PD Presentation: |
X8192 X2,9,3,10 X10,3,11,4 X6718 X18,11,19,12 X16,6,17,5 X4,18,5,17 X20,13,21,14 X22,15,7,16 X12,19,13,20 X14,21,15,22 |
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, 202]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 202]] |
Out[4]= | PD[X[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[6, 7, 1, 8],
> X[18, 11, 19, 12], X[16, 6, 17, 5], X[4, 18, 5, 17], X[20, 13, 21, 14],
> X[22, 15, 7, 16], X[12, 19, 13, 20], X[14, 21, 15, 22]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -7, 6, -4},
> {4, -1, 2, -3, 5, -10, 8, -11, 9, -6, 7, -5, 10, -8, 11, -9}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(25/2) 2 3 4 5 5 5 5 3
q - ----- + ----- - ----- + ----- - ----- + ----- - ----- + ---- -
23/2 21/2 19/2 17/2 15/2 13/2 11/2 9/2
q q q q q q q q
3 -(5/2) -(3/2)
> ---- + q - q
7/2
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -36 -32 -28 -26 -22 2 -18 3 2 2 2 -8
-q - q - q - q - q + --- + q + --- + --- + --- + --- + q +
20 16 14 12 10
q q q q q
-6
> q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 202]][a, z] |
Out[8]= | 5 7 9
-3 a 5 a 2 a 5 7 9 5 3 7 3
----- + ---- - ---- - 13 a z + 19 a z - 7 a z - 16 a z + 30 a z -
z z z
9 3 5 5 7 5 9 5 5 7 7 7 9 7 7 9
> 11 a z - 7 a z + 23 a z - 6 a z - a z + 8 a z - a z + a z |
In[9]:= | Kauffman[Link[11, Alternating, 202]][a, z] |
Out[9]= | 5 7 9
6 8 12 3 a 5 a 2 a 5 7 9
-5 a - 5 a + a + ---- + ---- + ---- - 16 a z - 25 a z - 6 a z +
z z z
11 6 2 8 2 10 2 12 2 14 2 16 2
> 3 a z + 14 a z + 22 a z - a z - 6 a z + 2 a z - a z +
5 3 7 3 9 3 11 3 13 3 15 3 6 4
> 29 a z + 59 a z + 9 a z - 13 a z + 6 a z - 2 a z - 4 a z -
8 4 10 4 12 4 14 4 5 5 7 5
> 31 a z - 11 a z + 13 a z - 3 a z - 23 a z - 62 a z -
9 5 11 5 13 5 6 6 8 6 10 6
> 18 a z + 17 a z - 4 a z - 9 a z + 11 a z + 15 a z -
12 6 5 7 7 7 9 7 11 7 6 8 8 8
> 5 a z + 8 a z + 27 a z + 14 a z - 5 a z + 6 a z + 2 a z -
10 8 5 9 7 9 9 9 6 10 8 10
> 4 a z - a z - 4 a z - 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -8 3 1 1 1 2 1 2 2
q + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
6 26 9 24 8 22 8 22 7 20 7 20 6 18 6
q q t q t q t q t q t q t q t
3 2 2 3 3 2 2 4
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
18 5 16 5 16 4 14 4 14 3 12 3 12 2 10 2
q t q t q t q t q t q t q t q t
2
2 1 t t
> ----- + ---- + -- + --
10 8 6 2
q t q t q q |