PD Presentation: |
X6172 X12,3,13,4 X20,15,21,16 X16,7,17,8 X8,19,9,20 X18,9,19,10 X10,17,11,18 X22,13,5,14 X14,21,15,22 X2536 X4,11,1,12 |
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, 76]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 76]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[20, 15, 21, 16], X[16, 7, 17, 8],
> X[8, 19, 9, 20], X[18, 9, 19, 10], X[10, 17, 11, 18], X[22, 13, 5, 14],
> X[14, 21, 15, 22], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 4, -5, 6, -7, 11, -2, 8, -9, 3, -4, 7, -6,
> 5, -3, 9, -8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(25/2) 2 5 7 9 12 11 11 8
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
6 3 -(3/2)
> ---- + ---- - q
7/2 5/2
q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -40 2 2 3 2 2 5 2 3 -16 2 2
-q - --- - --- - --- + --- + --- + --- + --- + --- + q + --- - --- +
38 34 32 30 26 24 22 20 14 12
q q q q q q q q q q
2 -8 2 -4
> --- + q - -- + q
10 6
q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 76]][a, z] |
Out[8]= | 7 9 11 13
-2 a 2 a a a 5 7 9 11 3 3 5 3
----- + ---- + --- - --- - 2 a z - 4 a z + a z + 3 a z - a z - 3 a z -
z z z z
7 3 9 3
> 4 a z - 2 a z |
In[9]:= | Kauffman[Link[11, Alternating, 76]][a, z] |
Out[9]= | 7 9 11 13
8 10 12 14 2 a 2 a a a 5 7
2 a - 4 a - 9 a - 4 a - ---- - ---- + --- + --- - 2 a z + 7 a z +
z z z z
9 11 6 2 8 2 10 2 12 2 14 2
> 12 a z + 3 a z - 2 a z - 5 a z + 19 a z + 34 a z + 12 a z -
3 3 5 3 7 3 9 3 11 3 13 3 4 4
> a z + 5 a z - 11 a z - 26 a z - 3 a z + 6 a z - 3 a z +
6 4 8 4 10 4 12 4 14 4 5 5
> 10 a z + 2 a z - 46 a z - 48 a z - 13 a z - 6 a z +
7 5 9 5 11 5 13 5 6 6 8 6
> 18 a z + 19 a z - 20 a z - 15 a z - 8 a z + 13 a z +
10 6 12 6 14 6 7 7 9 7 11 7
> 38 a z + 23 a z + 6 a z - 9 a z + 4 a z + 23 a z +
13 7 8 8 10 8 12 8 14 8 9 9 11 9
> 10 a z - 7 a z - 7 a z - a z - a z - 4 a z - 6 a z -
13 9 10 10 12 10
> 2 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -4 -2 1 1 1 4 1 3 4
q + q + ------- + ------- + ------- + ------ + ------ + ------ + ------ +
26 11 24 10 22 10 22 9 20 9 20 8 18 8
q t q t q t q t q t q t q t
6 3 6 6 5 6 6 6
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
18 7 16 7 16 6 14 6 14 5 12 5 12 4 10 4
q t q t q t q t q t q t q t q t
3 5 3 3 3
> ------ + ----- + ----- + ----- + ----
10 3 8 3 8 2 6 2 4
q t q t q t q t q t |