Index: Doc/library/fractions.rst =================================================================== --- Doc/library/fractions.rst (revision 64525) +++ Doc/library/fractions.rst (working copy) @@ -9,79 +9,96 @@ .. versionadded:: 2.6 -The :mod:`fractions` module defines an immutable, infinite-precision -Fraction number class. +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 - ``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.Rational` and returns an instance of - :class:`Fraction` with the same value. The third version expects a - string of the form ``[-+]?[0-9]+(/[0-9]+)?``, optionally surrounded - by spaces. + :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:: - Implements all of the methods and operations from - :class:`numbers.Rational` and is immutable and hashable. + [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:: - .. method:: from_float(flt) + [sign] integer '.' [fraction] | [sign] ['.'] fraction - 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 ``Fraction(3, 10)`` + 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) - .. method:: from_decimal(dec) - This classmethod constructs a :class:`Fraction` representing the exact - value of *dec*, which must be a :class:`decimal.Decimal`. +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:: limit_denominator(max_denominator=1000000) +.. method:: from_float(flt) - 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: + 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)`` - >>> from fractions import Fraction - >>> Fraction('3.1415926535897932').limit_denominator(1000) - Fraction(355L, 113L) - or for recovering a rational number that's represented as a float: +.. method:: from_decimal(dec) - >>> from math import pi, cos - >>> Fraction.from_float(cos(pi/3)) - Fraction(4503599627370497L, 9007199254740992L) - >>> Fraction.from_float(cos(pi/3)).limit_denominator() - Fraction(1L, 2L) + This class method constructs a :class:`Fraction` representing the exact + value of *dec*, which must be a :class:`decimal.Decimal`. - .. method:: __floor__() +.. method:: limit_denominator(max_denominator=1000000) - Returns the greatest :class:`int` ``<= self``. + 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) - .. method:: __ceil__() + or for recovering a rational number that's represented as a float: - Returns the least :class:`int` ``>= self``. + >>> 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:: __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. - - .. seealso:: Module :mod:`numbers`