symbian-qemu-0.9.1-12/python-2.6.1/Doc/library/fractions.rst
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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.