The Jones Polynomial

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

q-1+\frac{2}{q}-\frac{2}{q^2}+\frac{2}{q^3}-\frac{2}{q^4}+\frac{1}{q^5}

Again:

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

Out[1]=

$q^{2}-q+2-{\frac {2}{q}}+{\frac {1}{q^{2}}}-{\frac {1}{q^{3}}}+{\frac {1}{q^{4}}}$

2-\frac{1}{q}+\frac{1}{q^2}-\frac{2}{q^3}+\frac{1}{q^4}-\frac{1}{q^5}+\frac{1}{q^6}

Again:

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

Out[2]=

$2-{\frac {1}{q}}+{\frac {1}{q^{2}}}-{\frac {2}{q^{3}}}+{\frac {1}{q^{4}}}-{\frac {1}{q^{5}}}+{\frac {1}{q^{6}}}$