moving random_element to category of rings

Author: fchapoton

src/sage/categories/rings.py

@@ -16,6 +16,7 @@
 
 from sage.misc.cachefunc import cached_method
 from sage.misc.lazy_import import LazyImport
+from sage.misc.prandom import randint
 from sage.categories.category_with_axiom import CategoryWithAxiom
 from sage.categories.rngs import Rngs
 from sage.structure.element import Element
@@ -1646,6 +1647,30 @@ def _random_nonzero_element(self, *args, **kwds):
                 if not x.is_zero():
                     return x
 
+        def random_element(self, bound=2):
+            """
+            Return a random integer coerced into this ring.
+
+            The integer is chosen uniformly
+            from the interval ``[-bound,bound]``.
+
+            INPUT:
+
+            - ``bound`` -- integer (default: 2)
+
+            ALGORITHM:
+
+            This uses Python's ``randint``.
+
+            EXAMPLES::
+
+                sage: ZZ.random_element(8)   # random
+                1
+                sage: QQ.random_element(8)   # random
+                2
+            """
+            return randint(-bound, bound) * self.one()
+
     class ElementMethods:
         def is_unit(self) -> bool:
             r"""

src/sage/rings/ring.pyx

@@ -114,7 +114,6 @@ from sage.misc.superseded import deprecation
 from sage.structure.coerce cimport coercion_model
 from sage.structure.parent cimport Parent
 from sage.structure.category_object cimport check_default_category
-from sage.misc.prandom import randint
 from sage.categories.rings import Rings
 from sage.categories.algebras import Algebras
 from sage.categories.commutative_algebras import CommutativeAlgebras
@@ -637,36 +636,6 @@ cdef class Ring(ParentWithGens):
         """
         return self.zeta().multiplicative_order()
 
-    def random_element(self, bound=2):
-        """
-        Return a random integer coerced into this ring, where the
-        integer is chosen uniformly from the interval ``[-bound,bound]``.
-
-        INPUT:
-
-        - ``bound`` -- integer (default: 2)
-
-        ALGORITHM:
-
-        Uses Python's randint.
-
-        TESTS:
-
-        The following example returns a :exc:`NotImplementedError` since the
-        generic ring class ``__call__`` function returns a
-        :exc:`NotImplementedError`. Note that
-        ``sage.rings.ring.Ring.random_element`` performs a call in the generic
-        ring class by a random integer::
-
-            sage: R = sage.rings.ring.Ring(ZZ); R
-            <sage.rings.ring.Ring object at ...>
-            sage: R.random_element()
-            Traceback (most recent call last):
-            ...
-            NotImplementedError: cannot construct elements of <sage.rings.ring.Ring object at ...>
-        """
-        return self(randint(-bound,bound))
-
     @cached_method
     def epsilon(self):
         """