The Jones Polynomial: Difference between revisions
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<!--$$ Jones[Knot[6, 2]][q] $$--> |
<!--$$ Jones[Knot[6, 2]][q] $$--> |
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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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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> |
<tt>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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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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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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Revision as of 18:09, 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]=
Again:
In[1]:= Jones[Knot[6, 1]][q]
| Out[1]= |
In[2]:= Jones[Knot[9, 46]][q]
Out[2]=
Again:
In[2]:= Jones[Knot[6, 1]][q]
| Out[2]= |
