bpo-41911: Update docs for various expressions (GH-27470)

Co-authored-by: Łukasz Langa <lukasz@langa.pl>

Doc/reference/expressions.rst

@@ -1153,6 +1153,7 @@ Raising ``0.0`` to a negative power results in a :exc:`ZeroDivisionError`.
 Raising a negative number to a fractional power results in a :class:`complex`
 number. (In earlier versions it raised a :exc:`ValueError`.)
 
+This operation can be customized using the special :meth:`__pow__` method.
 
 .. _unary:
 
@@ -1174,22 +1175,27 @@ All unary arithmetic and bitwise operations have the same priority:
    single: operator; - (minus)
    single: - (minus); unary operator
 
-The unary ``-`` (minus) operator yields the negation of its numeric argument.
+The unary ``-`` (minus) operator yields the negation of its numeric argument; the
+operation can be overridden with the :meth:`__neg__` special method.
 
 .. index::
    single: plus
    single: operator; + (plus)
    single: + (plus); unary operator
 
-The unary ``+`` (plus) operator yields its numeric argument unchanged.
+The unary ``+`` (plus) operator yields its numeric argument unchanged; the
+operation can be overridden with the :meth:`__pos__` special method.
 
 .. index::
    single: inversion
    operator: ~ (tilde)
 
 The unary ``~`` (invert) operator yields the bitwise inversion of its integer
 argument.  The bitwise inversion of ``x`` is defined as ``-(x+1)``.  It only
-applies to integral numbers.
+applies to integral numbers or to custom objects that override the
+:meth:`__invert__` special method.
+
+
 
 .. index:: exception: TypeError
 
@@ -1225,6 +1231,9 @@ the other must be a sequence. In the former case, the numbers are converted to a
 common type and then multiplied together.  In the latter case, sequence
 repetition is performed; a negative repetition factor yields an empty sequence.
 
+This operation can be customized using the special :meth:`__mul__` and
+:meth:`__rmul__` methods.
+
 .. index::
    single: matrix multiplication
    operator: @ (at)
@@ -1247,6 +1256,9 @@ integer; the result is that of mathematical division with the 'floor' function
 applied to the result.  Division by zero raises the :exc:`ZeroDivisionError`
 exception.
 
+This operation can be customized using the special :meth:`__div__` and
+:meth:`__floordiv__` methods.
+
 .. index::
    single: modulo
    operator: % (percent)
@@ -1270,6 +1282,8 @@ also overloaded by string objects to perform old-style string formatting (also
 known as interpolation).  The syntax for string formatting is described in the
 Python Library Reference, section :ref:`old-string-formatting`.
 
+The *modulo* operation can be customized using the special :meth:`__mod__` method.
+
 The floor division operator, the modulo operator, and the :func:`divmod`
 function are not defined for complex numbers.  Instead, convert to a floating
 point number using the :func:`abs` function if appropriate.
@@ -1284,6 +1298,9 @@ must either both be numbers or both be sequences of the same type.  In the
 former case, the numbers are converted to a common type and then added together.
 In the latter case, the sequences are concatenated.
 
+This operation can be customized using the special :meth:`__add__` and
+:meth:`__radd__` methods.
+
 .. index::
    single: subtraction
    single: operator; - (minus)
@@ -1292,6 +1309,8 @@ In the latter case, the sequences are concatenated.
 The ``-`` (subtraction) operator yields the difference of its arguments.  The
 numeric arguments are first converted to a common type.
 
+This operation can be customized using the special :meth:`__sub__` method.
+
 
 .. _shifting:
 
@@ -1311,6 +1330,9 @@ The shifting operations have lower priority than the arithmetic operations:
 These operators accept integers as arguments.  They shift the first argument to
 the left or right by the number of bits given by the second argument.
 
+This operation can be customized using the special :meth:`__lshift__` and
+:meth:`__rshift__` methods.
+
 .. index:: exception: ValueError
 
 A right shift by *n* bits is defined as floor division by ``pow(2,n)``.  A left
@@ -1336,23 +1358,26 @@ Each of the three bitwise operations has a different priority level:
    operator: & (ampersand)
 
 The ``&`` operator yields the bitwise AND of its arguments, which must be
-integers.
+integers or one of them must be a custom object overriding :meth:`__and__` or
+:meth:`__rand__` special methods.
 
 .. index::
    pair: bitwise; xor
    pair: exclusive; or
    operator: ^ (caret)
 
 The ``^`` operator yields the bitwise XOR (exclusive OR) of its arguments, which
-must be integers.
+must be integers or one of them must be a custom object overriding :meth:`__xor__` or
+:meth:`__rxor__` special methods.
 
 .. index::
    pair: bitwise; or
    pair: inclusive; or
    operator: | (vertical bar)
 
 The ``|`` operator yields the bitwise (inclusive) OR of its arguments, which
-must be integers.
+must be integers or one of them must be a custom object overriding :meth:`__or__` or
+:meth:`__ror__` special methods.
 
 
 .. _comparisons:
@@ -1380,7 +1405,9 @@ in mathematics:
    comp_operator: "<" | ">" | "==" | ">=" | "<=" | "!="
                 : | "is" ["not"] | ["not"] "in"
 
-Comparisons yield boolean values: ``True`` or ``False``.
+Comparisons yield boolean values: ``True`` or ``False``. Custom
+:dfn:`rich comparison methods` may return non-boolean values. In this case
+Python will call :func:`bool` on such value in boolean contexts.
 
 .. index:: pair: chaining; comparisons