, Order):
+        elif ((R is ZZ) or isinstance(R, Order)) and R.is_integrally_closed(): # Ensure maximal order
             is_ring_of_ints = True
         else:
             raise NotImplementedError("self must be a projective space over a number field or a ring of integers")