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")

src/sage/misc/latex.py

@@ -557,7 +557,7 @@ def has_latex_attr(x):
         sage: T._latex_()
         Traceback (most recent call last):
         ...
-        TypeError: descriptor '_latex_' of 'sage.matrix.matrix0.Matrix' object needs an argument
+        TypeError: unbound method cython_function_or_method object must be called with Matrix_integer_dense instance as first argument (got nothing instead)
         sage: has_latex_attr(T)
         False
     """

src/sage/misc/lazy_attribute.pyx

@@ -72,7 +72,7 @@ cdef class _lazy_attribute(object):
             sage: Parent.element_class.__name__
             'element_class'
             sage: Parent.element_class.__module__
-            'sage.misc.lazy_attribute'
+            'sage.structure.parent'
         """
         raise NotImplementedError("Only instantiate wrapper python class")
 

src/sage/modular/modsym/p1list.pyx

@@ -773,10 +773,9 @@ cdef class P1List(object):
 
             sage: L = P1List(8)
             sage: L.__reduce__()
-            (<built-in function _make_p1list>, (8,))
+            (<cyfunction _make_p1list at ...>, (8,))
         """
-        import sage.modular.modsym.p1list
-        return sage.modular.modsym.p1list._make_p1list, (self.__N, )
+        return type(self), (self.__N, )
 
     def __getitem__(self, n):
         r"""
@@ -1373,6 +1372,7 @@ def _make_p1list(n):
         sage: from sage.modular.modsym.p1list import _make_p1list
         sage: _make_p1list(3)
         The projective line over the integers modulo 3
-
     """
+    from sage.misc.superseded import deprecation
+    deprecation(25848, '_make_p1list() is deprecated')
     return P1List(n)

src/sage/modules/free_module_element.pyx

@@ -3904,6 +3904,8 @@ cdef class FreeModuleElement(Vector):   # abstract base class
 #############################################
 # Generic dense element
 #############################################
+
+@cython.binding(True)
 def make_FreeModuleElement_generic_dense(parent, entries, degree):
     """
     EXAMPLES::
@@ -3922,6 +3924,8 @@ def make_FreeModuleElement_generic_dense(parent, entries, degree):
     v._degree = degree
     return v
 
+
+@cython.binding(True)
 def make_FreeModuleElement_generic_dense_v1(parent, entries, degree, is_mutable):
     """
     EXAMPLES::
@@ -4210,7 +4214,7 @@ cdef class FreeModuleElement_generic_dense(FreeModuleElement):
 
             sage: v = vector([-1,0,3,pi])
             sage: v.__reduce__()
-            (<built-in function make_FreeModuleElement_generic_dense_v1>, (Vector space of dimension 4 over Symbolic Ring, [-1, 0, 3, pi], 4, True))
+            (<cyfunction make_FreeModuleElement_generic_dense_v1 at ...>, (Vector space of dimension 4 over Symbolic Ring, [-1, 0, 3, pi], 4, True))
         """
         return (make_FreeModuleElement_generic_dense_v1, (self._parent, self._entries, self._degree, self._is_mutable))
 
@@ -4354,6 +4358,8 @@ cdef class FreeModuleElement_generic_dense(FreeModuleElement):
 #############################################
 # Generic sparse element
 #############################################
+
+@cython.binding(True)
 def make_FreeModuleElement_generic_sparse(parent, entries, degree):
     """
     EXAMPLES::
@@ -4368,6 +4374,8 @@ def make_FreeModuleElement_generic_sparse(parent, entries, degree):
     v._degree = degree
     return v
 
+
+@cython.binding(True)
 def make_FreeModuleElement_generic_sparse_v1(parent, entries, degree, is_mutable):
     """
     EXAMPLES::
@@ -4385,6 +4393,7 @@ def make_FreeModuleElement_generic_sparse_v1(parent, entries, degree, is_mutable
     v._is_mutable = is_mutable
     return v
 
+
 cdef class FreeModuleElement_generic_sparse(FreeModuleElement):
     """
     A generic sparse free module element is a dictionary with keys ints
@@ -4764,7 +4773,7 @@ cdef class FreeModuleElement_generic_sparse(FreeModuleElement):
 
             sage: v = vector([1,2/3,pi], sparse=True)
             sage: v.__reduce__()
-            (<built-in function make_FreeModuleElement_generic_sparse_v1>, (Sparse vector space of dimension 3 over Symbolic Ring, {0: 1, 1: 2/3, 2: pi}, 3, True))
+            (<cyfunction make_FreeModuleElement_generic_sparse_v1 at ...>, (Sparse vector space of dimension 3 over Symbolic Ring, {0: 1, 1: 2/3, 2: pi}, 3, True))
         """
         return (make_FreeModuleElement_generic_sparse_v1, (self._parent, self._entries, self._degree, self._is_mutable))
 

src/sage/quivers/paths.pxd

@@ -10,5 +10,3 @@ cdef class QuiverPath(MonoidElement):
     cpdef tuple complement(self, QuiverPath subpath)
     cpdef bint has_subpath(self, QuiverPath subpath) except -1
     cpdef bint has_prefix(self, QuiverPath subpath) except -1
-
-cpdef QuiverPath NewQuiverPath(Q, start, end, data)

src/sage/quivers/paths.pyx

@@ -17,8 +17,10 @@ Quiver Paths
 #
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+
 from __future__ import print_function
 
