PD Presentation: |
X6172 X10,3,11,4 X16,11,17,12 X14,7,15,8 X8,15,9,16 X20,13,21,14 X22,17,5,18 X18,21,19,22 X12,19,13,20 X2536 X4,9,1,10 |
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, 23]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 23]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 3, 11, 4], X[16, 11, 17, 12], X[14, 7, 15, 8],
> X[8, 15, 9, 16], X[20, 13, 21, 14], X[22, 17, 5, 18], X[18, 21, 19, 22],
> X[12, 19, 13, 20], X[2, 5, 3, 6], X[4, 9, 1, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 4, -5, 11, -2, 3, -9, 6, -4, 5, -3, 7, -8,
> 9, -6, 8, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(27/2) 3 8 13 17 20 20 18 12
q - ----- + ----- - ----- + ----- - ----- + ----- - ----- + ----- -
25/2 23/2 21/2 19/2 17/2 15/2 13/2 11/2
q q q q q q q q
8 3 -(5/2)
> ---- + ---- - q
9/2 7/2
q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -42 -40 -38 4 -34 2 3 4 2 4 -20 6
-q - q + q - --- - q + --- - --- + --- + --- + --- - q + --- -
36 32 30 28 24 22 18
q q q q q q q
-16 3 2 -8
> q + --- - --- + q
12 10
q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 23]][a, z] |
Out[8]= | 7 9 11 13
-2 a 2 a a a 5 7 9 11 13 5 3
----- + ---- + --- - --- - a z - 7 a z + 3 a z + 4 a z - a z - 2 a z -
z z z z
7 3 9 3 11 3 5 5 7 5 9 5
> 8 a z - 2 a z + 3 a z - a z - 3 a z - 2 a z |
In[9]:= | Kauffman[Link[11, Alternating, 23]][a, z] |
Out[9]= | 7 9 11 13
8 12 16 2 a 2 a a a 5 7 9
3 a - 3 a + a - ---- - ---- + --- + --- - a z + 8 a z + 8 a z -
z z z z
11 13 15 6 2 8 2 10 2 12 2 14 2
> 3 a z - a z + a z - a z - 8 a z + 3 a z + 14 a z + a z -
16 2 5 3 7 3 9 3 11 3 13 3 15 3
> 3 a z + 2 a z - 12 a z - 18 a z - 5 a z - 6 a z - 5 a z +
6 4 8 4 10 4 12 4 14 4 16 4 5 5
> 4 a z + 5 a z - 20 a z - 29 a z - 5 a z + 3 a z - a z +
7 5 9 5 11 5 13 5 15 5 6 6
> 11 a z + 19 a z + 11 a z + 11 a z + 7 a z - 3 a z +
8 6 10 6 12 6 14 6 16 6 7 7 9 7
> 4 a z + 30 a z + 34 a z + 10 a z - a z - 6 a z - 5 a z +
11 7 13 7 15 7 8 8 10 8 12 8 14 8
> 5 a z + a z - 3 a z - 6 a z - 14 a z - 13 a z - 5 a z -
9 9 11 9 13 9 10 10 12 10
> 4 a z - 8 a z - 4 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -6 -4 1 2 1 6 2 7 6
q + q + ------- + ------- + ------- + ------ + ------ + ------ + ------ +
28 11 26 10 24 10 24 9 22 9 22 8 20 8
q t q t q t q t q t q t q t
10 7 10 10 10 10 8 11
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
20 7 18 7 18 6 16 6 16 5 14 5 14 4 12 4
q t q t q t q t q t q t q t q t
5 7 3 5 3
> ------ + ------ + ------ + ----- + ----
12 3 10 3 10 2 8 2 6
q t q t q t q t q t |