Getting Started#

This is a PyPI package which uses only Python standard libraries, and is supported on any Linux, Mac OS or Windows system supporting Python 3.10, 3.11, or 3.12. It is CI-tested on Ubuntu Linux (22.04.3 LTS), Mac OS (12.7.3) and Windows (Windows Server 2022), but should also install on any other platform supporting these Python versions.

Installation#

A standard pip install is sufficient:

pip install continuedfractions

Potential contributors may want look at the project TOML, and then the contributions overview.

Package Structure#

The continuedfractions package consists of two core libraries.

Each is summarised below. Or you can go straight to the API reference.

`continuedfractions.lib`#

This is a library of standalone functions, the most important of which are summarised below.

continued_fraction_rational() - generates the (ordered) sequence of elements (coefficients) of the unique simple continued fraction of a given rational number, given as a fractions.Fraction instance
continued_fraction_real() - generates the sequence of elements of a simple continued fraction of a real number, given as a single int, float, str, or decimal.Decimal value; the results for float inputs may be approximate and not necessarily unique
fraction_from_elements() - returns a fractions.Fraction instance of the rational number represented by a simple continued fraction with the given sequence of elements
convergent() - returns the \(k\)-th convergent (for a positive integer \(k\)) from a sequence of elements of a (finite) simple continued fraction; the convergent is returned as a fractions.Fraction instance
mediant() - returns the \(k\)-th left or right mediant of two rational numbers, given as fractions.Fraction values; the mediant is returned as a fractions.Fraction instance

Note

There are also two “wrapper” functions for computing left- and right-mediants - left_mediant() and right_mediant() - but these just call mediant().

`continuedfractions.continuedfraction`#

This is a library containing a single main class:

ContinuedFraction - a subclass of fractions.Fraction, designed to represent (finite) simple continued fractions as Python objects, which are fully operable as rational numbers.