pd-code-de-r1

Remove Reidemeister-I crossings from a planar-diagram code.

Installation

pip install pd-code-de-r1

Usage example

from pd_code_de_r1 import de_r1

pd = [[1, 1, 2, 2]]
print(de_r1(pd))  # []

Algorithm

A Reidemeister-I crossing contains a locally repeated arc pattern. The algorithm builds the opposite-slot strand graph, identifies labels trapped in the one-crossing loop, removes the crossing, reconnects its surviving strand endpoints, and renumbers labels along each remaining cycle. Removal is repeated because one reduction can expose another R1 crossing.

Input conventions

A PD code is represented as a list of four-entry crossings. Arc labels normally occur exactly twice. Public functions validate inputs and return new values rather than mutating caller-owned data unless their API explicitly says otherwise.

External software

No external software is required.

Development

Run examples and package checks before release. Python packages require Python 3.10 or newer. Build PyPI artifacts with:

poetry check
poetry build

License

MIT. See LICENSE.