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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>
+.. versionadded:: 2.6
+
+
+The :mod:`fractions` module provides support for rational number arithmetic.
+
+
+A Fraction instance can be constructed from a pair of integers, from
+another rational number, or from a string.
+
+.. 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
+ :class:`Fraction` instance with value ``numerator/denominator``. If
+ *denominator* is :const:`0`, it raises a
+ :exc:`ZeroDivisionError`. The second version requires that
+ *other_fraction* is an instance of :class:`numbers.Rational` and
+ returns an :class:`Fraction` instance with the same value. The
+ last version of the constructor expects a string or unicode
+ instance in one of two possible forms. The first form is::
+
+ [sign] numerator ['/' denominator]
+
+ where the optional ``sign`` may be either '+' or '-' and
+ ``numerator`` and ``denominator`` (if present) are strings of
+ decimal digits. The second permitted form is that of a number
+ containing a decimal point::
+
+ [sign] integer '.' [fraction] | [sign] '.' fraction
+
+ where ``integer`` and ``fraction`` are strings of digits. In
+ either form the input string may also have leading and/or trailing
+ whitespace. Here are some examples::
+
+ >>> from fractions import Fraction
+ >>> Fraction(16, -10)
+ Fraction(-8, 5)
+ >>> Fraction(123)
+ Fraction(123, 1)
+ >>> Fraction()
+ Fraction(0, 1)
+ >>> Fraction('3/7')
+ Fraction(3, 7)
+ [40794 refs]
+ >>> Fraction(' -3/7 ')
+ Fraction(-3, 7)
+ >>> Fraction('1.414213 \t\n')
+ Fraction(1414213, 1000000)
+ >>> Fraction('-.125')
+ Fraction(-1, 8)
+
+
+ The :class:`Fraction` class inherits from the abstract base class
+ :class:`numbers.Rational`, and implements all of the methods and
+ operations from that class. :class:`Fraction` instances are hashable,
+ and should be treated as immutable. In addition,
+ :class:`Fraction` has the following methods:
+
+
+ .. method:: from_float(flt)
+
+ This class method 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 ``Fraction(3, 10)``
+
+
+ .. method:: from_decimal(dec)
+
+ This class method 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)
+
+
+.. function:: gcd(a, b)
+
+ Return the greatest common divisor of the integers `a` and `b`. If
+ either `a` or `b` is nonzero, then the absolute value of `gcd(a,
+ b)` is the largest integer that divides both `a` and `b`. `gcd(a,b)`
+ has the same sign as `b` if `b` is nonzero; otherwise it takes the sign
+ of `a`. `gcd(0, 0)` returns `0`.
+
+
+.. seealso::
+
+ Module :mod:`numbers`
+ The abstract base classes making up the numeric tower.