=============================
fractions -- Rational Numbers
=============================
.. module:: fractions
:synopsis: Implements a class for working with rational numbers.
:Purpose: Implements a class for working with rational numbers.
:Python Version: 2.6 and later
The Fraction class implements numerical operations for rational numbers based on the API defined by :class:`Rational` in :mod:`numbers`.
Creating Fraction Instances
===========================
As with :mod:`decimal`, new values can be created in several ways. One easy way is to create them from separate numerator and denominator values:
.. include:: fractions_create_integers.py
:literal:
:start-after: #end_pymotw_header
The lowest common denominator is maintained as new values are computed.
.. {{{cog
.. cog.out(run_script(cog.inFile, 'fractions_create_integers.py'))
.. }}}
::
$ python fractions_create_integers.py
1/2 = 1/2
2/4 = 1/2
3/6 = 1/2
.. {{{end}}}
Another way to create a Fraction is using a string representation of ``<numerator> / <denominator>``:
.. include:: fractions_create_strings.py
:literal:
:start-after: #end_pymotw_header
.. {{{cog
.. cog.out(run_script(cog.inFile, 'fractions_create_strings.py'))
.. }}}
::
$ python fractions_create_strings.py
1/2 = 1/2
2/4 = 1/2
3/6 = 1/2
.. {{{end}}}
Strings can also use the more usual decimal or floating point notation of ``[<digits>].[<digits>]``.
.. include:: fractions_create_strings_floats.py
:literal:
:start-after: #end_pymotw_header
.. {{{cog
.. cog.out(run_script(cog.inFile, 'fractions_create_strings_floats.py'))
.. }}}
::
$ python fractions_create_strings_floats.py
0.5 = 1/2
1.5 = 3/2
2.0 = 2
.. {{{end}}}
There are class methods for creating Fraction instances directly from other representations of rational values such as float or :mod:`decimal`.
.. include:: fractions_from_float.py
:literal:
:start-after: #end_pymotw_header
Notice that for floating point values that cannot be expressed exactly the rational representation may yield unexpected results.
.. {{{cog
.. cog.out(run_script(cog.inFile, 'fractions_from_float.py'))
.. }}}
::
$ python fractions_from_float.py
0.1 = 3602879701896397/36028797018963968
0.5 = 1/2
1.5 = 3/2
2.0 = 2
.. {{{end}}}
Using :mod:`decimal` representations of the values gives the expected results.
.. include:: fractions_from_decimal.py
:literal:
:start-after: #end_pymotw_header
.. {{{cog
.. cog.out(run_script(cog.inFile, 'fractions_from_decimal.py'))
.. }}}
::
$ python fractions_from_decimal.py
0.1 = 1/10
0.5 = 1/2
1.5 = 3/2
2.0 = 2
.. {{{end}}}
Arithmetic
==========
Once the fractions are instantiated, they can be used in mathematical expressions as you would expect.
.. include:: fractions_arithmetic.py
:literal:
:start-after: #end_pymotw_header
.. {{{cog
.. cog.out(run_script(cog.inFile, 'fractions_arithmetic.py'))
.. }}}
::
$ python fractions_arithmetic.py
1/2 + 3/4 = 5/4
1/2 - 3/4 = -1/4
1/2 * 3/4 = 3/8
1/2 / 3/4 = 2/3
.. {{{end}}}
Approximating Values
====================
A useful feature of Fraction is the ability to convert a floating point number to an approximate rational value by limiting the size of the denominator.
.. include:: fractions_limit_denominator.py
:literal:
:start-after: #end_pymotw_header
.. {{{cog
.. cog.out(run_script(cog.inFile, 'fractions_limit_denominator.py'))
.. }}}
::
$ python fractions_limit_denominator.py
PI = 3.14159265359
No limit = 314159265359/100000000000
1 = 3
6 = 19/6
11 = 22/7
16 = 22/7
21 = 22/7
26 = 22/7
31 = 22/7
36 = 22/7
41 = 22/7
46 = 22/7
51 = 22/7
56 = 22/7
61 = 179/57
66 = 201/64
71 = 223/71
76 = 223/71
81 = 245/78
86 = 267/85
91 = 267/85
96 = 289/92
.. {{{end}}}
.. seealso::
`fractions <http://docs.python.org/library/fractions.html>`_
The standard library documentation for this module.
:mod:`decimal`
The decimal module provides an API for fixed and floating point math.
:mod:`numbers`
Numeric abstract base classes.