src/doc/en/developer/coding_in_cython.rst

@@ -184,7 +184,7 @@ original object. As an example, the following code snippet is the
 
             sage: n = 5
             sage: t = n.__reduce__(); t
-            (<built-in function make_integer>, ('5',))
+            (<cyfunction make_integer at ...>, ('5',))
             sage: t[0](*t[1])
             5
             sage: loads(dumps(n)) == n

src/doc/en/prep/Programming.rst

@@ -102,14 +102,17 @@ Then we do the row\-reduced echelon form.
 It is very important to keep in the parentheses.
 
 .. note::
-   Things that would be legal without them would be called 'attributes',
-   but Sage prefers stylistically to hide them, since math is made of functions
-   and not elements of sets. Or so a category\-theorist would say.
 
-   ::
+    Things that would be legal without them would be called 'attributes',
+    but Sage prefers stylistically to hide them, since math is made of
+    functions and not elements of sets.
+    Or so a category-theorist would say.
+
+    ::
 
-       sage: A.det # Won't work
-       <built-in method det of sage.matrix.matrix_integer_dense.Matrix_integer_dense object at ...>
+        sage: A.det  # Won't work
+        <bound method Matrix_integer_dense.det of [1 2]
+        [3 4]>
 
 This is so useful because we can use the 'tab' key, remember!
 

src/doc/en/prep/Symbolics-and-Basic-Plotting.rst

@@ -199,7 +199,7 @@ This is a good place for a few reminders of basic help.
 ::
 
     sage: z.simplify
-    <built-in method simplify of sage.symbolic.expression.Expression object at ...>
+    <bound method Expression.simplify of -((x + 1)*sqrt(x - 1) - (x - 1)^(3/2))/sqrt((x + 1)*(x - 1))>
 
 Finally, recall that you can get nicely typeset versions of the output
 in several ways.

src/doc/en/reference/sets/index.rst

@@ -18,6 +18,7 @@ Set Constructions
    sage/sets/finite_set_maps
    sage/sets/finite_set_map_cy
    sage/sets/totally_ordered_finite_set
+   sage/sets/pythonclass
 
 Sets of Numbers
 ---------------

src/doc/en/thematic_tutorials/coercion_and_categories.rst

@@ -452,7 +452,7 @@ And indeed, ``MS2`` has *more* methods than ``MS1``::
     sage: len([s for s in dir(MS1) if inspect.ismethod(getattr(MS1,s,None))])
     79
     sage: len([s for s in dir(MS2) if inspect.ismethod(getattr(MS2,s,None))])
-    118
+    237
 
 This is because the class of ``MS2`` also inherits from the parent
 class for algebras::

src/sage/__init__.py

@@ -35,10 +35,16 @@ def isfunction(obj):
         sage: from sage.categories.coercion_methods import _mul_parent
         sage: isfunction(_mul_parent)
         True
+        sage: from sage.structure.richcmp import rich_to_bool
+        sage: isfunction(rich_to_bool)
+        True
         sage: isfunction(Integer.digits)     # unbound method
         False
         sage: isfunction(Integer(1).digits)  # bound method
         False
+        sage: from sage.geometry.point_collection import PointCollection
+        sage: isfunction(PointCollection.output_format)  # static method
+        True
 
     Verify that ipywidgets can correctly determine signatures of Cython
     functions::

src/sage/arith/misc.py

@@ -1870,9 +1870,9 @@ def get_gcd(order):
     EXAMPLES::
 
         sage: sage.arith.misc.get_gcd(4000)
-        <built-in method gcd_int of sage.rings.fast_arith.arith_int object at ...>
+        <bound method arith_int.gcd_int of <sage.rings.fast_arith.arith_int object at ...>>
         sage: sage.arith.misc.get_gcd(400000)
-        <built-in method gcd_longlong of sage.rings.fast_arith.arith_llong object at ...>
+        <bound method arith_llong.gcd_longlong of <sage.rings.fast_arith.arith_llong object at ...>>
         sage: sage.arith.misc.get_gcd(4000000000)
         <function gcd at ...>
     """
@@ -1891,9 +1891,9 @@ def get_inverse_mod(order):
     EXAMPLES::
 
