The Jones Polynomial: Difference between revisions

Revision as of 23:31, 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

@@ Line 4: / Line 4: @@
 <!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
 {{InOut1|n=2}}
- Jones[Knot[6, 3]][q]
+Jones[Knot[6, 3]][q]
 {{InOut2|n=2}}<pre style="border: 0px; padding: 0em"><nowiki>     -3   2    2            2    3
 - q   + -- - - - 2 q + 2 q  - q
@@ Line 15: / Line 15: @@
 <!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
 {{InOut1|n=3}}
- Jones[Knot[9, 48]][q]
+Jones[Knot[9, 48]][q]
 {{InOut2|n=3}}<pre style="border: 0px; padding: 0em"><nowiki>     1            2      3      4      5      6
 -3 + - + 4 q - 4 q  + 6 q  - 4 q  + 3 q  - 2 q
@@ Line 25: / Line 25: @@
 <!--The lines to END were generated by WikiSplice: do not edit; see manual.-->
 {{InOut1|n=4}}
- Jones[Knot[10, 112]][q]
+Jones[Knot[10, 112]][q]
 {{InOut2|n=4}}<pre style="border: 0px; padding: 0em"><nowiki>       -7   4    7    11   14   14   14            2    3
 -10 + q   - -- + -- - -- + -- - -- + -- + 7 q - 4 q  + q