Pure-Python implementation of Lagrange interpolation over finite fields.

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Pure Python implementation of the Lagrange interpolation algorithm over finite fields.

Package Installation and Usage

This library is available as a package on PyPI:

python -m pip install lagrange

The library can be imported in the usual way:

from lagrange import lagrange


Interpolation can be performed on collections of points represented in a variety of ways:

>>> lagrange({1: 15, 2: 9, 3: 3}, 17)
>>> lagrange([(1, 15), (2, 9), (3, 3)], 17)
>>> lagrange([15, 9, 3], 17)
>>> lagrange(\
    {1: 119182, 2: 11988467, 3: 6052427, 4: 8694701,\
     5: 9050123, 6: 3676518, 7: 558333, 8: 12198248,\
     9: 7344866, 10: 10114014, 11: 2239291, 12: 2515398},\
>>> lagrange(\
    [119182, 11988467, 6052427, 8694701, 9050123, 3676518,\
     558333, 12198248, 7344866, 10114014, 2239291, 2515398],\


All installation and development dependencies are managed using setuptools and are fully specified in The extras_require parameter is used to specify optional requirements for various development tasks. This makes it possible to specify additional options (such as docs, lint, and so on) when performing installation using pip:

python -m pip install .[docs,lint]


The library contains one module:

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

python -m pip install .[docs]
cd docs
sphinx-apidoc -f -E --templatedir=_templates -o _source .. ../ && make html

Testing and Conventions

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

python -m pip install .[test]
nosetests --cover-erase

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

python lagrange/ -v

Style conventions are enforced using Pylint:

python -m pip install .[lint]
pylint lagrange


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


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.


This library can be published as a package on PyPI by a package maintainer. First, install the dependencies required for packaging and publishing:

python -m pip install .[publish]

Remove any old build/distribution files. Then, package the source into a distribution archive using the wheel package:

rm -rf dist *.egg-info
python sdist bdist_wheel

Finally, upload the package distribution archive to PyPI using the twine package:

python -m twine upload dist/*