PD Presentation: |
X6172 X10,3,11,4 X18,11,19,12 X16,7,17,8 X8,17,9,18 X20,13,21,14 X22,15,5,16 X12,19,13,20 X14,21,15,22 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, 33]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 33]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 3, 11, 4], X[18, 11, 19, 12], X[16, 7, 17, 8],
> X[8, 17, 9, 18], X[20, 13, 21, 14], X[22, 15, 5, 16], X[12, 19, 13, 20],
> X[14, 21, 15, 22], 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, -8, 6, -9, 7, -4, 5, -3,
> 8, -6, 9, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(29/2) 2 5 7 9 11 10 9 6
q - ----- + ----- - ----- + ----- - ----- + ----- - ----- + ----- -
27/2 25/2 23/2 21/2 19/2 17/2 15/2 13/2
q q q q q q q q
5 2 -(7/2)
> ----- + ---- - q
11/2 9/2
q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -44 2 -40 3 -36 -34 -32 4 -28 5 -24 2
-q - --- - q - --- - q - q + q + --- + q + --- + q + --- +
42 38 30 26 22
q q q q q
2 2 -14 -12
> --- + --- - q + q
20 16
q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 33]][a, z] |
Out[8]= | 9 11 13
-4 a 7 a 3 a 7 9 11 13 7 3
----- + ----- - ----- - 3 a z - 13 a z + 18 a z - 4 a z - 7 a z -
z z z
9 3 11 3 13 3 7 5 9 5 11 5 7 7
> 19 a z + 14 a z - a z - 5 a z - 11 a z + 3 a z - a z -
9 7
> 2 a z |
In[9]:= | Kauffman[Link[11, Alternating, 33]][a, z] |
Out[9]= | 9 11 13
10 12 18 4 a 7 a 3 a 7 9 11
-7 a - 7 a - a + ---- + ----- + ----- + 3 a z - 16 a z - 31 a z -
z z z
13 8 2 10 2 12 2 14 2 16 2 18 2
> 12 a z + a z + 26 a z + 29 a z + a z - a z + 2 a z -
7 3 9 3 11 3 13 3 17 3 8 4
> 7 a z + 24 a z + 53 a z + 20 a z + 2 a z - 7 a z -
10 4 12 4 14 4 16 4 18 4 7 5 9 5
> 39 a z - 39 a z - 3 a z + 3 a z - a z + 5 a z - 23 a z -
11 5 13 5 15 5 17 5 8 6 10 6
> 49 a z - 17 a z + 2 a z - 2 a z + 8 a z + 23 a z +
12 6 14 6 16 6 7 7 9 7 11 7 13 7
> 22 a z + 4 a z - 3 a z - a z + 14 a z + 27 a z + 9 a z -
15 7 8 8 10 8 12 8 14 8 9 9 11 9
> 3 a z - 2 a z - 2 a z - 3 a z - 3 a z - 3 a z - 6 a z -
13 9 10 10 12 10
> 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -8 -6 1 1 1 4 1 3 4
q + q + ------- + ------- + ------- + ------ + ------ + ------ + ------ +
30 11 28 10 26 10 26 9 24 9 24 8 22 8
q t q t q t q t q t q t q t
6 3 5 6 5 5 4 6
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
22 7 20 7 20 6 18 6 18 5 16 5 16 4 14 4
q t q t q t q t q t q t q t q t
3 3 2 3 2
> ------ + ------ + ------ + ------ + ----
14 3 12 3 12 2 10 2 8
q t q t q t q t q t |