Please see the polynomial description page for up-to-date descriptions of the conventions used in KnotInfo for the Jones, Homfly, and Kauffman polynomials.

We follow some historical conventions: the HOMFLY polynomial is given in variables v and z (Hugh Morton), while the Kauffman polynomial is given in variables a and z (Kauffman).

Any polynomial with two variables can be thought of as a polynomial
in one variable with coefficients that are polynomial in the other
variable. The HOMFLY and Kauffman polynomials are given as
semicolon-delimited list of coefficients with respect to the variable
z^{2}. Because odd powers of the variables never appear in
either HOMFLY or Kauffman polynomials, we leave them out of the
encoding. Each coefficient in turn is a space-delimited
representation of a polynomial in the secondary
variable: v^{2} or a^{2}, respectively. The format
for each polynomial is as follows:

<lowest exponent> <highest exponent> <coefficients>

For example, consider the following encoding of a two-variable polynomial:

-4 2 1 0 -2 2; -4 2 1 -2 -3 1; -2 0 -1 -1

The corresponding (HOMFLY) polynomial is:

(v^{-4})-2+2*v^{2}) + (v^{-4})-2*v^{-2}-3+v^{2})*z^{2} +
(-v^{-2}-1)*z^{4}