The Jones Polynomial: Difference between revisions
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<!--$$ Jones[Knot[6, 3]][q] $$--> |
<!--$$ Jones[Knot[6, 3]][q] $$--> |
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<tt>In[1]:=</tt> <code> Jones[Knot[6, |
<tt>In[1]:=</tt> <code> Jones[Knot[6, 3]][q] </code> |
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<tt>Out[1]=</tt> <math>q |
<tt>Out[1]=</tt> <math>-q^3+2 q^2-2 q+3-\frac{2}{q}+\frac{2}{q^2}-\frac{1}{q^3}</math> |
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<!--$$ Jones[Knot[9, 48]][q] $$--> |
<!--$$ Jones[Knot[9, 48]][q] $$--> |
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<tt>In[2]:=</tt> <code> Jones[Knot[9, |
<tt>In[2]:=</tt> <code> Jones[Knot[9, 48]][q] </code> |
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<tt>Out[2]=</tt> <math>2 |
<tt>Out[2]=</tt> <math>-2 q^6+3 q^5-4 q^4+6 q^3-4 q^2+4 q-3+\frac{1}{q}</math> |
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<!--$$ Jones[Knot[10, 112]][q] $$--> |
<!--$$ Jones[Knot[10, 112]][q] $$--> |
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<tt>In[3]:=</tt> <code> Jones[Knot[10, 112]][q] </code> |
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<tt>Out[3]=</tt> <math>q^3-4 q^2+7 q-10+\frac{14}{q}-\frac{14}{q^2}+\frac{14}{q^3}-\frac{11}{q^4}+\frac{7}{q^5}-\frac{4}{q^6}+\frac{1}{q^7}</math> |
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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, 3]][q]
Out[1]=
In[2]:= Jones[Knot[9, 48]][q]
Out[2]=
In[3]:= Jones[Knot[10, 112]][q]
Out[3]=
