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#: ../Doc/library/numbers.rst:2
msgid ":mod:`numbers` --- Numeric abstract base classes"
msgstr ""

#: ../Doc/library/numbers.rst:7
msgid "**Source code:** :source:`Lib/numbers.py`"
msgstr ""

#: ../Doc/library/numbers.rst:11
msgid ""
"The :mod:`numbers` module (:pep:`3141`) defines a hierarchy of numeric :term:"
"`abstract base classes <abstract base class>` which progressively define "
"more operations.  None of the types defined in this module can be "
"instantiated."
msgstr ""

#: ../Doc/library/numbers.rst:18
msgid ""
"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)``."
msgstr ""

#: ../Doc/library/numbers.rst:23
msgid "The numeric tower"
msgstr ""

#: ../Doc/library/numbers.rst:27
msgid ""
"Subclasses of this type describe complex numbers and include the operations "
"that work on the built-in :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."
msgstr ""

#: ../Doc/library/numbers.rst:35
msgid "Abstract. Retrieves the real component of this number."
msgstr ""

#: ../Doc/library/numbers.rst:39
msgid "Abstract. Retrieves the imaginary component of this number."
msgstr ""

#: ../Doc/library/numbers.rst:43
msgid ""
"Abstract. Returns the complex conjugate. For example, ``(1+3j).conjugate() "
"== (1-3j)``."
msgstr ""

#: ../Doc/library/numbers.rst:48
msgid ""
"To :class:`Complex`, :class:`Real` adds the operations that work on real "
"numbers."
msgstr ""

#: ../Doc/library/numbers.rst:51
msgid ""
"In short, those are: a conversion to :class:`float`, :func:`math.trunc`, :"
"func:`round`, :func:`math.floor`, :func:`math.ceil`, :func:`divmod`, ``//``, "
"``%``, ``<``, ``<=``, ``>``, and ``>=``."
msgstr ""

#: ../Doc/library/numbers.rst:55
msgid ""
"Real also provides defaults for :func:`complex`, :attr:`~Complex.real`, :"
"attr:`~Complex.imag`, and :meth:`~Complex.conjugate`."
msgstr ""

#: ../Doc/library/numbers.rst:61
msgid ""
"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`."
msgstr ""

#: ../Doc/library/numbers.rst:68 ../Doc/library/numbers.rst:72
msgid "Abstract."
msgstr "Résumé."

#: ../Doc/library/numbers.rst:77
msgid ""
"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: ``<<``, ``>>``, ``&``, ``^``, ``|``, ``~``."
msgstr ""

#: ../Doc/library/numbers.rst:84
msgid "Notes for type implementors"
msgstr ""

#: ../Doc/library/numbers.rst:86
msgid ""
"Implementors should be careful to make equal numbers equal and hash them to "
"the same values. This may be subtle if there are two different extensions of "
"the real numbers. For example, :class:`fractions.Fraction` implements :func:"
"`hash` as follows::"
msgstr ""

#: ../Doc/library/numbers.rst:105
msgid "Adding More Numeric ABCs"
msgstr ""

#: ../Doc/library/numbers.rst:107
msgid ""
"There are, of course, more possible ABCs for numbers, and this would be a "
"poor hierarchy if it precluded the possibility of adding those. You can add "
"``MyFoo`` between :class:`Complex` and :class:`Real` with::"
msgstr ""

#: ../Doc/library/numbers.rst:119
msgid "Implementing the arithmetic operations"
msgstr ""

#: ../Doc/library/numbers.rst:121
msgid ""
"We want to implement the arithmetic operations so that mixed-mode operations "
"either call an implementation whose author knew about the types of both "
"arguments, or convert both to the nearest built in type and do the operation "
"there. For subtypes of :class:`Integral`, this means that :meth:`__add__` "
"and :meth:`__radd__` should be defined as::"
msgstr ""

#: ../Doc/library/numbers.rst:152
msgid ""
"There are 5 different cases for a mixed-type operation on subclasses of :"
"class:`Complex`. I'll refer to all of the above code that doesn't refer to "
"``MyIntegral`` and ``OtherTypeIKnowAbout`` as \"boilerplate\". ``a`` will be "
"an instance of ``A``, which is a subtype of :class:`Complex` (``a : A <: "
"Complex``), and ``b : B <: Complex``. I'll consider ``a + b``:"
msgstr ""

#: ../Doc/library/numbers.rst:159
msgid "If ``A`` defines an :meth:`__add__` which accepts ``b``, all is well."
msgstr ""

#: ../Doc/library/numbers.rst:161
msgid ""
"If ``A`` falls back to the boilerplate code, and it were to return a value "
"from :meth:`__add__`, we'd miss the possibility that ``B`` defines a more "
"intelligent :meth:`__radd__`, so the boilerplate should return :const:"
"`NotImplemented` from :meth:`__add__`. (Or ``A`` may not implement :meth:"
"`__add__` at all.)"
msgstr ""

#: ../Doc/library/numbers.rst:167
msgid ""
"Then ``B``'s :meth:`__radd__` gets a chance. If it accepts ``a``, all is "
"well."
msgstr ""

#: ../Doc/library/numbers.rst:169
msgid ""
"If it falls back to the boilerplate, there are no more possible methods to "
"try, so this is where the default implementation should live."
msgstr ""

#: ../Doc/library/numbers.rst:172
msgid ""
"If ``B <: A``, Python tries ``B.__radd__`` before ``A.__add__``. This is ok, "
"because it was implemented with knowledge of ``A``, so it can handle those "
"instances before delegating to :class:`Complex`."
msgstr ""

#: ../Doc/library/numbers.rst:177
msgid ""
"If ``A <: Complex`` and ``B <: Real`` without sharing any other knowledge, "
"then the appropriate shared operation is the one involving the built in :"
"class:`complex`, and both :meth:`__radd__` s land there, so ``a+b == b+a``."
msgstr ""

#: ../Doc/library/numbers.rst:182
msgid ""
"Because most of the operations on any given type will be very similar, it "
"can be useful to define a helper function which generates the forward and "
"reverse instances of any given operator. For example, :class:`fractions."
"Fraction` uses::"
msgstr ""