Homfly Library in SageMath
HOMFLY polynomial http://doc.sagemath.org/html/en/reference/knots/sage/knots/link.html#sage.knots.link.Link.homfly_polynomial
L^-2*M^2 - L^-2 - L^-4*M^2 + L^-4 + L^-6
HOMFLY polynomial http://doc.sagemath.org/html/en/reference/knots/sage/knots/link.html#sage.knots.link.Link.homfly_polynomial