support renaming of Functor (define _repr_(), not __repr__())

src/sage/categories/action.pyx

@@ -126,7 +126,7 @@ cdef class Action(Functor):
     def is_left(self):
         return self._is_left
 
-    def __repr__(self):
+    def _repr_(self):
         side = "Left" if self._is_left else "Right"
         return "%s %s by %r on %r"%(side, self._repr_name_(), self.G,
                                     self.underlying_set())
@@ -339,7 +339,7 @@ cdef class PrecomposedAction(Action):
     def __invert__(self):
         return PrecomposedAction(~self._action, self.left_precomposition, self.right_precomposition)
 
-    def __repr__(self):
+    def _repr_(self):
         s = repr(self._action)
         if self.left_precomposition is not None:
             s += "\nwith precomposition on left by %s" % self.left_precomposition._default_repr_()

src/sage/categories/functor.pyx

@@ -285,14 +285,22 @@ cdef class Functor(SageObject):
             raise TypeError, "x (=%s) is not in %s"%(x, self.__domain)
         return x
 
-    def __repr__(self):
+    def _repr_(self):
         """
         TESTS::
             sage: from sage.categories.functor import Functor
             sage: F = Functor(Rings(),Fields())
             sage: F #indirect doctest
             Functor from Category of rings to Category of fields
 
+        A functor can be renamed if its type is a Python class
+        (see :trac:`16156)::
+
+            sage: I = IdentityFunctor(Rings()); I
+            The identity functor on Category of rings
+            sage: I.rename('Id'); I
+            Id
+
         """
         return "Functor from %s to %s"%(self.__domain, self.__codomain)
 
@@ -453,7 +461,7 @@ class ForgetfulFunctor_generic(Functor):
         """
         return ForgetfulFunctor, (self.domain(), self.codomain())
 
-    def __repr__(self):
+    def _repr_(self):
         """
         TESTS::
 
@@ -557,7 +565,7 @@ class IdentityFunctor_generic(ForgetfulFunctor_generic):
         """
         return IdentityFunctor, (self.domain(), )
 
-    def __repr__(self):
+    def _repr_(self):
         """
         TESTS::
 

src/sage/categories/morphism.pyx

@@ -303,7 +303,7 @@ cdef class Morphism(Map):
             gens = domain.gens()
             definition = tuple([self(x) for x in gens])
         except (AttributeError, NotImplementedError):
-            definition = self.__repr__()
+            definition = repr(self)
         return hash((domain, codomain, definition))
 
     def __richcmp__(left, right, int op):

src/sage/categories/pushout.py

@@ -191,7 +191,7 @@ def __str__(self):
         import re
         return re.sub("<.*'.*\.([^.]*)'>", "\\1", s)
 
-    def __repr__(self):
+    def _repr_(self):
         """
         NOTE:
 
@@ -2926,7 +2926,7 @@ def __init__(self, gens, domain):
         self._gens = gens
         self._domain = domain
 
-    def __repr__(self):
+    def _repr_(self):
         """
         EXAMPLES::
 

src/sage/categories/weyl_groups.py

@@ -136,7 +136,7 @@ def quantum_bruhat_graph(self, index_set = ()):
             from sage.graphs.digraph import DiGraph
             WP = [x for x in self if x==x.coset_representative(index_set)]
             return DiGraph([[x,i[0],i[1]] for x in WP for i in x.quantum_bruhat_successors(index_set, roots = True)],
-                           name="Parabolic Quantum Bruhat Graph of %s for nodes %s"%(self.__repr__(),index_set))
+                           name="Parabolic Quantum Bruhat Graph of %s for nodes %s"%(self, index_set))
 
     class ElementMethods: