bracket_polynomial

bracket_polynomial(k: PlanarDiagram, variable='A', normalize=True) → Expr

Return the (Kauffman) Bracket polynomial defined via the skein relations <L_X> = A <L_0> + 1/A <L_inf>, <L ⊔ U> = (-A^2 - A^-2) <L> and <unknot> = 1.

param k:

Planar diagram

param variable:

variable used for the polynomial

param normalize:

should we normalize it by multiplying by the factor (-A^3)^wr(k), where wr is the writhe of the

diagram d :return: (Laurent) polynomial in variable

TODO: take care of vertices connected by two arcs, TODO: take care that we unframe once we add the framing to the polynomial TODO: canonical