Introduction

Frank Lübeck maintains a list of pre-computed Conway polynomial coefficients at,

https://www.math.rwth-aachen.de/~Frank.Luebeck/data/ConwayPol/index.html

These are used in several computer algebra systems such as GAP and SageMath to provide quick access to those Conway polynomials. The aim of this package is to make them available through a generic python interface. The package consists of a single module containing a single function that returns a dict of dicts, conway_polynomials.database(). The dictionary’s format is {p: {n: coefficients}}, where p represents your prime and n your degree. The tuple of coefficients is returned in ascending order; that is, the first coefficient (at index zero) is for the constant (degree zero) term.

This package is an evolution of the SageMath conway_polynomials package hosted at,

http://files.sagemath.org/spkg/upstream/conway_polynomials/

and is maintained by the same team of developers. We have kept the versioning scheme consistent to reflect that.

Examples

Retrieve the coefficients of the Conway polynomial for prime p=2 and degree n=5:

>>> import conway_polynomials
>>> cpdb = conway_polynomials.database()
>>> cpdb[2][5]
(1, 0, 1, 0, 0, 1)

The result is cached, so subsequent computations should be fast even if you call the function again:

>>> conway_polynomials.database() is conway_polynomials.database()
True

However, the result is also mutable, so if you need to modify it for some reason then you should create a copy; otherwise your changes will affect future calls:

>>> cpdb = conway_polynomials.database()
>>> cpdb[5][5]
(3, 4, 0, 0, 0, 1)
>>> cpdb[5][5] = (8, 6, 7, 5, 3, 0, 9)
>>> conway_polynomials.database()[5][5]
(8, 6, 7, 5, 3, 0, 9)

Testing

A few doctests within the module (and this README) ensure that everything is working. You can run them from the repository or from a release tarball using:

PYTHONPATH=src python -m doctest \
  README.rst \
  src/conway_polynomials/__init__.py

Or, if you have pytest installed, with simply:

pytest