+cimport cython
 from cysignals.signals cimport sig_check, sig_on, sig_off
 
 from sage.data_structures.bounded_integer_sequences cimport *
@@ -787,7 +789,9 @@ cdef class QuiverPath(MonoidElement):
             biseq_inititem(out._path, i, biseq_getitem(self._path, l-i))
         return out
 
-cpdef QuiverPath NewQuiverPath(Q, start, end, biseq_data):
+
+@cython.binding(True)
+def NewQuiverPath(Q, start, end, biseq_data):
     """
     Return a new quiver path for given defining data.
 
@@ -812,7 +816,7 @@ cpdef QuiverPath NewQuiverPath(Q, start, end, biseq_data):
         sage: loads(dumps(p)) == p   # indirect doctest
         True
         sage: p.__reduce__()
-        (<...NewQuiverPath>,
+        (<cyfunction NewQuiverPath at ...>,
          (Partial semigroup formed by the directed paths of Multi-digraph on 3 vertices,
           1,
           3,

src/sage/rings/complex_double.pyx

@@ -2426,7 +2426,7 @@ cdef class FloatToCDF(Morphism):
         """
         from sage.categories.homset import Hom
         if isinstance(R, type):
-            from sage.structure.parent import Set_PythonType
+            from sage.sets.pythonclass import Set_PythonType
             R = Set_PythonType(R)
         Morphism.__init__(self, Hom(R, CDF))
 
@@ -2476,7 +2476,7 @@ cdef class ComplexToCDF(Morphism):
     def __init__(self, R):
         from sage.categories.homset import Hom
         if isinstance(R, type):
-            from sage.structure.parent import Set_PythonType
+            from sage.sets.pythonclass import Set_PythonType
             R = Set_PythonType(R)
         Morphism.__init__(self, Hom(R, CDF))
 

src/sage/rings/complex_interval_field.py

@@ -51,20 +51,6 @@ from .complex_field import ComplexField
 from sage.misc.cachefunc import cached_method
 
 
-NumberFieldElement_quadratic = None
-def late_import():
-    """
-    Import the objects/modules after build (when needed).
-
-    TESTS::
-
-        sage: sage.rings.complex_interval_field.late_import()
-    """
-    global NumberFieldElement_quadratic
-    if NumberFieldElement_quadratic is None:
-        import sage.rings.number_field.number_field_element_quadratic as nfeq
-        NumberFieldElement_quadratic = nfeq.NumberFieldElement_quadratic
-
 def is_ComplexIntervalField(x):
     """
     Check if ``x`` is a :class:`ComplexIntervalField`.

src/sage/rings/finite_rings/integer_mod.pyx

@@ -4370,7 +4370,7 @@ cdef class Int_to_IntegerMod(IntegerMod_hom):
     """
     def __init__(self, R):
         import sage.categories.homset
-        from sage.structure.parent import Set_PythonType
+        from sage.sets.pythonclass import Set_PythonType
         IntegerMod_hom.__init__(self, sage.categories.homset.Hom(Set_PythonType(int), R))
 
     cpdef Element _call_(self, x):

src/sage/rings/integer.pxd

@@ -34,8 +34,6 @@ cdef class Integer(EuclideanDomainElement):
     cdef bint _pseudoprime_is_prime(self, proof) except -1
     cpdef list _pari_divisors_small(self)
 
-    cdef _reduce_set(self, s) # do not use, since integers are immutable.
-
 cdef int mpz_set_str_python(mpz_ptr z, char* s, int base) except -1
 
 cdef Integer smallInteger(long value)

src/sage/rings/integer.pyx

@@ -754,7 +754,7 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
 
             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
@@ -769,17 +769,6 @@ cdef class Integer(sage.structure.element.EuclideanDomainElement):
         # if we don't do this.
         return sage.rings.integer.make_integer, (self.str(32),)
 
-    cdef _reduce_set(self, s):
-        """
-        Set this integer from a string in base 32.
-
-        .. NOTE::
-
-           Integers are supposed to be immutable, so you should not
-           use this function.
-        """
-        mpz_set_str(self.value, str_to_bytes(s), 32)
-
     def __index__(self):
         """
         Needed so integers can be used as list indices.
@@ -7012,6 +7001,8 @@ def GCD_list(v):
 
     return z
 
+
+@cython.binding(True)
 def make_integer(s):
     """
     Create a Sage integer from the base-32 Python *string* s. This is
@@ -7028,9 +7019,10 @@ def make_integer(s):
         TypeError: expected str...Integer found
     """
     cdef Integer r = PY_NEW(Integer)
-    r._reduce_set(s)
+    mpz_set_str(r.value, str_to_bytes(s), 32)
     return r
 
