bpo-26680: Updates documentation for Real.is_integer and built-ins in…

…t and float.

The call x.is_integer() is now listed in the table of operations
which apply to all numeric types except complex, with a reference
to the full documentation for Real.is_integer().  Mention of
is_integer() has been removed from the section 'Additional Methods
on Float'.

The documentation for Real.is_integer() describes its purpose, and
mentions that it should be overridden for performance reasons, or
to handle special values like NaN.

Doc/library/numbers.rst

@@ -49,19 +49,30 @@ The numeric tower
    numbers.
 
    In short, those are: a conversion to :class:`float`, :func:`math.trunc`,
-   :func:`round`, :func:`math.floor`, :func:`math.ceil`, :func:`divmod`, ``//``,
-   ``%``, ``<``, ``<=``, ``>``, and ``>=``.
+   :func:`round`, :func:`math.floor`, :func:`math.ceil`, :func:`divmod`,
+   :func:`~Real.is_integer`, ``//``, ``%``, ``<``, ``<=``, ``>``, and ``>=``.
 
    Real also provides defaults for :func:`complex`, :attr:`~Complex.real`,
    :attr:`~Complex.imag`, and :meth:`~Complex.conjugate`.
 
+   .. method:: is_integer()
+
+      Returns :const:`True` if this number has a finite and integral value,
+      otherwise :const:`False`.  This is a default implementation which
+      relies on successful conversion to :class:`int`. It may be overridden
+      in subclasses (such as it is in :class:`float`) for better performance,
+      or to handle special values such as NaN which are not
+      convertible to :class:`int`.
+
+      .. versionadded:: 3.10
+
 
 .. class:: Rational
 
    Subtypes :class:`Real` and adds
    :attr:`~Rational.numerator` and :attr:`~Rational.denominator` properties, which
-   should be in lowest terms. With these, it provides a default for
-   :func:`float`.
+   should be in lowest terms. With these, it provides defaults for
+   :func:`float` and :func:`~Real.is_integer`.
 
    .. attribute:: numerator
 
@@ -75,9 +86,10 @@ The numeric tower
 .. class:: Integral
 
    Subtypes :class:`Rational` and adds a conversion to :class:`int`.  Provides
-   defaults for :func:`float`, :attr:`~Rational.numerator`, and
-   :attr:`~Rational.denominator`.  Adds abstract methods for ``**`` and
-   bit-string operations: ``<<``, ``>>``, ``&``, ``^``, ``|``, ``~``.
+   defaults for :func:`float`, :attr:`~Rational.numerator`,
+   :attr:`~Rational.denominator`, and :func:`~Real.is_integer`.  Adds abstract
+   methods for ``**`` and bit-string operations: ``<<``, ``>>``, ``&``, ``^``,
+   ``|``, ``~``.
 
 
 Notes for type implementors

Doc/library/stdtypes.rst

@@ -310,6 +310,10 @@ the operations, see :ref:`operator-summary`):
 +---------------------+---------------------------------+---------+--------------------+
 | ``x ** y``          | *x* to the power *y*            | \(5)    |                    |
 +---------------------+---------------------------------+---------+--------------------+
+| ``x.is_integer()``  | ``True`` if *x* has a finite    |         | :func:`~numbers\   |
+|                     | and integral value, otherwise   |         | .Real.is_integer`  |
+|                     | ``False``.                      |         |                    |
++---------------------+---------------------------------+---------+--------------------+
 
 .. index::
    triple: operations on; numeric; types
@@ -583,16 +587,6 @@ class`. float also has the following additional methods.
    :exc:`OverflowError` on infinities and a :exc:`ValueError` on
    NaNs.
 
-.. method:: float.is_integer()
-
-   Return ``True`` if the float instance is finite with integral
-   value, and ``False`` otherwise::
-
-      >>> (-2.0).is_integer()
-      True
-      >>> (3.2).is_integer()
-      False
-
 Two methods support conversion to
 and from hexadecimal strings.  Since Python's floats are stored
 internally as binary numbers, converting a float to or from a