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

alexander

arrow

bracket

The bracket polynomial <.> (aka the Kauffman bracket) is a polynomial invariant of unoriented framed links.

cache

fundamental_group

homflypt

There are three variations: l-m: l * P(L+) + l^-1 * P(L-) + m * P(L0) = 0 v-z: v^-1 * P(L+) - v * P(L-) - z * P(L0) = 0 α-z: α * P(L+) - a^-1 * P(L-) - z * P(L0) = 0 xyz: x * P(L+) + y * P(L-) + z * P(L0) = 0

jones

The bracket polynomial <.> (aka the Kauffman bracket) is a polynomial invariant of unoriented framed links.

kauffman

The Kauffman 2-variable polynomial.

mock_alexander

module

R-module

tests

tutte

unplugging(k)

Computes the "unplugging" invariant T.

writhe(k)

The writhe is the total number of positive crossings minus the total number of negative crossings.

yamada

Compute the Yamada polynomial of a knotted planar diagram described in [Yamada, S.