The Jones Polynomial: Difference between revisions
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The knots 6_1 and 9_46 have the same Alexander polynomial. Their Jones polynomials are different, though: |
The knots 6_1 and 9_46 have the same Alexander polynomial. Their Jones polynomials are different, though: |
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<!--$$ Jones[Knot[6, |
<!--$$ Jones[Knot[6, 2]][q] $$--> |
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<tt>In[1]:=</tt> <code>Jones[Knot[6, 1]][q]</code> |
<tt>In[1]:=</tt> <code>Jones[Knot[6, 1]][q]</code> |
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Revision as of 18:55, 22 August 2005
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] |
