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 18:07, 22 August 2005
The knots 6_1 and 9_46 have the same Alexander polynomial. Their Jones polynomials are different, though:
![{\displaystyle In[1]:=</tt><code>Jones[Knot[6,2]][q]</code>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}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7bd974ce631fb92e73e6a23fe60af22d4000c9cc)
Again:
In[1]:= Jones[Knot[6, 1]][q]
| Out[1]= |
![{\displaystyle In[2]:=</tt><code>Jones[Knot[9,46]][q]</code>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}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/13fd1751d5a47e1fbb5dc3aaf4e294907e8d9d72)
Again:
In[2]:= Jones[Knot[6, 1]][q]
| Out[2]= |
