The Jones Polynomial
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The knots 6_1 and 9_46 have the same Alexander polynomial. Their Jones polynomials are different, though:
In[1]:= Jones[Knot[6, 1]][q]
| Out[1]= | [math]\displaystyle{ q^2-q+2-\frac{2}{q}+\frac{1}{q^2}-\frac{1}{q^3}+\frac{1}{q^4} }[/math] |
Again:
In[1]:= Jones[Knot[6, 1]][q]
| Out[1]= | [math]\displaystyle{ q^2-q+2-\frac{2}{q}+\frac{1}{q^2}-\frac{1}{q^3}+\frac{1}{q^4} }[/math] |
In[2]:= Jones[Knot[6, 1]][q]
| Out[2]= | [math]\displaystyle{ 2-\frac{1}{q}+\frac{1}{q^2}-\frac{2}{q^3}+\frac{1}{q^4}-\frac{1}{q^5}+\frac{1}{q^6} }[/math] |
Again:
In[2]:= Jones[Knot[6, 1]][q]
| Out[2]= | [math]\displaystyle{ 2-\frac{1}{q}+\frac{1}{q^2}-\frac{2}{q^3}+\frac{1}{q^4}-\frac{1}{q^5}+\frac{1}{q^6} }[/math] |
