PD Presentation: |
X6172 X14,3,15,4 X22,15,5,16 X16,7,17,8 X8,21,9,22 X20,11,21,12 X18,9,19,10 X10,19,11,20 X12,17,13,18 X2536 X4,13,1,14 |
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, 109]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 109]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 3, 15, 4], X[22, 15, 5, 16], X[16, 7, 17, 8],
> X[8, 21, 9, 22], X[20, 11, 21, 12], X[18, 9, 19, 10], X[10, 19, 11, 20],
> X[12, 17, 13, 18], X[2, 5, 3, 6], X[4, 13, 1, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 4, -5, 7, -8, 6, -9, 11, -2, 3, -4, 9, -7,
> 8, -6, 5, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(27/2) 3 7 11 15 17 17 16 10
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
7 3 -(5/2)
> ---- + ---- - q
9/2 7/2
q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -42 -40 -38 3 -34 -32 3 3 2 4 6 2
-q - q + q - --- - q + q - --- + --- + --- + --- + --- + --- -
36 30 28 24 22 18 12
q q q q q q q
2 -8
> --- + q
10
q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 109]][a, z] |
Out[8]= | 7 9 11 13
-2 a 2 a a a 7 9 11 13 5 3
----- + ---- + --- - --- - 8 a z + 2 a z + 5 a z - a z - 2 a z -
z z z z
7 3 9 3 11 3 5 5 7 5 9 5
> 9 a z - 3 a z + 3 a z - a z - 3 a z - 2 a z |
In[9]:= | Kauffman[Link[11, Alternating, 109]][a, z] |
Out[9]= | 7 9 11 13
8 12 16 2 a 2 a a a 7 9 11
3 a - 3 a + a - ---- - ---- + --- + --- + 8 a z + 6 a z - 3 a z +
z z z z
15 8 2 10 2 12 2 14 2 16 2 5 3
> a z - 3 a z + 10 a z + 13 a z - 3 a z - 3 a z + 2 a z -
7 3 9 3 11 3 13 3 15 3 6 4 8 4
> 16 a z - 14 a z + 4 a z - 6 a z - 6 a z + 5 a z - 7 a z -
10 4 12 4 14 4 16 4 5 5 7 5 9 5
> 30 a z - 20 a z + a z + 3 a z - a z + 15 a z + 7 a z -
11 5 13 5 15 5 6 6 8 6 10 6
> 6 a z + 11 a z + 8 a z - 3 a z + 11 a z + 28 a z +
12 6 14 6 16 6 7 7 9 7 11 7 15 7
> 22 a z + 7 a z - a z - 6 a z + 2 a z + 11 a z - 3 a z -
8 8 10 8 12 8 14 8 9 9 11 9 13 9
> 6 a z - 10 a z - 8 a z - 4 a z - 4 a z - 7 a z - 3 a z -
10 10 12 10
> a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -6 -4 1 2 1 5 2 6 5
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
9 6 8 9 9 8 7 10
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
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
4 6 3 4 3
> ------ + ------ + ------ + ----- + ----
12 3 10 3 10 2 8 2 6
q t q t q t q t q t |