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:mod:`fractions` --- Rational numbers
=====================================
.. module:: fractions
:synopsis: Rational numbers.
.. moduleauthor:: Jeffrey Yasskin <jyasskin at gmail.com>
.. sectionauthor:: Jeffrey Yasskin <jyasskin at gmail.com>
The :mod:`fractions` module defines an immutable, infinite-precision
Rational number class.
.. class:: Fraction(numerator=0, denominator=1)
Fraction(other_fraction)
Fraction(string)
The first version requires that *numerator* and *denominator* are
instances of :class:`numbers.Integral` and returns a new
``Fraction`` representing ``numerator/denominator``. If
*denominator* is :const:`0`, raises a :exc:`ZeroDivisionError`. The
second version requires that *other_fraction* is an instance of
:class:`numbers.Fraction` and returns an instance of
:class:`Rational` with the same value. The third version expects a
string of the form ``[-+]?[0-9]+(/[0-9]+)?``, optionally surrounded
by spaces.
Implements all of the methods and operations from
:class:`numbers.Rational` and is immutable and hashable.
.. method:: from_float(flt)
This classmethod constructs a :class:`Fraction` representing the exact
value of *flt*, which must be a :class:`float`. Beware that
``Fraction.from_float(0.3)`` is not the same value as ``Rational(3, 10)``
.. method:: from_decimal(dec)
This classmethod constructs a :class:`Fraction` representing the exact
value of *dec*, which must be a :class:`decimal.Decimal`.
.. method:: limit_denominator(max_denominator=1000000)
Finds and returns the closest :class:`Fraction` to ``self`` that has
denominator at most max_denominator. This method is useful for finding
rational approximations to a given floating-point number:
>>> from fractions import Fraction
>>> Fraction('3.1415926535897932').limit_denominator(1000)
Fraction(355, 113)
or for recovering a rational number that's represented as a float:
>>> from math import pi, cos
>>> Fraction.from_float(cos(pi/3))
Fraction(4503599627370497, 9007199254740992)
>>> Fraction.from_float(cos(pi/3)).limit_denominator()
Fraction(1, 2)
.. method:: __floor__()
Returns the greatest :class:`int` ``<= self``. Will be accessible through
:func:`math.floor` in Py3k.
.. method:: __ceil__()
Returns the least :class:`int` ``>= self``. Will be accessible through
:func:`math.ceil` in Py3k.
.. method:: __round__()
__round__(ndigits)
The first version returns the nearest :class:`int` to ``self``, rounding
half to even. The second version rounds ``self`` to the nearest multiple
of ``Fraction(1, 10**ndigits)`` (logically, if ``ndigits`` is negative),
again rounding half toward even. Will be accessible through :func:`round`
in Py3k.
.. seealso::
Module :mod:`numbers`
The abstract base classes making up the numeric tower.
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