invariants#

List of possible invairants to implement:

Alexander Polynomial Conway Polynomial Jones Polynomial HOMFLY-PT Polynomial Kauffman 2-variable Polynomial (F polynomial) Writhe Linking Number Seifert Genus (Upper Bound) Turaev Genus (more advanced but diagrammatic) Tricolorability n-Colorability (mod n coloring)

Modules

affine_index

Affine index polynomial for knotoids.

alexander(k[, symmetric])

Compute the one-variable Alexander polynomial via HOMFLY-PT specialization.

arrow

Arrow polynomial for knotoids (per Kauffman et al.).

bracket(k[, normalize])

Compute the Kauffman bracket polynomial ⟨·⟩.

cache

Lightweight LFU cache with an optional size cap.

classifier

coloring

conway(k)

Return the Alexander–Conway polynomial of a knot or link.

fundamental_group(k[, return_dict])

Return a presentation of the fundamental group of the complement of k in S³.

homflypt(k[, variables])

Compute the HOMFLY–PT polynomial.

jones(k)

Compute the Jones polynomial via the normalized Kauffman bracket.

kauffman(k)

mock_alexander

Mock Alexander-like polynomial (face-marking heuristic).

skein

Implementations of Skein operations.

tests

tutte

Tutte polynomial for planar graphs represented as PlanarDiagram objects.

unplugging(k)

Computes the "unplugging" invariant T.

writhe(k)

Return the writhe of k.

yamada(k[, normalize])

Return the Yamada polynomial of a given planar diagram.