PD Presentation: |
X12,1,13,2 X14,4,15,3 X22,14,11,13 X16,6,17,5 X2,11,3,12 X4,16,5,15 X6,22,7,21 X20,10,21,9 X18,8,19,7 X8,20,9,19 X10,18,1,17 |
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, 361]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 361]] |
Out[4]= | PD[X[12, 1, 13, 2], X[14, 4, 15, 3], X[22, 14, 11, 13], X[16, 6, 17, 5],
> X[2, 11, 3, 12], X[4, 16, 5, 15], X[6, 22, 7, 21], X[20, 10, 21, 9],
> X[18, 8, 19, 7], X[8, 20, 9, 19], X[10, 18, 1, 17]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -5, 2, -6, 4, -7, 9, -10, 8, -11},
> {5, -1, 3, -2, 6, -4, 11, -9, 10, -8, 7, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | 3/2 5/2 7/2 9/2 11/2 13/2
-Sqrt[q] + 2 q - 5 q + 8 q - 11 q + 13 q - 14 q +
15/2 17/2 19/2 21/2 23/2
> 12 q - 10 q + 6 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | 2 6 8 10 12 14 16 18 22 24 26
q + q + q - 2 q + 2 q - 2 q + 2 q + 2 q + 4 q - q + 2 q -
30 32 34
> q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 361]][a, z] |
Out[8]= | 3 3 3 3 5 5
1 1 2 z 3 z 4 z 3 z 5 z 4 z 4 z z 4 z
-(----) + ---- + --- - --- + --- + ---- - ---- - ---- + ---- + -- - ---- -
7 5 9 7 3 9 7 5 3 9 7
a z a z a a a a a a a a a
5 5 7 7
4 z z z z
> ---- + -- - -- - --
5 3 7 5
a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 361]][a, z] |
Out[9]= | 2 2 2 2
-6 1 1 z 2 z 5 z 2 z 4 z z 2 z 3 z 2 z
-a + ---- + ---- - --- + --- - --- - --- + --- + --- - ---- - ---- - ---- +
7 5 13 9 7 5 3 14 12 10 8
a z a z a a a a a a a a a
2 3 3 3 3 3 3 4 4 4 4
2 z 3 z 4 z 3 z 9 z 3 z 8 z z 5 z 2 z z
> ---- + ---- - ---- - ---- + ---- - ---- - ---- - --- + ---- + ---- + -- -
4 13 11 9 7 5 3 14 12 10 8
a a a a a a a a a a a
4 4 5 5 5 5 5 6 6 6
4 z 9 z 3 z 7 z 6 z 9 z 5 z 5 z 4 z 9 z
> ---- - ---- - ---- + ---- + ---- - ---- + ---- - ---- + ---- + ---- +
6 4 13 11 9 7 3 12 10 8
a a a a a a a a a a
6 6 7 7 7 7 8 8 8 8 9
8 z 8 z 6 z 12 z 5 z z 5 z 4 z z 2 z 3 z
> ---- + ---- - ---- + ----- + ---- - -- - ---- - ---- - -- - ---- - ---- -
6 4 11 7 5 3 10 8 6 4 9
a a a a a a a a a a a
9 9 10 10
5 z 2 z z z
> ---- - ---- - --- - ---
7 5 8 6
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
4 q + 2 q + t + -- + -- + 5 q t + 3 q t + 6 q t + 5 q t + 7 q t +
t t
12 3 12 4 14 4 14 5 16 5 16 6
> 6 q t + 7 q t + 7 q t + 5 q t + 7 q t + 5 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 |