Pure-Python implementation of Lagrange interpolation over finite fields.

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This library provides a pure-Python implementation of the Lagrange interpolation algorithm over finite fields.

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 fully specified in pyproject.toml. The project.optional-dependencies object 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 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 the pyproject.toml file for configuration details):

python -m pip install .[test]
python -m pytest

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

python src/lagrange/ -v

Style conventions are enforced using Pylint:

python -m pip install .[lint]
python -m pylint src/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]

Ensure that the correct version number appears in pyproject.toml, and that any links in this README document to the Read the Docs documentation of this package (or its dependencies) have appropriate version numbers. Also ensure that the Read the Docs project for this library has an automation rule that activates and sets as the default all tagged versions. Create and push a tag for this version (replacing ?.?.? with the version number):

git tag ?.?.?
git push origin ?.?.?

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

rm -rf build dist src/*.egg-info
python -m build --sdist --wheel .

Finally, upload the package distribution archive to PyPI:

python -m twine upload dist/*