PD Presentation: |
X10,1,11,2 X12,3,13,4 X22,20,9,19 X18,7,19,8 X16,5,17,6 X4,15,5,16 X6,17,7,18 X14,22,15,21 X20,14,21,13 X2,9,3,10 X8,11,1,12 |
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, 294]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 294]] |
Out[4]= | PD[X[10, 1, 11, 2], X[12, 3, 13, 4], X[22, 20, 9, 19], X[18, 7, 19, 8],
> X[16, 5, 17, 6], X[4, 15, 5, 16], X[6, 17, 7, 18], X[14, 22, 15, 21],
> X[20, 14, 21, 13], X[2, 9, 3, 10], X[8, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -6, 5, -7, 4, -11},
> {10, -1, 11, -2, 9, -8, 6, -5, 7, -4, 3, -9, 8, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(19/2) 2 5 8 11 12 13 11 8
-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
5 3/2
> ------- - 3 Sqrt[q] + q
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -28 2 2 3 -16 2 -12 -10 2 3 -4 2 4
q + --- + --- + --- - q + --- + q - q + -- - -- + q + q - q
24 22 18 14 8 6
q q q q q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 294]][a, z] |
Out[8]= | 3 5 7
a 3 a 2 a 5 7 3 3 3 5 3
-- - ---- + ---- + a z - 10 a z + 5 a z + 3 a z - 4 a z - 10 a z +
z z z
7 3 5 3 5 5 5 7 5 3 7 5 7
> 4 a z + a z - 4 a z - 5 a z + a z - a z - a z |
In[9]:= | Kauffman[Link[11, Alternating, 294]][a, z] |
Out[9]= | 3 5 7
2 4 6 a 3 a 2 a 3 5 7
-a - 3 a - 3 a + -- + ---- + ---- + a z - a z - 16 a z - 10 a z +
z z z
9 11 2 2 2 4 2 6 2 8 2 10 2
> 2 a z - 2 a z - z + 4 a z + 20 a z + 18 a z + 2 a z - a z -
3 3 3 5 3 7 3 9 3 11 3 4
> 7 a z - a z + 34 a z + 21 a z - 4 a z + 3 a z + 3 z -
2 4 4 4 6 4 8 4 10 4 5 3 5
> 11 a z - 36 a z - 30 a z - 4 a z + 4 a z + 10 a z - 2 a z -
5 5 7 5 9 5 11 5 6 2 6 4 6
> 39 a z - 20 a z + 6 a z - a z - z + 13 a z + 23 a z +
6 6 8 6 10 6 7 3 7 5 7 7 7
> 16 a z + 5 a z - 2 a z - 3 a z + 7 a z + 22 a z + 9 a z -
9 7 2 8 4 8 6 8 8 8 3 9 5 9
> 3 a z - 4 a z - 4 a z - 3 a z - 3 a z - 3 a z - 6 a z -
7 9 4 10 6 10
> 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 4 5 1 1 2 3 2 5 3
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 2 20 8 18 8 18 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
6 5 6 6 7 6 4 7
> ------ + ------ + ------ + ----- + ----- + ----- + ---- + ---- + 3 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
2 t 2 2 2 4 3
> --- + t + 2 q t + q t
2
q |