continuedfractions

A simple extension of the Python fractions standard library for working with (finite, simple) continued fractions as Python objects.

This is a PyPI package. It is updated as necessary with improvements, features and fixes. Only standard libraries are used, and the package is tested on Python 3.10-3.13, although it should be compatible with many earlier versions as well.

pip install -U continuedfractions

See the project docs for more details, which includes the API reference.

Continued fractions are beautiful and interesting mathematical objects, with many connections in number theory and also very useful practical applications, including the rational approximation of real numbers.

The continuedfractions package is designed for users interested in:

• learning about and working with (finite, simple) continued fractions as Python objects, in an intuitive object-oriented way
• exploring their key properties, such as elements/coefficients, convergents, semiconvergents, remainders, and others
• operating on them as rationals and instances of the standard library fractions.Fraction class
• making approximations of and experimental computations for irrational numbers
• exploring other related objects, such as mediants, and special sequences of rational numbers such as Farey sequences

Currently, it does not support the following features:

• infinite and generalised continued fractions
• symbolic representations of or operations with continued fractions

Some - but not necessarily all - of these features may be considered for future release.

The project is licensed under the Mozilla Public License 2.0.