PD Presentation: |
X6172 X12,3,13,4 X16,8,17,7 X22,18,5,17 X18,9,19,10 X8,21,9,22 X10,14,11,13 X20,15,21,16 X14,19,15,20 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, 70]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 70]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[16, 8, 17, 7], X[22, 18, 5, 17],
> X[18, 9, 19, 10], X[8, 21, 9, 22], X[10, 14, 11, 13], X[20, 15, 21, 16],
> X[14, 19, 15, 20], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -6, 5, -7, 11, -2, 7, -9, 8, -3, 4, -5,
> 9, -8, 6, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(19/2) 3 7 13 19 22 23 20 16
-q + ----- - ----- + ----- - ----- + ---- - ---- + ---- - ---- +
17/2 15/2 13/2 11/2 9/2 7/2 5/2 3/2
q q q q q q q q
10 3/2
> ------- - 5 Sqrt[q] + q
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -30 -28 -26 2 4 3 3 2 3 -10 6 4
-2 + q + q - q + --- - --- + --- - --- + --- + --- - q + -- - -- +
24 20 18 16 14 12 8 6
q q q q q q q q
3 -2 2 4
> -- + q + 3 q - q
4
q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 70]][a, z] |
Out[8]= | 3 5 7 9
-2 a 4 a 3 a a 3 5 7 9 3
----- + ---- - ---- + -- - a z - 4 a z + 8 a z - 6 a z + a z + a z -
z z z z
3 3 5 3 7 3 5 3 5 5 5 3 7
> 4 a z + 8 a z - 3 a z + a z - 3 a z + 3 a z - a z |
In[9]:= | Kauffman[Link[11, Alternating, 70]][a, z] |
Out[9]= | 3 5 7 9
4 6 8 10 2 a 4 a 3 a a 3 5
2 a + 3 a + 3 a + a - ---- - ---- - ---- - -- - a z + 7 a z + 18 a z +
z z z z
7 9 11 2 2 4 2 6 2 8 2 10 2
> 13 a z + 2 a z - a z + a z + 2 a z - 4 a z - 8 a z - 3 a z -
3 3 3 5 3 7 3 9 3 11 3 4
> 4 a z - 15 a z - 30 a z - 24 a z - 3 a z + 2 a z + z -
2 4 4 4 6 4 8 4 10 4 5 3 5
> 10 a z - 26 a z - 16 a z + 4 a z + 5 a z + 10 a z + 15 a z +
5 5 7 5 9 5 11 5 6 2 6 4 6
> 15 a z + 17 a z + 6 a z - a z - z + 20 a z + 42 a z +
6 6 8 6 10 6 7 3 7 5 7 7 7
> 28 a z + 4 a z - 3 a z - 5 a z + 6 a z + 14 a z - 2 a z -
9 7 2 8 4 8 6 8 8 8 3 9 5 9
> 5 a z - 9 a z - 15 a z - 12 a z - 6 a z - 7 a z - 12 a z -
7 9 4 10 6 10
> 5 a z - 2 a z - 2 a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 7 10 1 2 1 5 2 8 5
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 2 20 8 18 7 16 7 16 6 14 6 14 5 12 5
q q q t q t q t q t q t q t q t
11 9 12 10 11 12 9 11
> ------ + ------ + ------ + ----- + ----- + ----- + ---- + ---- + 6 t +
12 4 10 4 10 3 8 3 8 2 6 2 6 4
q t q t q t q t q t q t q t q t
4 t 2 2 2 4 3
> --- + t + 4 q t + q t
2
q |