         sage: sage.arith.misc.get_inverse_mod(6000)
-        <built-in method inverse_mod_int of sage.rings.fast_arith.arith_int object at ...>
+        <bound method arith_int.inverse_mod_int of <sage.rings.fast_arith.arith_int object at ...>>
         sage: sage.arith.misc.get_inverse_mod(600000)
-        <built-in method inverse_mod_longlong of sage.rings.fast_arith.arith_llong object at ...>
+        <bound method arith_llong.inverse_mod_longlong of <sage.rings.fast_arith.arith_llong object at ...>>
         sage: sage.arith.misc.get_inverse_mod(6000000000)
         <function inverse_mod at ...>
     """

src/sage/categories/category.py

@@ -2214,7 +2214,7 @@ class Category(UniqueRepresentation, SageObject):
         """
         return self
 
-    _flatten_categories = _flatten_categories
+    _flatten_categories = staticmethod(_flatten_categories)  # a cythonised helper
 
     @staticmethod
     def _sort(categories):
@@ -2263,7 +2263,7 @@ class Category(UniqueRepresentation, SageObject):
         """
         return tuple(sorted(categories, key=category_sort_key, reverse=True))
 
-    _sort_uniq = _sort_uniq   # a cythonised helper
+    _sort_uniq = staticmethod(_sort_uniq)  # a cythonised helper
 
     def __and__(self, other):
         """

src/sage/categories/homset.py

@@ -273,8 +273,9 @@ def Hom(X, Y, category=None, check=True):
 
     Facade parents over plain Python types are supported::
 
-        sage: R = sage.structure.parent.Set_PythonType(int)
-        sage: S = sage.structure.parent.Set_PythonType(float)
+        sage: from sage.sets.pythonclass import Set_PythonType
+        sage: R = Set_PythonType(int)
+        sage: S = Set_PythonType(float)
         sage: Hom(R, S)
         Set of Morphisms from Set of Python objects of class 'int' to Set of Python objects of class 'float' in Category of sets
 

src/sage/categories/map.pyx

@@ -25,7 +25,7 @@ from . import homset
 import weakref
 from sage.ext.stdsage cimport HAS_DICTIONARY
 from sage.arith.power cimport generic_power
-from sage.structure.parent cimport Set_PythonType
+from sage.sets.pythonclass cimport Set_PythonType
 from sage.misc.constant_function import ConstantFunction
 from sage.misc.superseded import deprecated_function_alias
 from sage.structure.element cimport parent

src/sage/categories/modules.py

@@ -589,6 +589,7 @@ class Modules(Category_module):
                 :meth:`sage.structure.category_object.CategoryObject.base_ring`::
 
                     sage: H.base_ring.__module__
+                    'sage.structure.category_object'
 
                 Here we call it directly::
 

src/sage/categories/primer.py

@@ -913,12 +913,10 @@ Where do all the operations on ``S`` and its elements come from?
     sage: x = S('a')
 
 ``_repr_`` is a technical method which comes with the data structure
-(:class:`ElementWrapper`); since it's implemented in Cython, we need
-to use Sage's introspection tools to recover where it's implemented::
+(:class:`ElementWrapper`)::
 
     sage: x._repr_.__module__
-    sage: sage.misc.sageinspect.sage_getfile(x._repr_)
-    '.../sage/structure/element_wrapper.pyx'
+    'sage.structure.element_wrapper'
 
 ``_pow_int`` is a generic method for all finite semigroups::
 

src/sage/combinat/sf/classical.py

@@ -51,7 +51,7 @@ def init():
         sage: sage.combinat.sf.classical.conversion_functions = {}
         sage: init()
         sage: sage.combinat.sf.classical.conversion_functions[('Schur', 'powersum')]
-        <built-in function t_SCHUR_POWSYM_symmetrica>
+        <cyfunction t_SCHUR_POWSYM_symmetrica at ...>
 
     The following checks if the bug described in :trac:`15312` is fixed. ::
 

src/sage/combinat/words/alphabet.py

@@ -265,7 +265,7 @@ def build_alphabet(data=None, names=None, name=None):
 
