Skip to main content

Continued fractions and convergents

Project description

ContFrac

Continued fractions are a representation of numbers expressed as recursive sums of integer parts and reciprocals of other numbers. ContFrac is a pure-Python3 lightweight module to compute and evaluate continued fractions, as well as using them to approximate any number.

Features

  • Supports conversion into continued fractions of int, float, fractions.Fraction and rational numbers expressed as tuples of 2 integers (numerator, denominator), generated iteratively.
  • Computes the convergents of the same data types, generated iteratively.
  • Computes the value of a finite continued fraction.
  • Generates the arithmetical expression as string of a continued fraction.

Installation

pip install contfrac

or just include the contfrac.py file in your project (copy-paste).

Example usage

>>> import contfrac
>>> value = 415/93  # Express as (415, 93) to avoid rounding continued frac.
>>> coefficients = list(contfrac.continued_fraction(value))
>>> print(coefficients)
[4, 2, 6, 7]

>>> expression = contfrac.arithmetical_expr(coefficients)
>>> print('Value: {:f} = {:s}'.format(value, expression))
Value: 4.462366 = 4 + 1/(2 + 1/(6 + 1/(7)))

>>> # The evaluation of a float value from a continued fraction is subject
>>> # to floating point rounding errors
>>> eval_value = contfrac.evaluate(coefficients)
>>> print(eval_value, value)  # Visible rounding errors
4.46236559139785 4.462365591397849

>>> convergents = list(contfrac.convergents(value))
>>> print(convergents)
[(4, 1), (9, 2), (58, 13), (415, 93)]

>>> import math
>>> coefficients = list(contfrac.continued_fraction(math.e, maxlen=10))
>>> print(coefficients)
[2, 1, 2, 1, 1, 4, 1, 1, 6, 1]

>>> convergent = contfrac.convergent(math.e, 3)  # Low convergent grade
>>> print(convergent, convergent[0]/convergent[1], math.e)
(11, 4) 2.75 2.718281828459045

>>> convergent = contfrac.convergent(math.e, 7)  # Higher grade = more accurate
>>> print(convergent, convergent[0]/convergent[1], math.e)
(193, 71) 2.7183098591549295 2.718281828459045

Similar libraries

Project details


Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Source Distribution

ContFrac-1.0.0.tar.gz (7.4 kB view hashes)

Uploaded Source

Built Distribution

ContFrac-1.0.0-py3-none-any.whl (5.8 kB view hashes)

Uploaded Python 3

Supported by

AWS AWS Cloud computing and Security Sponsor Datadog Datadog Monitoring Fastly Fastly CDN Google Google Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Sentry Sentry Error logging StatusPage StatusPage Status page