The Jones Polynomial: Difference between revisions
From Knot Atlas
Jump to navigationJump to search
DrorsRobot (talk | contribs) No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
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: |
||
<!--$$ |
<!--$$Jones[Knot[6, 3]][q]$$--> |
||
<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
<!--The lines to END were generated by WikiSplice: do not edit; see manual.--> |
||
{{InOut1|n=2}} |
{{InOut1|n=2}} |
||
| Line 12: | Line 12: | ||
<!--END--> |
<!--END--> |
||
<!--$$ |
<!--$$Jones[Knot[9, 48]][q] $$--> |
||
<!--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.--> |
||
{{InOut1|n=3}} |
{{InOut1|n=3}} |
||
| Line 22: | Line 22: | ||
<!--END--> |
<!--END--> |
||
<!--$$ |
<!--$$Jones[Knot[10, 112]][q] $$--> |
||
<!--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.--> |
||
{{InOut1|n=4}} |
{{InOut1|n=4}} |
||
Revision as of 22:31, 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
|
