PD Presentation: |
X10,1,11,2 X2,11,3,12 X12,3,13,4 X6,9,7,10 X16,7,17,8 X8,15,1,16 X20,13,21,14 X18,6,19,5 X4,20,5,19 X22,17,9,18 X14,21,15,22 |
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, 316]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 316]] |
Out[4]= | PD[X[10, 1, 11, 2], X[2, 11, 3, 12], X[12, 3, 13, 4], X[6, 9, 7, 10],
> X[16, 7, 17, 8], X[8, 15, 1, 16], X[20, 13, 21, 14], X[18, 6, 19, 5],
> X[4, 20, 5, 19], X[22, 17, 9, 18], X[14, 21, 15, 22]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -9, 8, -4, 5, -6},
> {4, -1, 2, -3, 7, -11, 6, -5, 10, -8, 9, -7, 11, -10}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(23/2) 3 6 10 14 16 15 14 10 7
q - ----- + ----- - ----- + ----- - ----- + ----- - ---- + ---- - ---- +
21/2 19/2 17/2 15/2 13/2 11/2 9/2 7/2 5/2
q q q q q q q q q
3 1
> ---- - -------
3/2 Sqrt[q]
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -34 -32 -30 -28 -26 3 3 2 4 -14 4 -10
-q + q - q - q + q - --- + --- + --- + --- - q + --- - q +
24 22 18 16 12
q q q q q
-8 -6 -4 -2
> q + q - q + q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 316]][a, z] |
Out[8]= | 5 7 9
-2 a 3 a a 3 5 7 9 3 3 7 3
----- + ---- - -- - 2 a z - 4 a z + 6 a z - 2 a z - 3 a z + 6 a z -
z z z
9 3 3 5 5 5 7 5 9 5 5 7 7 7
> 3 a z - a z + 3 a z + 4 a z - a z + a z + a z |
In[9]:= | Kauffman[Link[11, Alternating, 316]][a, z] |
Out[9]= | 5 7 9
6 8 10 2 a 3 a a 3 5 7 9
-3 a - 3 a - a + ---- + ---- + -- + 2 a z - 6 a z - 11 a z - a z +
z z z
11 4 2 6 2 8 2 10 2 12 2 14 2
> 2 a z + 3 a z + 13 a z + 18 a z + 6 a z - a z + a z -
3 3 5 3 7 3 9 3 11 3 13 3 4 4
> 5 a z + 7 a z + 22 a z - a z - 8 a z + 3 a z - 11 a z -
6 4 8 4 10 4 12 4 14 4 3 5 5 5
> 26 a z - 39 a z - 18 a z + 5 a z - a z + 4 a z - 11 a z -
7 5 9 5 11 5 13 5 4 6 6 6
> 35 a z - 6 a z + 11 a z - 3 a z + 11 a z + 21 a z +
8 6 10 6 12 6 3 7 5 7 7 7 9 7
> 33 a z + 18 a z - 5 a z - a z + 13 a z + 33 a z + 12 a z -
11 7 4 8 6 8 8 8 10 8 5 9 7 9
> 7 a z - 3 a z - a z - 6 a z - 8 a z - 4 a z - 10 a z -
9 9 6 10 8 10
> 6 a z - 2 a z - 2 a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 5 1 2 1 4 2 6 4
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
6 4 24 9 22 8 20 8 20 7 18 7 18 6 16 6
q q q t q t q t q t q t q t q t
8 6 8 9 8 7 6 8
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ----- +
16 5 14 5 14 4 12 4 12 3 10 3 10 2 8 2
q t q t q t q t q t q t q t q t
4 6 t 2 t 2
> ---- + ---- + -- + --- + t
8 6 4 2
q t q t q q |