Move _is_coercion from DefaultConvertMap to Map and make it accurate

src/sage/categories/map.pxd

@@ -20,7 +20,7 @@ cdef class Map(Element):
     cdef object _category_for  # category in which this is a morphism
 
     cdef public _repr_type_str
-
+    cdef public bint _is_coercion
 
 cdef class Section(Map):
     cdef Map _inverse

src/sage/categories/map.pyx

@@ -131,6 +131,7 @@ cdef class Map(Element):
         self._codomain = C
         self.domain    = ConstantFunction(D)
         self.codomain  = ConstantFunction(C)
+        self._is_coercion = False
         if D.is_exact() and C.is_exact():
             self._coerce_cost = 10 # default value.
         else:
@@ -403,6 +404,11 @@ cdef class Map(Element):
             self._repr_type_str = _slots['_repr_type_str']
         else:
             self._repr_type_str = None
+        # Same for _is_coercion
+        if '_is_coercion' in _slots:
+            self._is_coercion = _slots['_is_coercion']
+        else:
+            self._is_coercion = None
 
     def _update_slots_test(self, _slots):
         """
@@ -438,6 +444,7 @@ cdef class Map(Element):
         """
         _slots['_domain'] = self.domain()
         _slots['_codomain'] = self._codomain
+        _slots['_is_coercion'] = self._is_coercion
         _slots['_repr_type_str'] = self._repr_type_str
         return _slots
 
@@ -452,6 +459,7 @@ cdef class Map(Element):
             sage: f._extra_slots_test({"bla": 1})
             {'_codomain': Integer Ring,
              '_domain': Rational Field,
+            '_is_coercion': False,
              '_repr_type_str': None,
              'bla': 1}
         """

src/sage/categories/morphism.pyx

@@ -502,6 +502,7 @@ cdef class SetMorphism(Morphism):
             {'_codomain': Integer Ring,
              '_domain': Integer Ring,
              '_function': <built-in function __abs__>,
+             '_is_coercion': False,
              '_repr_type_str': None,
              'bla': 1}
         """

src/sage/structure/coerce_maps.pxd

@@ -3,7 +3,6 @@ from sage.categories.map cimport Map
 
 cdef class DefaultConvertMap(Map):
     cdef public bint _force_use
-    cdef public bint _is_coercion
 
 cdef class DefaultConvertMap_unique(DefaultConvertMap):
     pass

src/sage/structure/coerce_maps.pyx

@@ -20,6 +20,13 @@ cdef class DefaultConvertMap(Map):
     """
     This morphism simply calls the codomain's element_constructor method,
     passing in the codomain as the first argument.
+
+    EXAMPLES::
+
+        sage: QQ[['x']].coerce_map_from(QQ)
+        Conversion map:
+          From: Rational Field
+          To:   Power Series Ring in x over Rational Field
     """
     def __init__(self, domain, codomain, force_use=False):
         """
@@ -34,6 +41,13 @@ cdef class DefaultConvertMap(Map):
               To:   Finite Field of size 11
             sage: f.parent()
             Set of Morphisms from Finite Field of size 7 to Finite Field of size 11 in Category of sets with partial maps
+
+        Test that `trac`:23211 is resolved::
+
+            sage: f._is_coercion
+            False
+            sage: QQ[['x']].coerce_map_from(QQ)._is_coercion
+            True
         """
         if not isinstance(domain, Parent):
             domain = Set_PythonType(domain)
@@ -48,15 +62,22 @@ cdef class DefaultConvertMap(Map):
 
     cdef dict _extra_slots(self, dict _slots):
         _slots['_force_use'] = self._force_use
-        _slots['_is_coercion'] = self._is_coercion
         return Map._extra_slots(self, _slots)
 
     cdef _update_slots(self, dict _slots):
         self._force_use = _slots['_force_use']
-        self._is_coercion = _slots['_is_coercion']
         Map._update_slots(self, _slots)
 
     cpdef Element _call_(self, x):
+        """
+        Create an element of the codomain from a single element of the domain.
+
+        EXAMPLES::
+
+            sage: f = QQ[['x']].coerce_map_from(QQ)
+            sage: f(2/3).parent()
+            Power Series Ring in x over Rational Field
+        """
         cdef Parent C = self._codomain
         try:
             return C._element_constructor(C, x)
@@ -67,6 +88,15 @@ cdef class DefaultConvertMap(Map):
             raise
 
     cpdef Element _call_with_args(self, x, args=(), kwds={}):
+        """
+        Create an element of the codomain from an element of the domain, with extra arguments.
+
+        EXAMPLES::
+
+            sage: f = QQ[['x']].coerce_map_from(QQ)
+            sage: f(2/3, 4)
+            2/3 + O(x^4)
+        """
         cdef Parent C = self._codomain
         try:
             if len(args) == 0:

src/sage/structure/parent.pyx

@@ -1566,6 +1566,7 @@ cdef class Parent(category_object.CategoryObject):
         D = mor.domain()
 
         assert not (self._coercions_used and D in self._coerce_from_hash), "coercion from {} to {} already registered or discovered".format(D, self)
+        mor._is_coercion = True
         self._coerce_from_list.append(mor)
         self._registered_domains.append(D)
         self._coerce_from_hash.set(D,mor)
@@ -2046,6 +2047,7 @@ cdef class Parent(category_object.CategoryObject):
         if S is self:
             from sage.categories.homset import Hom
             mor = Hom(self, self).identity()
+            mor._is_coercion = True
             self._coerce_from_hash.set(S, mor)
             return mor
 
@@ -2054,6 +2056,7 @@ cdef class Parent(category_object.CategoryObject):
             if debug.unique_parent_warnings:
                 print("Warning: non-unique parents %s" % (type(S)))
             mor = self._generic_convert_map(S)
+            mor._is_coercion = True
             self._coerce_from_hash.set(S, mor)
             mor._make_weak_references()
             return mor
@@ -2081,6 +2084,7 @@ cdef class Parent(category_object.CategoryObject):
             if (mor is not None) or _may_cache_none(self, S, "coerce"):
                 self._coerce_from_hash.set(S,mor)
                 if mor is not None:
+                    mor._is_coercion = True
                     mor._make_weak_references()
             return mor
         except CoercionException as ex: