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