The Jones Polynomial: Difference between revisions
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<!--$$ Jones[Knot[6, 3]][q] $$--> |
<!--$$ Jones[Knot[6, 3]][q] $$--> |
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{{InOut1|n=2}} |
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Jones[Knot[6, 3]][q] |
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{{InOut2|n=2}}<pre style="border: 0px; padding: 0em"><nowiki> -3 2 2 2 3 |
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<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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3 - q + -- - - - 2 q + 2 q - q |
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2 q |
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q</nowiki></pre> |
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{{InOut3}} |
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<!--$$ Jones[Knot[9, 48]][q] $$--> |
<!--$$ Jones[Knot[9, 48]][q] $$--> |
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{{InOut1|n=3}} |
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Jones[Knot[9, 48]][q] |
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{{InOut2|n=3}}<pre style="border: 0px; padding: 0em"><nowiki> 1 2 3 4 5 6 |
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<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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-3 + - + 4 q - 4 q + 6 q - 4 q + 3 q - 2 q |
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q</nowiki></pre> |
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{{InOut3}} |
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<!--$$ Jones[Knot[10, 112]][q] $$--> |
<!--$$ Jones[Knot[10, 112]][q] $$--> |
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{{InOut1|n=4}} |
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Jones[Knot[10, 112]][q] |
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{{InOut2|n=4}}<pre style="border: 0px; padding: 0em"><nowiki> -7 4 7 11 14 14 14 2 3 |
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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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-10 + q - -- + -- - -- + -- - -- + -- + 7 q - 4 q + q |
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6 5 4 3 2 q |
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q q q q q</nowiki></pre> |
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{{InOut3}} |
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Revision as of 22:30, 25 August 2005
The knots 6_1 and 9_46 have the same Alexander polynomial. Their Jones polynomials are different, though:
| In[2]:= |
Jones[Knot[6, 3]][q] |
| Out[2]= | -3 2 2 2 3
3 - q + -- - - - 2 q + 2 q - q
2 q
q
|
| In[3]:= |
Jones[Knot[9, 48]][q] |
| Out[3]= | 1 2 3 4 5 6
-3 + - + 4 q - 4 q + 6 q - 4 q + 3 q - 2 q
q
|
| In[4]:= |
Jones[Knot[10, 112]][q] |
| Out[4]= | -7 4 7 11 14 14 14 2 3
-10 + q - -- + -- - -- + -- - -- + -- + 7 q - 4 q + q
6 5 4 3 2 q
q q q q q
|
