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Pure Python library for working with modular arithmetic, congruence classes, and finite fields.

Project description

Pure Python library for working with modular arithmetic and congruence classes.

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Purpose

The library allows users to work with congruence classes (including finite field elements) as objects, with support for many common operations.

Package Installation and Usage

The package is available on PyPI:

python -m pip install modulo

The library can be imported in the usual way:

from modulo import modulo

Examples

This library makes it possible to work with congruence classes (and sets of congruence classes such as finite fields) as objects. A congruence class is defined using a representative integer and a modulus:

>>> from modulo import modulo
>>> modulo(3, 7)
modulo(3, 7)

Built-in operators can be used to perform modular addition, modular subtraction, and modular negation of congruence classes:

>>> modulo(3, 7) + modulo(5, 7)
modulo(1, 7)
>>> modulo(1, 7) - modulo(4, 7)
modulo(4, 7)
>>> -modulo(5, 7)
modulo(2, 7)

Modular multiplication, division, inversion, and exponentiation are also supported (when they are defined):

>>> modulo(3, 7) * modulo(5, 7)
modulo(1, 7)
>>> modulo(1, 7) // modulo(3, 7)
modulo(5, 7)
>>> modulo(5, 7) ** 2
modulo(4, 7)
>>> modulo(5, 7) ** (-1)
modulo(3, 7)

A set of congruence classes such as a finite field can also be defined. The built-in length function and the membership operator are supported:

>>> len(modulo(7))
7
>>> modulo(3, 7) in modulo(7)
True

Documentation

The documentation can be generated automatically from the source files using Sphinx:

cd docs
python -m pip install -r requirements.txt
sphinx-apidoc -f -E --templatedir=_templates -o _source .. ../setup.py && make html

Testing and Conventions

All unit tests are executed and their coverage is measured when using nose (see setup.cfg for configuration details):

python -m pip install nose coverage
nosetests --cover-erase

Alternatively, all unit tests are included in the module itself and can be executed using doctest:

python modulo/modulo.py -v

Style conventions are enforced using Pylint:

python -m pip install pylint
pylint modulo

Contributions

In order to contribute to the source code, open an issue or submit a pull request on the GitHub page for this library.

Versioning

Beginning with version 0.2.0, the version number format for this library and the changes to the library associated with version number increments conform with Semantic Versioning 2.0.0.

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