PD Presentation: |
X8192 X12,4,13,3 X20,10,21,9 X22,12,7,11 X10,22,11,21 X16,6,17,5 X18,16,19,15 X14,20,15,19 X2738 X4,14,5,13 X6,18,1,17 |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Length[Skeleton[L]] |
Out[2]= | 2 |
In[3]:= | Show[DrawMorseLink[Link[11, Alternating, 218]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 218]] |
Out[4]= | PD[X[8, 1, 9, 2], X[12, 4, 13, 3], X[20, 10, 21, 9], X[22, 12, 7, 11],
> X[10, 22, 11, 21], X[16, 6, 17, 5], X[18, 16, 19, 15], X[14, 20, 15, 19],
> X[2, 7, 3, 8], X[4, 14, 5, 13], X[6, 18, 1, 17]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 2, -10, 6, -11},
> {9, -1, 3, -5, 4, -2, 10, -8, 7, -6, 11, -7, 8, -3, 5, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | 3/2 5/2 7/2 9/2 11/2 13/2
-Sqrt[q] + 2 q - 6 q + 8 q - 12 q + 14 q - 14 q +
15/2 17/2 19/2 21/2 23/2
> 13 q - 10 q + 6 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | 2 6 8 10 12 14 16 18 20 22 24
q + 2 q + 3 q + q + 5 q - q + q - q - 3 q + 2 q - 2 q +
26 30 32 34
> 2 q - q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 218]][a, z] |
Out[8]= | 3 3 3 3 5
1 3 2 2 z 2 z 4 z 5 z 3 z 5 z 5 z 4 z z
---- - ---- + ---- + --- - --- - --- + --- + ---- - ---- - ---- + ---- + -- -
7 5 3 9 7 5 3 9 7 5 3 9
a z a z a z a a a a a a a a a
5 5 5 7 7
4 z 4 z z z z
> ---- - ---- + -- - -- - --
7 5 3 7 5
a a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 218]][a, z] |
Out[9]= | 2 2
-8 3 3 1 3 2 2 z 2 z 3 z 10 z 7 z z z
a + -- + -- - ---- - ---- - ---- + --- + --- + --- + ---- + --- + --- - --- +
6 4 7 5 3 11 9 7 5 3 14 12
a a a z a z a z a a a a a a a
2 2 2 2 3 3 3 3 3 3
6 z 9 z 2 z 3 z 3 z 10 z 10 z 5 z 17 z 9 z
> ---- + ---- - ---- - ---- + ---- - ----- - ----- - ---- - ----- - ---- -
10 8 6 4 13 11 9 7 5 3
a a a a a a a a a a
4 4 4 4 4 4 5 5 5 5
z 5 z 16 z 28 z 11 z 5 z 3 z 12 z 8 z 3 z
> --- + ---- - ----- - ----- - ----- - ---- - ---- + ----- + ---- - ---- +
14 12 10 8 6 4 13 11 9 7
a a a a a a a a a a
5 5 6 6 6 6 6 7 7 7
9 z 5 z 5 z 15 z 29 z 16 z 7 z 7 z 3 z 14 z
> ---- + ---- - ---- + ----- + ----- + ----- + ---- - ---- + ---- + ----- +
5 3 12 10 8 6 4 11 9 7
a a a a a a a a a a
7 7 8 8 8 8 9 9 9 10 10
3 z z 7 z 8 z 3 z 2 z 4 z 6 z 2 z z z
> ---- - -- - ---- - ---- - ---- - ---- - ---- - ---- - ---- - --- - ---
5 3 10 8 6 4 9 7 5 8 6
a a a a a a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 4
4 6 -2 q q 6 8 8 2 10 2 10 3
5 q + 2 q + t + -- + -- + 4 q t + 4 q t + 8 q t + 5 q t + 7 q t +
t t
12 3 12 4 14 4 14 5 16 5 16 6
> 7 q t + 7 q t + 7 q t + 6 q t + 7 q t + 4 q t +
18 6 18 7 20 7 20 8 22 8 24 9
> 6 q t + 2 q t + 4 q t + q t + 2 q t + q t |