PD Presentation: |
X8192 X2,11,3,12 X12,3,13,4 X16,5,17,6 X18,13,19,14 X14,17,15,18 X6718 X4,15,5,16 X22,20,7,19 X20,10,21,9 X10,22,11,21 |
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, 230]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 230]] |
Out[4]= | PD[X[8, 1, 9, 2], X[2, 11, 3, 12], X[12, 3, 13, 4], X[16, 5, 17, 6],
> X[18, 13, 19, 14], X[14, 17, 15, 18], X[6, 7, 1, 8], X[4, 15, 5, 16],
> X[22, 20, 7, 19], X[20, 10, 21, 9], X[10, 22, 11, 21]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -8, 4, -7},
> {7, -1, 10, -11, 2, -3, 5, -6, 8, -4, 6, -5, 9, -10, 11, -9}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(19/2) 3 7 12 16 18 19 15 12
-q + ----- - ----- + ----- - ----- + ---- - ---- + ---- - ---- +
17/2 15/2 13/2 11/2 9/2 7/2 5/2 3/2
q q q q q q q q
7 3/2
> ------- - 3 Sqrt[q] + q
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -28 -26 2 3 3 2 4 3 -10 5 3 2
-2 + q - q + --- - --- + --- - --- + --- + --- + q + -- - -- + -- -
24 20 18 16 14 12 8 6 4
q q q q q q q q q
-2 2 4
> q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 230]][a, z] |
Out[8]= | 3 5
a 3 a 2 a 3 5 7 3 3 3
- - ---- + ---- + 3 a z - 7 a z - 2 a z + 3 a z + 3 a z - 7 a z -
z z z
5 3 7 3 5 3 5 5 5 7 5 3 7 5 7
> 6 a z + 3 a z + a z - 4 a z - 4 a z + a z - a z - a z |
In[9]:= | Kauffman[Link[11, Alternating, 230]][a, z] |
Out[9]= | 3 5
2 4 a 3 a 2 a 3 5 7 9
1 + 3 a + 3 a - - - ---- - ---- + 3 a z + 10 a z + 4 a z - a z + a z -
z z z
11 2 2 2 4 2 6 2 8 2 10 2 3
> a z - 3 z - 8 a z - 2 a z + 9 a z + 4 a z - 2 a z - 7 a z -
3 3 5 3 7 3 9 3 11 3 4 2 4
> 18 a z - 10 a z - 4 a z - 3 a z + 2 a z + 3 z + 4 a z -
4 4 6 4 8 4 10 4 5 3 5 5 5
> 10 a z - 24 a z - 8 a z + 5 a z + 8 a z + 18 a z + 8 a z +
7 5 9 5 11 5 6 2 6 4 6 6 6 8 6
> 6 a z + 7 a z - a z - z + 6 a z + 21 a z + 26 a z + 9 a z -
10 6 7 3 7 5 7 9 7 2 8 4 8
> 3 a z - 3 a z - 2 a z + 6 a z - 5 a z - 4 a z - 9 a z -
6 8 8 8 3 9 5 9 7 9 4 10 6 10
> 11 a z - 6 a z - 3 a z - 7 a z - 4 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 6 7 1 2 1 5 3 8 4
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 2 20 8 18 7 16 7 16 6 14 6 14 5 12 5
q q q t q t q t q t q t q t q t
8 8 10 8 9 10 6 9
> ------ + ------ + ------ + ----- + ----- + ----- + ---- + ---- + 5 t +
12 4 10 4 10 3 8 3 8 2 6 2 6 4
q t q t q t q t q t q t q t q t
2 t 2 2 2 4 3
> --- + t + 2 q t + q t
2
q |