+
 cdef class int_to_Z(Morphism):
     """
     Morphism from Python ints to Sage integers.
@@ -7080,7 +7072,7 @@ cdef class int_to_Z(Morphism):
             Set of Morphisms from Set of Python objects of class 'int' to Integer Ring in Category of sets
         """
         import sage.categories.homset
-        from sage.structure.parent import Set_PythonType
+        from sage.sets.pythonclass import Set_PythonType
         Morphism.__init__(self, sage.categories.homset.Hom(Set_PythonType(int), integer_ring.ZZ))
 
     cpdef Element _call_(self, a):
@@ -7126,7 +7118,7 @@ cdef class long_to_Z(Morphism):
     """
     def __init__(self):
         import sage.categories.homset
-        from sage.structure.parent import Set_PythonType
+        from sage.sets.pythonclass import Set_PythonType
         Morphism.__init__(self, sage.categories.homset.Hom(Set_PythonType(long), integer_ring.ZZ))
 
     cpdef Element _call_(self, a):

src/sage/rings/number_field/number_field_element.pyx

@@ -108,42 +108,43 @@ def is_NumberFieldElement(x):
     """
     return isinstance(x, NumberFieldElement)
 
+
 def __create__NumberFieldElement_version0(parent, poly):
     """
     Used in unpickling elements of number fields pickled under very old Sage versions.
 
-    EXAMPLES::
+    TESTS::
 
         sage: k.<a> = NumberField(x^3 - 2)
         sage: R.<z> = QQ[]
         sage: sage.rings.number_field.number_field_element.__create__NumberFieldElement_version0(k, z^2 + z + 1)
+        doctest:...: DeprecationWarning: __create__NumberFieldElement_version0() is deprecated
+        See https://trac.sagemath.org/25848 for details.
         a^2 + a + 1
     """
+    from sage.misc.superseded import deprecation
+    deprecation(25848, '__create__NumberFieldElement_version0() is deprecated')
     return NumberFieldElement(parent, poly)
 
+
 def __create__NumberFieldElement_version1(parent, cls, poly):
     """
-    Used in unpickling elements of number fields.
+    Used in unpickling elements of number fields pickled under old Sage versions.
 
-    EXAMPLES:
-
-    Since this is just used in unpickling, we unpickle.
-
-    ::
+    TESTS::
 
         sage: k.<a> = NumberField(x^3 - 2)
-        sage: loads(dumps(a+1)) == a + 1 # indirect doctest
-        True
-
-    This also gets called for unpickling order elements; we check that
-    :trac:`6462` is fixed::
-
-        sage: L = NumberField(x^3 - x - 1,'a'); OL = L.maximal_order(); w = OL.0
-        sage: loads(dumps(w)) == w # indirect doctest
-        True
+        sage: R.<z> = QQ[]
+        sage: sage.rings.number_field.number_field_element.__create__NumberFieldElement_version1(k, type(a), z^2 + z + 1)
+        doctest:...: DeprecationWarning: __create__NumberFieldElement_version1() is deprecated
+        See https://trac.sagemath.org/25848 for details.
+        a^2 + a + 1
     """
+    from sage.misc.superseded import deprecation
+    deprecation(25848, '__create__NumberFieldElement_version1() is deprecated')
     return cls(parent, poly)
 
+
 def _inverse_mod_generic(elt, I):
     r"""
     Return an inverse of elt modulo the given ideal. This is a separate
@@ -414,18 +415,30 @@ cdef class NumberFieldElement(FieldElement):
         """
         Used in pickling number field elements.
 
-        Note for developers: If this is changed, please also change the doctests of __create__NumberFieldElement_version1.
-
         EXAMPLES::
 
             sage: k.<a> = NumberField(x^3 - 17*x^2 + 1)
             sage: t = a.__reduce__(); t
-            (<built-in function __create__NumberFieldElement_version1>, (Number Field in a with defining polynomial x^3 - 17*x^2 + 1, <type 'sage.rings.number_field.number_field_element.NumberFieldElement_absolute'>, x))
+            (<type 'sage.rings.number_field.number_field_element.NumberFieldElement_absolute'>,
+             (Number Field in a with defining polynomial x^3 - 17*x^2 + 1, x))
             sage: t[0](*t[1]) == a
             True
+
+        ::
+
+            sage: k.<a> = NumberField(x^3 - 2)
+            sage: loads(dumps(a+1)) == a + 1 # indirect doctest
+            True
+
+        This also gets called for unpickling order elements; we check that
+        :trac:`6462` is fixed::
+
+            sage: L = NumberField(x^3 - x - 1,'a'); OL = L.maximal_order(); w = OL.0
+            sage: loads(dumps(w)) == w # indirect doctest
+            True
         """
-        return __create__NumberFieldElement_version1, \
-               (self.parent(), type(self), self.polynomial())
+        args = (self.parent(), self.polynomial())
+        return type(self), args
 
     def _repr_(self):
         """

src/sage/rings/polynomial/__init__.py

-# Initialization file for polynomials
+# Resolve a cyclic import
+import sage.rings.convert.mpfi

src/sage/rings/rational.pyx

@@ -52,6 +52,7 @@ TESTS::
 
 from __future__ import absolute_import
 
+cimport cython
 from cpython cimport *
 from cpython.object cimport Py_EQ, Py_NE
 
