PD Presentation: |
X10,1,11,2 X2,11,3,12 X12,3,13,4 X14,5,15,6 X18,7,19,8 X22,20,9,19 X20,16,21,15 X16,22,17,21 X8,9,1,10 X4,13,5,14 X6,17,7,18 |
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, 276]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 276]] |
Out[4]= | PD[X[10, 1, 11, 2], X[2, 11, 3, 12], X[12, 3, 13, 4], X[14, 5, 15, 6],
> X[18, 7, 19, 8], X[22, 20, 9, 19], X[20, 16, 21, 15], X[16, 22, 17, 21],
> X[8, 9, 1, 10], X[4, 13, 5, 14], X[6, 17, 7, 18]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -10, 4, -11, 5, -9},
> {9, -1, 2, -3, 10, -4, 7, -8, 11, -5, 6, -7, 8, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(21/2) 2 4 5 6 7 7 5 5 3
-q + ----- - ----- + ----- - ----- + ----- - ---- + ---- - ---- + ---- -
19/2 17/2 15/2 13/2 11/2 9/2 7/2 5/2 3/2
q q q q q q q q q
2
> ------- + Sqrt[q]
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -30 2 -24 -22 -18 2 3 -10 -8 -4
-1 + q + --- + q + q - q + --- + --- + q + q - q
26 16 12
q q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 276]][a, z] |
Out[8]= | 3 5 7
a 3 a 2 a 3 5 7 3 3 5 3
-- - ---- + ---- + 7 a z - 21 a z + 10 a z + 11 a z - 34 a z +
z z z
7 3 3 5 5 5 7 5 3 7 5 7 7 7 5 9
> 12 a z + 6 a z - 24 a z + 6 a z + a z - 8 a z + a z - a z |
In[9]:= | Kauffman[Link[11, Alternating, 276]][a, z] |
Out[9]= | 3 5 7
2 4 6 a 3 a 2 a 3 5 7 9
-a - 3 a - 3 a + -- + ---- + ---- - 7 a z - 23 a z - 12 a z + a z -
z z z
11 13 2 2 4 2 6 2 8 2 10 2
> 2 a z + a z + 7 a z + 20 a z + 19 a z + 4 a z - a z +
12 2 3 3 5 3 7 3 9 3 11 3 13 3
> a z + 18 a z + 48 a z + 24 a z - 2 a z + 3 a z - a z -
2 4 4 4 6 4 8 4 10 4 12 4 3 5
> 11 a z - 30 a z - 30 a z - 6 a z + 3 a z - 2 a z - 23 a z -
5 5 7 5 9 5 11 5 2 6 4 6 6 6
> 53 a z - 22 a z + 5 a z - 3 a z + 6 a z + 11 a z + 16 a z +
8 6 10 6 3 7 5 7 7 7 9 7 2 8
> 8 a z - 3 a z + 12 a z + 28 a z + 13 a z - 3 a z - a z +
4 8 8 8 3 9 5 9 7 9 4 10 6 10
> 2 a z - 3 a z - 2 a z - 5 a z - 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 3 1 1 2 2 2 3 2
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
6 4 22 8 20 8 20 7 18 6 16 6 16 5 14 5
q q q t q t q t q t q t q t q t
3 3 4 3 3 4 2 3 t
> ------ + ------ + ------ + ------ + ------ + ----- + ---- + ---- + -- +
14 4 12 4 12 3 10 3 10 2 8 2 8 6 4
q t q t q t q t q t q t q t q t q
2
2 t 2 t 2 3
> --- + t + -- + q t
2 2
q q |