mirror of https://github.com/python/cpython
100 lines
3.0 KiB
ReStructuredText
100 lines
3.0 KiB
ReStructuredText
|
|
:mod:`numbers` --- Numeric abstract base classes
|
|
================================================
|
|
|
|
.. module:: numbers
|
|
:synopsis: Numeric abstract base classes (Complex, Real, Integral, etc.).
|
|
|
|
The :mod:`numbers` module (:pep:`3141`) defines a hierarchy of numeric abstract
|
|
base classes which progressively define more operations. These concepts also
|
|
provide a way to distinguish exact from inexact types. None of the types defined
|
|
in this module can be instantiated.
|
|
|
|
|
|
.. class:: Number
|
|
|
|
The root of the numeric hierarchy. If you just want to check if an argument
|
|
*x* is a number, without caring what kind, use ``isinstance(x, Number)``.
|
|
|
|
|
|
Exact and inexact operations
|
|
----------------------------
|
|
|
|
.. class:: Exact
|
|
|
|
Subclasses of this type have exact operations.
|
|
|
|
As long as the result of a homogenous operation is of the same type, you can
|
|
assume that it was computed exactly, and there are no round-off errors. Laws
|
|
like commutativity and associativity hold.
|
|
|
|
|
|
.. class:: Inexact
|
|
|
|
Subclasses of this type have inexact operations.
|
|
|
|
Given X, an instance of :class:`Inexact`, it is possible that ``(X + -X) + 3
|
|
== 3``, but ``X + (-X + 3) == 0``. The exact form this error takes will vary
|
|
by type, but it's generally unsafe to compare this type for equality.
|
|
|
|
|
|
The numeric tower
|
|
-----------------
|
|
|
|
.. class:: Complex
|
|
|
|
Subclasses of this type describe complex numbers and include the operations
|
|
that work on the builtin :class:`complex` type. These are: conversions to
|
|
:class:`complex` and :class:`bool`, :attr:`.real`, :attr:`.imag`, ``+``,
|
|
``-``, ``*``, ``/``, :func:`abs`, :meth:`conjugate`, ``==``, and ``!=``. All
|
|
except ``-`` and ``!=`` are abstract.
|
|
|
|
.. attribute:: Complex.real
|
|
|
|
Abstract. Retrieves the :class:`Real` component of this number.
|
|
|
|
.. attribute:: Complex.imag
|
|
|
|
Abstract. Retrieves the :class:`Real` component of this number.
|
|
|
|
.. method:: Complex.conjugate()
|
|
|
|
Abstract. Returns the complex conjugate. For example, ``(1+3j).conjugate() ==
|
|
(1-3j)``.
|
|
|
|
.. class:: Real
|
|
|
|
To :class:`Complex`, :class:`Real` adds the operations that work on real
|
|
numbers.
|
|
|
|
In short, those are: a conversion to :class:`float`, :func:`trunc`,
|
|
:func:`round`, :func:`math.floor`, :func:`math.ceil`, :func:`divmod`, ``//``,
|
|
``%``, ``<``, ``<=``, ``>``, and ``>=``.
|
|
|
|
Real also provides defaults for :func:`complex`, :attr:`Complex.real`,
|
|
:attr:`Complex.imag`, and :meth:`Complex.conjugate`.
|
|
|
|
|
|
.. class:: Rational
|
|
|
|
Subtypes both :class:`Real` and :class:`Exact`, 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`.
|
|
|
|
.. attribute:: Rational.numerator
|
|
|
|
Abstract.
|
|
|
|
.. attribute:: Rational.denominator
|
|
|
|
Abstract.
|
|
|
|
|
|
.. class:: Integral
|
|
|
|
Subtypes :class:`Rational` and adds a conversion to :class:`long`, the
|
|
3-argument form of :func:`pow`, and the bit-string operations: ``<<``,
|
|
``>>``, ``&``, ``^``, ``|``, ``~``. Provides defaults for :func:`float`,
|
|
:attr:`Rational.numerator`, and :attr:`Rational.denominator`.
|