@@ -507,7 +508,7 @@ cdef class Rational(sage.structure.element.FieldElement):
 
             sage: a = 3/5
             sage: a.__reduce__()
-            (<built-in function make_rational>, ('3/5',))
+            (<cyfunction make_rational at ...>, ('3/5',))
         """
         return sage.rings.rational.make_rational, (self.str(32),)
 
@@ -529,35 +530,6 @@ cdef class Rational(sage.structure.element.FieldElement):
             return int(self)
         raise TypeError("rational is not an integer")
 
-    def _reduce_set(self, s):
-        """
-        Used in setting a rational number when unpickling. Do not call this
-        from external code since it violates immutability.
-
-        INPUT:
-
-        -  ``s`` - string representation of rational in base 32
-
-        EXAMPLES::
-
-            sage: a = -17/3730; _, (s,) = a.__reduce__(); s
-            '-h/3ki'
-            sage: b = 2/3; b._reduce_set('-h/3ki'); b
-            -17/3730
-
-            sage: Rational(pari(-345/7687))
-            -345/7687
-            sage: Rational(pari(-345))
-            -345
-            sage: Rational(pari('Mod(2,3)'))
-            2
-            sage: Rational(pari('x'))
-            Traceback (most recent call last):
-            ...
-            TypeError: Unable to coerce PARI x to an Integer
-        """
-        mpq_set_str(self.value, str_to_bytes(s), 32)
-
     cdef __set_value(self, x, unsigned int base):
         cdef int n
         cdef Rational temp_rational
@@ -4062,6 +4034,7 @@ cdef double mpq_get_d_nearest(mpq_t x) except? -648555075988944.5:
     return ldexp(d, shift)
 
 
+@cython.binding(True)
 def make_rational(s):
     """
     Make a rational number from ``s`` (a string in base 32)
@@ -4080,9 +4053,10 @@ def make_rational(s):
         -7/15
     """
     r = Rational()
-    r._reduce_set(s)
+    mpq_set_str(r.value, str_to_bytes(s), 32)
     return r
 
+
 cdef class Z_to_Q(Morphism):
     r"""
     A morphism from `\ZZ` to `\QQ`.
@@ -4221,7 +4195,7 @@ cdef class int_to_Q(Morphism):
         """
         from . import rational_field
         import sage.categories.homset
-        from sage.structure.parent import Set_PythonType
+        from sage.sets.pythonclass import Set_PythonType
         Morphism.__init__(self, sage.categories.homset.Hom(Set_PythonType(int), rational_field.QQ))
 
     cpdef Element _call_(self, a):
@@ -4281,7 +4255,7 @@ cdef class long_to_Q(Morphism):
         """
         from . import rational_field
         import sage.categories.homset
-        from sage.structure.parent import Set_PythonType
+        from sage.sets.pythonclass import Set_PythonType
         Morphism.__init__(self, sage.categories.homset.Hom(
             Set_PythonType(long), rational_field.QQ))
 

src/sage/rings/real_double.pyx

@@ -2703,7 +2703,7 @@ cdef class ToRDF(Morphism):
         """
         from sage.categories.homset import Hom
         if isinstance(R, type):
-            from sage.structure.parent import Set_PythonType
+            from sage.sets.pythonclass import Set_PythonType
             R = Set_PythonType(R)
         Morphism.__init__(self, Hom(R, RDF))
 

src/sage/rings/real_lazy.pyx

@@ -158,7 +158,7 @@ cdef class LazyField(Field):
         """
         if isinstance(R, type):
             if R in [int, long]:
-                from sage.structure.parent import Set_PythonType
+                from sage.sets.pythonclass import Set_PythonType
                 return LazyWrapperMorphism(Set_PythonType(R), self)
         elif R.is_exact():
             ivf = self.interval_field()

src/sage/sets/disjoint_set.pyx

@@ -358,14 +358,14 @@ cdef class DisjointSet_of_integers(DisjointSet_class):
 
             sage: d = DisjointSet(5)
             sage: d.__reduce__()
-            (<built-in function DisjointSet>, (5,), [0, 1, 2, 3, 4])
+            (<cyfunction DisjointSet at ...>, (5,), [0, 1, 2, 3, 4])
 
         ::
 
             sage: d.union(2,4)
             sage: d.union(1,3)
             sage: d.__reduce__()
-            (<built-in function DisjointSet>, (5,), [0, 1, 2, 1, 2])
+            (<cyfunction DisjointSet at ...>, (5,), [0, 1, 2, 1, 2])
         """
         return DisjointSet, (self._nodes.degree,), self.__getstate__()
 