     # Alphabet(**nothing**)
     if data is None:  # name is also None
-        from sage.structure.parent import Set_PythonType
+        from sage.sets.pythonclass import Set_PythonType
         return Set_PythonType(object)
 
     raise ValueError("unable to construct an alphabet from the given parameters")

src/sage/finance/time_series.pyx

@@ -45,8 +45,10 @@ AUTHOR:
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+
 from __future__ import absolute_import
 
+cimport cython
 from cpython.bytes cimport PyBytes_FromStringAndSize, PyBytes_AsString
 from libc.math cimport exp, floor, log, pow, sqrt
 from libc.string cimport memcpy
@@ -177,7 +179,7 @@ cdef class TimeSeries:
 
             sage: v = finance.TimeSeries([1,-3.5])
             sage: v.__reduce__()
-            (<built-in function unpickle_time_series_v1>, (..., 2))
+            (<cyfunction unpickle_time_series_v1 at ...>, (..., 2))
             sage: loads(dumps(v)) == v
             True
 
@@ -2562,6 +2564,8 @@ cdef new_time_series(Py_ssize_t length):
     t._values = <double*> sig_malloc(sizeof(double)*length)
     return t
 
+
+@cython.binding(True)
 def unpickle_time_series_v1(bytes v, Py_ssize_t n):
     """
     Version 1 unpickle method.
@@ -2590,8 +2594,6 @@ def unpickle_time_series_v1(bytes v, Py_ssize_t n):
     return t
 
 
-
-
 def autoregressive_fit(acvs):
     r"""
     Given a sequence of lagged autocovariances of length `M` produce

src/sage/graphs/strongly_regular_db.pyx

@@ -1148,7 +1148,7 @@ def is_RSHCD(int v,int k,int l,int mu):
 
         sage: from sage.graphs.strongly_regular_db import is_RSHCD
         sage: t = is_RSHCD(64,27,10,12); t
-        [<built-in function SRG_from_RSHCD>, 64, 27, 10, 12]
+        [<cyfunction SRG_from_RSHCD at ...>, 64, 27, 10, 12]
         sage: g = t[0](*t[1:]); g
         Graph on 64 vertices
         sage: g.is_strongly_regular(parameters=True)

src/sage/interfaces/sage0.py

@@ -556,7 +556,7 @@ class SageFunction(FunctionElement):
         EXAMPLES::
 
             sage: sage0(4).gcd
-            <built-in method gcd of sage.rings.integer.Integer object at 0x...>
+            <bound method Integer.gcd of 4>
         """
         return str(self._obj.parent().eval('%s.%s' % (self._obj._name,
                                                       self._name)))

src/sage/libs/singular/ring.pyx

@@ -655,7 +655,7 @@ cpdef poison_currRing(frame, event, arg):
         sage: from sage.libs.singular.ring import poison_currRing
         sage: sys.settrace(poison_currRing)
         sage: sys.gettrace()
-        <built-in function poison_currRing>
+        <cyfunction poison_currRing at ...>
         sage: sys.settrace(previous_trace_func)  # switch it off again
     """
     global currRing

src/sage/misc/c3_controlled.pyx

@@ -1090,7 +1090,7 @@ class HierarchyElement(object, metaclass=ClasscallMetaclass):
             sage: x._bases
             [5, 2]
             sage: x._key
-            <built-in function identity>
+            <cyfunction identity at ...>
             sage: x._key(10)
             10
 

src/sage/misc/fpickle.pyx

 # cython: old_style_globals=True
+# cython: binding=True
 """
 Function pickling
 
@@ -20,7 +21,7 @@ def code_ctor(*args):
 
         sage: def foo(a,b,c=10): return a+b+c
         sage: sage.misc.fpickle.reduce_code(foo.__code__)
-        (<built-in function code_ctor>, ...)
+        (<cyfunction code_ctor at ...>, ...)
         sage: unpickle_function(pickle_function(foo))
         <function foo at ...>
     """
@@ -33,7 +34,7 @@ def reduce_code(co):
 
         sage: def foo(N): return N+1
         sage: sage.misc.fpickle.reduce_code(foo.__code__)
-        (<built-in function code_ctor>, ...)
+        (<cyfunction code_ctor at ...>, ...)
     """
     if co.co_freevars or co.co_cellvars:
         raise ValueError("Cannot pickle code objects from closures")