The Jones Polynomial: Difference between revisions
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<!--$$ Jones[Knot[6, 2]][q] $$--> |
<!--$$ Jones[Knot[6, 2]][q] $$--> |
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<math>In[1]:=</tt> <code> Jones[Knot[6, 2]][q] </code> |
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<math>q-1+\frac{2}{q}-\frac{2}{q^2}+\frac{2}{q^3}-\frac{2}{q^4}+\frac{1}{q^5}</math> |
Out[1]=</tt> <math>q-1+\frac{2}{q}-\frac{2}{q^2}+\frac{2}{q^3}-\frac{2}{q^4}+\frac{1}{q^5}</math> |
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<!--$$ Jones[Knot[9, 46]][q] $$--> |
<!--$$ Jones[Knot[9, 46]][q] $$--> |
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<math>In[2]:=</tt> <code> Jones[Knot[9, 46]][q] </code> |
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<math>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> |
Out[2]=</tt> <math>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> |
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Revision as of 19:07, 22 August 2005
The knots 6_1 and 9_46 have the same Alexander polynomial. Their Jones polynomials are different, though:
[math]\displaystyle{ In[1]:=\lt /tt\gt \lt code\gt Jones[Knot[6, 2]][q] \lt /code\gt Out[1]=\lt /tt\gt \lt math\gt q-1+\frac{2}{q}-\frac{2}{q^2}+\frac{2}{q^3}-\frac{2}{q^4}+\frac{1}{q^5} }[/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] |
[math]\displaystyle{ In[2]:=\lt /tt\gt \lt code\gt Jones[Knot[9, 46]][q] \lt /code\gt Out[2]=\lt /tt\gt \lt math\gt 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] |