@@ -674,7 +674,7 @@ cdef class DisjointSet_of_hashables(DisjointSet_class):
             {{0}, {1}, {2}, {3}, {4}}
             sage: d = _
             sage: d.__reduce__()
-            (<built-in function DisjointSet>,
+            (<cyfunction DisjointSet at ...>,
              ([0, 1, 2, 3, 4],),
              [(0, 0), (1, 1), (2, 2), (3, 3), (4, 4)])
 
@@ -683,7 +683,7 @@ cdef class DisjointSet_of_hashables(DisjointSet_class):
             sage: d.union(2,4)
             sage: d.union(1,3)
             sage: d.__reduce__()
-            (<built-in function DisjointSet>,
+            (<cyfunction DisjointSet at ...>,
              ([0, 1, 2, 3, 4],),
              [(0, 0), (1, 1), (2, 2), (3, 1), (4, 2)])
         """

src/sage/sets/finite_enumerated_set.py

@@ -342,7 +342,7 @@ class FiniteEnumeratedSet(UniqueRepresentation, Parent):
             2
             sage: phi.register_as_conversion()
 
-            sage: from sage.structure.parent import Set_PythonType_class
+            sage: from sage.sets.pythonclass import Set_PythonType_class
             sage: psi = Hom(Set_PythonType_class(str), F, Sets())(lambda s: ZZ(len(s)))
             sage: psi.register_as_conversion()
             sage: psi('a')

src/sage/sets/pythonclass.pxd

+from sage.structure.parent cimport Set_generic
+
+
+cdef class Set_PythonType_class(Set_generic):
+    cdef type _type
+
+
+cpdef Set_PythonType(typ)

