A New Algorithm for Numerical Calculation of Link Invariants
  We propose a new method for numerical calculation of link plynomials for knots given in 3 dimensions. We calculate derivatives of the Jones polynomial in a computational time proportional to $N^{\alpha}$ with respect to the system size $N$ . This method gives a new tool for determining topology of knotted closed loops in three dimensions using computers. 
Tetsuo Deguchi and Kyoichi Tsurusaki