The Jones Polynomial

The knots 6_1 and 9_46 have the same Alexander polynomial. Their Jones polynomials are different, though:

In[1]:= Jones[Knot[6, 2]][q]

Out[1]= $q-1+{\frac {2}{q}}-{\frac {2}{q^{2}}}+{\frac {2}{q^{3}}}-{\frac {2}{q^{4}}}+{\frac {1}{q^{5}}}$

In[2]:= Jones[Knot[9, 46]][q]

Out[2]= $2-{\frac {1}{q}}+{\frac {1}{q^{2}}}-{\frac {2}{q^{3}}}+{\frac {1}{q^{4}}}-{\frac {1}{q^{5}}}+{\frac {1}{q^{6}}}$