src/sage/sets/pythonclass.pyx

+"""
+Set of all objects of a given Python class
+"""
+
+#*****************************************************************************
+#       Copyright (C) 2018 Jeroen Demeyer <J.Demeyer@UGent.be>
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 2 of the License, or
+# (at your option) any later version.
+#                  http://www.gnu.org/licenses/
+#*****************************************************************************
+
+from cpython.object cimport Py_EQ, Py_NE
+from cpython.version cimport PY_MAJOR_VERSION
+from sage.structure.richcmp cimport rich_to_bool
+from sage.categories.sets_cat import Sets
+
+
+cdef dict _type_set_cache = {}
+
+cpdef Set_PythonType(typ):
+    """
+    Return the (unique) Parent that represents the set of Python objects
+    of a specified type.
+
+    EXAMPLES::
+
+        sage: from sage.sets.pythonclass import Set_PythonType
+        sage: Set_PythonType(list)
+        Set of Python objects of class 'list'
+        sage: Set_PythonType(list) is Set_PythonType(list)
+        True
+        sage: S = Set_PythonType(tuple)
+        sage: S([1,2,3])
+        (1, 2, 3)
+
+    S is a parent which models the set of all lists::
+
+        sage: S.category()
+        Category of sets
+    """
+    try:
+        return _type_set_cache[typ]
+    except KeyError:
+        _type_set_cache[typ] = theSet = Set_PythonType_class(typ)
+        return theSet
+
+
+cdef class Set_PythonType_class(Set_generic):
+    r"""
+    The set of Python objects of a given class.
+
+    The elements of this set are not instances of
+    :class:`~sage.structure.element.Element`; they are instances of
+    the given class.
+
+    INPUT:
+
+    - ``typ`` -- a Python (new-style) class
+
+    EXAMPLES::
+
+        sage: from sage.sets.pythonclass import Set_PythonType
+        sage: S = Set_PythonType(int); S
+        Set of Python objects of class 'int'
+        sage: int('1') in S
+        True
+        sage: Integer('1') in S
+        False
+
+        sage: Set_PythonType(2)
+        Traceback (most recent call last):
+        ...
+        TypeError: must be initialized with a class, not 2
+    """
+
+    def __init__(self, typ):
+        """
+        EXAMPLES::
+
+            sage: from sage.sets.pythonclass import Set_PythonType
+            sage: Set_PythonType(float).category()
+            Category of sets
+        """
+        if not isinstance(typ, type):
+            raise TypeError(f"must be initialized with a class, not {typ!r}")
+        super().__init__(category=Sets())
+        self._type = <type>typ
+
+    def _element_constructor_(self, *args, **kwds):
+        """
+        Construct an instance of the class.
+
+        EXAMPLES::
+
+            sage: from sage.sets.pythonclass import Set_PythonType
+            sage: S = Set_PythonType(complex)
+            sage: S._element_constructor_(5)
+            (5+0j)
+            sage: S._element_constructor_(1, 5/2)
+            (1+2.5j)
+        """
+        return self._type(*args, **kwds)
+
+    def __reduce__(self):
+        r"""
+        Pickling support
+
+        TESTS::
+
+            sage: from sage.sets.pythonclass import Set_PythonType
+            sage: S = Set_PythonType(object)
+            sage: loads(dumps(S))
+            Set of Python objects of class 'object'
+        """
+        return type(self), (self._type,)
+
+    def __call__(self, x):
+        """
+        Construct a new instance from ``x``. If ``x`` is already an
+        instance of the correct class, directly return ``x`` itself.
+
+        EXAMPLES::
+
+            sage: from sage.sets.pythonclass import Set_PythonType
+            sage: S = Set_PythonType(float)
+            sage: S(5)
+            5.0
+            sage: S(9/3)
+            3.0
+            sage: S(1/3)
+            0.333333333333333...
+            sage: a = float(3); S(a) is a
+            True
+        """
+        if isinstance(x, self._type):
+            return x
+        return self._type(x)
+
+    def __hash__(self):
+        """
+        TESTS::
+
+            sage: from sage.sets.pythonclass import Set_PythonType
+            sage: S = Set_PythonType(int)
+            sage: hash(S) == -hash(int)
+            True
+        """
+        return -hash(self._type)
+
+    def __richcmp__(self, other, int op):
+        """
+        Two Python class sets are considered the same if they contain
+        the same class.
+
+        EXAMPLES::
+
+            sage: from sage.sets.pythonclass import Set_PythonType
+            sage: S = Set_PythonType(int)
+            sage: T = Set_PythonType(int)
+            sage: U = type(S)(int)  # bypass caching
+            sage: S is T
+            True
+            sage: S == T
+            True
+            sage: S is U
+            False
+            sage: S == U
+            True
+            sage: S == Set_PythonType(float)
+            False
+            sage: S == int
+            False
+        """
+        if not (op == Py_EQ or op == Py_NE):
+            return NotImplemented
+        if self is other:
+            return rich_to_bool(op, 0)
+        if not isinstance(other, Set_PythonType_class):
+            return rich_to_bool(op, 1)
+        s = (<Set_PythonType_class>self)._type
+        o = (<Set_PythonType_class>other)._type
+        return rich_to_bool(op, s is not o)
+
+    def __contains__(self, x):
+        """
+        Only things of the right class (or subclasses thereof) are
+        considered to belong to the set.
+
+        EXAMPLES::
+
+            sage: from sage.sets.pythonclass import Set_PythonType
+            sage: S = Set_PythonType(tuple)
+            sage: (1,2,3) in S
+            True
+            sage: () in S
+            True
+            sage: [1,2] in S
+            False
+        """
+        return isinstance(x, self._type)
+
+    def _repr_(self):
+        """
+        EXAMPLES::
+
+            sage: from sage.sets.pythonclass import Set_PythonType
+            sage: Set_PythonType(tuple)
+            Set of Python objects of class 'tuple'
+            sage: Set_PythonType(Integer)
+            Set of Python objects of class 'Integer'
+            sage: Set_PythonType(Parent)
+            Set of Python objects of class 'Parent'
+        """
+        return f"Set of Python objects of class '{self._type.__name__}'"
+
+    def object(self):
+        """
+        EXAMPLES::
+
+            sage: from sage.sets.pythonclass import Set_PythonType
+            sage: Set_PythonType(tuple).object()
+            <... 'tuple'>
+        """
+        return self._type
+
+    def cardinality(self):
+        """
+        EXAMPLES::
+
+            sage: from sage.sets.pythonclass import Set_PythonType
+            sage: S = Set_PythonType(bool)
+            sage: S.cardinality()
+            2
+            sage: S = Set_PythonType(int)
+            sage: S.cardinality()
+            +Infinity
+        """
+        if self._type is bool:
+            from sage.rings.integer import Integer
+            return Integer(2)
+        else:
+            # Probably infinite
+            import sage.rings.infinity
+            return sage.rings.infinity.infinity

src/sage/stats/intlist.pyx

@@ -28,6 +28,7 @@ AUTHOR:
 # Global parameter that sets the maximum number of entries of an IntList to print.
 max_print = 10
 
+cimport cython
 from libc.string cimport memcpy
 from cysignals.memory cimport sig_malloc, sig_free
 from cysignals.signals cimport sig_on, sig_off
@@ -287,12 +288,9 @@ cdef class IntList:
             sage: loads(dumps(a)) == a
             True
 
-
             sage: v = stats.IntList([1,-3])
-            sage: v.__reduce__()  # py2
-            (<built-in function unpickle_intlist_v1>, ('...', 2))
-            sage: v.__reduce__()  # py3
-            (<built-in function unpickle_intlist_v1>, (b'...', 2))
+            sage: v.__reduce__()
+            (<cyfunction unpickle_intlist_v1 at ...>, (..., 2))
             sage: loads(dumps(v)) == v
             True
 
@@ -302,7 +300,6 @@ cdef class IntList:
             sage: v = stats.IntList([1..10^5])
             sage: loads(dumps(v, compress=False),compress=False) == v
             True
-
         """
         buf = PyBytes_FromStringAndSize(<char*>self._values, self._length*sizeof(int)/sizeof(char))
         return unpickle_intlist_v1, (buf, self._length)
@@ -562,6 +559,7 @@ cdef IntList new_int_list(Py_ssize_t length):
     return t
 
