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, 3]][q] $$--> |
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<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
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<tt>In[1]:=</tt> <code> Jones[Knot[6, 2]][q] </code> |
<tt>In[1]:=</tt> <code> Jones[Knot[6, 2]][q] </code> |
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<!--$$ Jones[Knot[9, |
<!--$$ Jones[Knot[9, 48]][q] $$--> |
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<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
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<tt>In[2]:=</tt> <code> Jones[Knot[9, 46]][q] </code> |
<tt>In[2]:=</tt> <code> Jones[Knot[9, 46]][q] </code> |
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<tt>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> |
<tt>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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<!--$$ Jones[Knot[10, 112]][q] $$--> |
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Revision as of 18:12, 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, 2]][q]
Out[1]=
In[2]:= Jones[Knot[9, 46]][q]
Out[2]=
