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.
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.
Project details
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