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(k)

Compute the Tutte polynomial T(_x, _y) of a planar graph (no crossings).

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.