The Jones Polynomial: Difference between revisions
From Knot Atlas
Jump to navigationJump to search
DrorsRobot (talk | contribs) No edit summary |
DrorsRobot (talk | contribs) No edit summary |
||
| Line 3: | Line 3: | ||
<!--$$ Jones[Knot[6, 2]][q] $$--> |
<!--$$ Jones[Knot[6, 2]][q] $$--> |
||
<!--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.--> |
||
In[1]:=</tt> <code> Jones[Knot[6, 2]][q] </code> |
<tt>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}</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> |
||
<!--END--> |
<!--END--> |
||
| Line 17: | Line 18: | ||
<!--$$ Jones[Knot[9, 46]][q] $$--> |
<!--$$ Jones[Knot[9, 46]][q] $$--> |
||
<!--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.--> |
||
In[2]:=</tt> <code> Jones[Knot[9, 46]][q] </code> |
<tt>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}</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> |
||
<!--END--> |
<!--END--> |
||
Revision as of 19:09, 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]= [math]\displaystyle{ q-1+\frac{2}{q}-\frac{2}{q^2}+\frac{2}{q^3}-\frac{2}{q^4}+\frac{1}{q^5} }[/math]
Again:
In[1]:= Jones[Knot[6, 1]][q]
| Out[1]= | [math]\displaystyle{ q^2-q+2-\frac{2}{q}+\frac{1}{q^2}-\frac{1}{q^3}+\frac{1}{q^4} }[/math] |
In[2]:= Jones[Knot[9, 46]][q]
Out[2]= [math]\displaystyle{ 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]
Again:
In[2]:= Jones[Knot[6, 1]][q]
| Out[2]= | [math]\displaystyle{ 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] |
