Ticket #12988: trac_12988.patch

sage/categories/algebras_with_basis.py

@@ -62 +62 @@
         running ._test_an_element() . . . pass
         running ._test_associativity() . . . pass
         running ._test_category() . . . pass
+        running ._test_characteristic() . . . pass
         running ._test_distributivity() . . . pass
         running ._test_elements() . . .
           Running the test suite of self.an_element()

sage/categories/fields.py

@@ -181 +181 @@
             """
             return True
 
+        def _test_characteristic_fields(self, **options):
+            """
+            Run generic tests on the method :meth:`.characteristic`.
+
+            EXAMPLES::
+
+                sage: QQ._test_characteristic_fields()
+
+            .. NOTE::
+
+                We cannot call this method ``_test_characteristic`` since that
+                would overwrite the method in the super category, and for
+                cython classes just calling
+                ``super(sage.categories.fields.Fields().parent_class,
+                self)._test_characteristic`` doesn't have the desired effect.
+
+            .. SEEALSO::
+
+                :meth:`sage.categories.rings.Rings.ParentMethods._test_characteristic`
+            """
+            tester = self._tester(**options)
+            try:
+                char = self.characteristic()
+                tester.assertTrue(char.is_zero() or char.is_prime())
+            except AttributeError:
+                return
+                # raised when self.one() does not have a additive_order() [or when char is an int and not an Integer which is already checked by _test_characteristic for rings]
+            except NotImplementedError:
+                return
+
     class ElementMethods:
         # Fields are unique factorization domains, so, there is gcd and lcm
         # Of course, in general gcd and lcm in a field are not very interesting.

sage/categories/hopf_algebras_with_basis.py

@@ -71 +71 @@
         running ._test_an_element() . . . pass
         running ._test_associativity() . . . pass
         running ._test_category() . . . pass
+        running ._test_characteristic() . . . pass
         running ._test_distributivity() . . . pass
         running ._test_elements() . . .
           Running the test suite of self.an_element()

sage/categories/rings.py

@@ -216 +216 @@
                 from sage.rings.noncommutative_ideals import IdealMonoid_nc
                 return IdealMonoid_nc(self)            
 
+        def characteristic(self):
+            """
+            Return the characteristic of this ring.
+
+            EXAMPLES::
+
+                sage: QQ.characteristic()
+                0
+                sage: GF(19).characteristic()
+                19
+                sage: Integers(8).characteristic()
+                8
+                sage: Zp(5).characteristic()
+                0
+            """
+            from sage.rings.infinity import infinity
+            from sage.rings.integer_ring import ZZ
+            order_1 = self.one().additive_order()
+            return ZZ.zero() if order_1 is infinity else order_1
+
+        def _test_characteristic(self, **options):
+            """
+            Run generic tests on the method :meth:`characteristic`.
+
+            See also: :class:`TestSuite`.
+
+            EXAMPLES::
+
+                sage: ZZ._test_characteristic()
+            """
+            tester = self._tester(**options)
+            try:
+                characteristic = self.characteristic()
+            except AttributeError:
+                return # raised when self.one() does not have a additive_order()
+            except NotImplementedError:
+                return
+
+            # test that #12988 is fixed
+            tester.assertEqual(type(characteristic),sage.rings.integer.Integer)
+
         def ideal(self, *args, **kwds):
             """
             Create an ideal of this ring.

sage/rings/integer_ring.pyx

@@ -230 +230 @@
         19
         sage: ZZ(2 + 3*5 + O(5^3))
         17
+
+    TESTS::
+
+        sage: TestSuite(ZZ).run()
     """
 
     def __init__(self):
@@ -883 +887 @@
     
     def characteristic(self):
         """
-        Return the characteristic of the integers, which is 0
+        Return the characteristic of the integers, which is 0.
         
         EXAMPLE::
         
             sage: ZZ.characteristic()
             0
         """
-        return 0
+        return ZZ.zero()
 
     def krull_dimension(self):
         """

sage/rings/number_field/number_field.py

@@ -2867 +2867 @@
             sage: k.characteristic()
             0
         """
-        return 0
+        return ZZ.zero()
 
     def class_group(self, proof=None, names='c'):
         r"""

sage/rings/real_double.pyx

@@ -395 +395 @@
             sage: RDF.characteristic()
             0
         """
-        return 0
+        return Integer(0)
 
     cdef _new_c(self, double value):
         cdef RealDoubleElement x

sage/rings/real_mpfi.pyx

@@ -754 +754 @@
             sage: RealIntervalField(10).characteristic()
             0
         """
-        return 0
+        return Integer(0)
     
     def name(self):
         return "IntervalRealIntervalField%s"%(self.__prec)

sage/rings/real_mpfr.pyx

@@ -719 +719 @@
             sage: RealField(10).characteristic()
             0
         """
-        return 0
+        return Integer(0)
     
     def name(self):
         """

sage/rings/ring.pyx

@@ -109 +109 @@
         running ._test_an_element() . . . pass
         running ._test_associativity() . . . pass
         running ._test_category() . . . pass
+        running ._test_characteristic() . . . pass
         running ._test_distributivity() . . . pass
         running ._test_elements() . . .
           Running the test suite of self.an_element()
@@ -1142 +1143 @@
         """
         raise NotImplementedError
 
-    def characteristic(self):
-        """
-        Return the characteristic of this ring.
-
-        EXAMPLES::
-
-            sage: QQ.characteristic()
-            0
-            sage: GF(19).characteristic()
-            19
-            sage: Integers(8).characteristic()
-            8
-            sage: Zp(5).characteristic()
-            0
-        """
-        from sage.rings.infinity import infinity
-        from sage.rings.integer_ring import ZZ
-        order_1 = self.one_element().additive_order()
-        return ZZ.zero_element() if order_1 is infinity else order_1
-
     def order(self):
         """
         The number of elements of self.

sage/structure/parent.pyx

@@ -832 +832 @@
             running ._test_an_element() . . . pass
             running ._test_associativity() . . . pass
             running ._test_category() . . . pass
+            running ._test_characteristic() . . . pass
             running ._test_distributivity() . . . pass
             running ._test_elements() . . . 
               Running the test suite of self.an_element()
@@ -894 +895 @@
             _test_an_element
             _test_associativity
             _test_category
+            _test_characteristic
             _test_distributivity
             _test_elements
             _test_elements_eq