HOMFLY polynomial http://doc.sagemath.org/html/en/reference/knots/sage/knots/link.html#sage.knots.link.Link.homfly_polynomial
B=BraidGroup(3) L=Link(B([1,1,1,2,-1,2])) L.homfly_polynomial()
L.plot()
sage: B = BraidGroup(3) sage: K = Knot(B([-1,-1,-1,-1,-1,-1,-2,1,-2,-2]))
K.plot()