 
+@cython.binding(True)
 def unpickle_intlist_v1(bytes v, Py_ssize_t n):
     """
     Version 1 unpickle method.

src/sage/structure/category_object.pyx

@@ -598,7 +598,7 @@ cdef class CategoryObject(SageObject):
             sage: F.base_ring()
             Integer Ring
             sage: F.__class__.base_ring
-            <method 'base_ring' of 'sage.structure.category_object.CategoryObject' objects>
+            <unbound method FreeModule_ambient_pid_with_category.base_ring>
 
         Note that the coordinates of the elements of a module can lie
         in a bigger ring, the ``coordinate_ring``::
@@ -618,7 +618,7 @@ cdef class CategoryObject(SageObject):
             sage: F.base_ring()
             Rational Field
             sage: F.__class__.base_ring
-            <method 'base_ring' of 'sage.structure.category_object.CategoryObject' objects>
+            <unbound method FreeAlgebra_generic_with_category.base_ring>
 
             sage: E = CombinatorialFreeModule(ZZ, [1,2,3])
             sage: F = CombinatorialFreeModule(ZZ, [2,3,4])
@@ -626,7 +626,7 @@ cdef class CategoryObject(SageObject):
             sage: H.base_ring()
             Integer Ring
             sage: H.__class__.base_ring
-            <method 'base_ring' of 'sage.structure.category_object.CategoryObject' objects>
+            <unbound method Homset_with_category_with_equality_by_id.base_ring>
 
         .. TODO::
 

src/sage/structure/coerce.pyx

@@ -94,7 +94,7 @@ except ImportError:
 
 from .richcmp cimport rich_to_bool, revop
 from .sage_object cimport SageObject
-from .parent cimport Set_PythonType, Parent_richcmp_element_without_coercion
+from .parent cimport Parent_richcmp_element_without_coercion
 from .element cimport bin_op_exception, parent, Element
 from .coerce_actions import LeftModuleAction, RightModuleAction
 from .coerce_exceptions import CoercionException
@@ -102,6 +102,7 @@ from sage.rings.integer_fake cimport is_Integer
 from sage.categories.map cimport Map
 from sage.categories.morphism import IdentityMorphism
 from sage.categories.action cimport Action, InverseAction, PrecomposedAction
+from sage.sets.pythonclass cimport Set_PythonType
 
 import traceback
 

src/sage/structure/coerce_actions.pyx

@@ -667,7 +667,7 @@ cdef class IntegerAction(Action):
     """
     def __init__(self, Z, S, is_left, op):
         if isinstance(Z, type):
-            from sage.structure.parent import Set_PythonType
+            from sage.sets.pythonclass import Set_PythonType
             Z = Set_PythonType(Z)
         super().__init__(Z, S, is_left, op)
 

src/sage/structure/coerce_maps.pyx

@@ -6,9 +6,9 @@ from __future__ import print_function, absolute_import
 import re
 import types
 
-from .parent import Set_PythonType
 from sage.structure.parent cimport Parent
 from sage.structure.element cimport Element
+from sage.sets.pythonclass cimport Set_PythonType
 
 cdef object BuiltinMethodType = type(repr)
 

src/sage/structure/element.pyx

@@ -283,11 +283,12 @@ continue down the MRO and find the ``_add_`` method in the category.
 
 from __future__ import absolute_import, division, print_function
 
+cimport cython
 from cpython cimport *
-from sage.ext.stdsage cimport *
-
 from cpython.ref cimport PyObject
 
+from sage.ext.stdsage cimport *
+
 import types
 cdef add, sub, mul, div, truediv, floordiv, mod, pow
 cdef iadd, isub, imul, idiv, itruediv, ifloordiv, imod, ipow
@@ -384,6 +385,7 @@ cdef class Element(SageObject):
     .. automethod:: __floordiv__
     .. automethod:: __mod__
     """
+    @cython.binding(False)
     def __getmetaclass__(_):
         from sage.misc.inherit_comparison import InheritComparisonMetaclass
         return InheritComparisonMetaclass

src/sage/structure/parent.pxd

@@ -98,10 +98,13 @@ cdef class Parent(sage.structure.category_object.CategoryObject):
     # An optional single Morphism that describes a canonical coercion out of self
     cdef _embedding
 
+
+cdef class Set_generic(Parent):
+    pass
+
+
 # Flags for Parent.flags
 cdef enum:
     # If this flag is set, call __richcmp__ on elements without
     # coercion. This allows a completely custom comparison function.
     Parent_richcmp_element_without_coercion = 1
-
-cpdef Parent Set_PythonType(theType)

src/sage/structure/parent.pyx

@@ -129,6 +129,7 @@ from sage.categories.sets_cat import Sets, EmptySetError
 from sage.misc.lazy_format import LazyFormat
 from .coerce_maps cimport (NamedConvertMap, DefaultConvertMap,
         DefaultConvertMap_unique, CallableConvertMap)
+from sage.sets.pythonclass cimport Set_PythonType_class, Set_PythonType
 
 
 cdef _record_exception():
@@ -2785,8 +2786,7 @@ cdef class Parent(sage.structure.category_object.CategoryObject):
 # Set base class --
 ############################################################################
 
-
-cdef class Set_generic(Parent): # Cannot use Parent because Element._parent is Parent
+cdef class Set_generic(Parent):
     """
     Abstract base class for sets.
 
