pd-code-delete-nugatory

Detect and remove nugatory crossings from PD codes.

Installation

pip install pd-code-delete-nugatory

Usage example

from pd_code_delete_nugatory import erase_all_nugatory, get_index_of_nugatory

pd = [[1, 1, 2, 2]]
print(get_index_of_nugatory(pd))
print(erase_all_nugatory(pd))

Algorithm

For each candidate crossing, the algorithm removes that crossing from a weak strand graph and compares graph connectivity. A crossing whose removal separates regions is nugatory. Erasing it reconnects the paired arcs, removes any induced Reidemeister-I crossing, and renumbers the remaining component cycles. The process repeats until no candidate remains.

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.