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, 3]][q]

Out[1]= [math]\displaystyle{ -q^3+2 q^2-2 q+3-\frac{2}{q}+\frac{2}{q^2}-\frac{1}{q^3} }[/math]

In[2]:= Jones[Knot[9, 48]][q]

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

In[3]:= Jones[Knot[10, 112]][q]

Out[3]= [math]\displaystyle{ q^3-4 q^2+7 q-10+\frac{14}{q}-\frac{14}{q^2}+\frac{14}{q^3}-\frac{11}{q^4}+\frac{7}{q^5}-\frac{4}{q^6}+\frac{1}{q^7} }[/math]