@@ -2822,249 +2822,6 @@ cdef class Set_generic(Parent): # Cannot use Parent because Element._parent is P
         return not (self.is_finite() and len(self) == 0)
 
 
-cdef _type_set_cache = {}
-
-cpdef Parent Set_PythonType(theType):
-    """
-    Return the (unique) Parent that represents the set of Python objects
-    of a specified type.
-
-    EXAMPLES::
-
-        sage: from sage.structure.parent import Set_PythonType
-        sage: Set_PythonType(list)
-        Set of Python objects of class 'list'
-        sage: Set_PythonType(list) is Set_PythonType(list)
-        True
-        sage: S = Set_PythonType(tuple)
-        sage: S([1,2,3])
-        (1, 2, 3)
-
-      S is a parent which models the set of all lists:
-        sage: S.category()
-        Category of sets
-
-    EXAMPLES::
-
-        sage: R = sage.structure.parent.Set_PythonType(int)
-        sage: S = sage.structure.parent.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
-
-    """
-    try:
-        return _type_set_cache[theType]
-    except KeyError:
-        _type_set_cache[theType] = theSet = Set_PythonType_class(theType)
-        return theSet
-
-
-cdef class Set_PythonType_class(Set_generic):
-    r"""
-    The set of Python objects of a given class.
-
-    The elements of this set are not instances of
-    :class:`~sage.structure.element.Element`; they are instances of
-    the given class.
-
-    INPUT:
-
-    - ``theType`` -- a Python (new-style) class
-
-    EXAMPLES::
-
-        sage: S = sage.structure.parent.Set_PythonType(int)
-        sage: S
-        Set of Python objects of class 'int'
-        sage: int('1') in S
-        True
-        sage: Integer('1') in S
-        False
-
-        sage: sage.structure.parent.Set_PythonType(2)
-        Traceback (most recent call last):
-        ...
-        TypeError: must be initialized with a class, not 2
-    """
-    cdef type _type
-
-    def __init__(self, theType):
-        """
-        EXAMPLES::
-
-            sage: S = sage.structure.parent.Set_PythonType(float)
-            sage: S.category()
-            Category of sets
-        """
-        if not isinstance(theType, type):
-            raise TypeError(f"must be initialized with a class, not {theType!r}")
-        super().__init__(category=Sets())
-        self._type = <type>theType
-
-    def _element_constructor_(self, *args, **kwds):
-        """
-        Construct an instance of the class.
-
-        EXAMPLES::
-
-            sage: S = sage.structure.parent.Set_PythonType(complex)
-            sage: S._element_constructor_(5)
-            (5+0j)
-            sage: S._element_constructor_(1, 5/2)
-            (1+2.5j)
-        """
-        return self._type(*args, **kwds)
-
-    def __reduce__(self):
-        r"""
-        Pickling support
-
-        TESTS::
-
-            sage: S = sage.structure.parent.Set_PythonType(object)
-            sage: loads(dumps(S))
-            Set of Python objects of class 'object'
-        """
-        return Set_PythonType, (self._type,)
-
-    def __call__(self, x):
-        """
-        Construct a new instance from ``x``. If ``x`` is already an
-        instance of the correct class, directly return ``x`` itself.
-
-        EXAMPLES::
-
-            sage: S = sage.structure.parent.Set_PythonType(float)
-            sage: S(5)
-            5.0
-            sage: S(9/3)
-            3.0
-            sage: S(1/3)
-            0.333333333333333...
-            sage: a = float(3); S(a) is a
-            True
-        """
-        if isinstance(x, self._type):
-            return x
-        return self._type(x)
-
-    def __hash__(self):
-        """
-        TESTS::
-
-            sage: S = sage.structure.parent.Set_PythonType(int)
-            sage: hash(S) == -hash(int)
-            True
-        """
-        return -hash(self._type)
-
-    def __richcmp__(self, other, int op):
-        """
-        Two Python class sets are considered the same if they contain
-        the same class.
-
-        EXAMPLES::
-
-            sage: from sage.structure.parent import Set_PythonType
-            sage: S = Set_PythonType(int)
-            sage: T = Set_PythonType(int)
-            sage: U = type(S)(int)  # bypass caching
-            sage: S is T
-            True
-            sage: S == T
-            True
-            sage: S is U
-            False
-            sage: S == U
-            True
-            sage: S == Set_PythonType(float)
-            False
-            sage: S == int
-            False
-        """
-        if not (op == Py_EQ or op == Py_NE):
-            return NotImplemented
-        if self is other