PD Presentation: |
X12,1,13,2 X16,8,17,7 X10,5,1,6 X6374 X4,9,5,10 X13,18,14,19 X19,22,20,11 X15,21,16,20 X21,15,22,14 X2,11,3,12 X8,18,9,17 |
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, NonAlternating, 242]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 242]] |
Out[4]= | PD[X[12, 1, 13, 2], X[16, 8, 17, 7], X[10, 5, 1, 6], X[6, 3, 7, 4],
> X[4, 9, 5, 10], X[13, 18, 14, 19], X[19, 22, 20, 11], X[15, 21, 16, 20],
> X[21, 15, 22, 14], X[2, 11, 3, 12], X[8, 18, 9, 17]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 4, -5, 3, -4, 2, -11, 5, -3},
> {10, -1, -6, 9, -8, -2, 11, 6, -7, 8, -9, 7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(15/2) 3 6 9 10 11 10 8
q - ----- + ----- - ---- + ---- - ---- + ---- - ------- + 4 Sqrt[q] -
13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q
3/2
> 2 q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -24 -22 -20 2 2 3 3 2 -4 -2 4 6
4 - q - q + q - --- + --- + --- + --- - -- - q - q + 2 q + 2 q
18 16 14 10 8
q q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 242]][a, z] |
Out[8]= | 3 5 7
-2 5 a 6 a 4 a a 2 z 3 5 7 3
--- + --- - ---- + ---- - -- - --- + 8 a z - 11 a z + 6 a z - a z + 4 a z -
a z z z z z a
3 3 5 3 3 5
> 7 a z + 3 a z - 2 a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 242]][a, z] |
Out[9]= | 3 5 7
2 4 6 8 2 5 a 6 a 4 a a 5 z
1 + a + 3 a + 3 a + a - --- - --- - ---- - ---- - -- + --- + 20 a z +
a z z z z z a
3
3 5 7 2 4 2 6 2 8 2 3 z
> 29 a z + 18 a z + 4 a z + z - 7 a z - 9 a z - 3 a z - ---- -
a
3 3 3 5 3 7 3 4 2 4 4 4
> 26 a z - 50 a z - 35 a z - 8 a z - 2 z - 10 a z - 3 a z +
6 4 8 4 5 3 5 5 5 7 5 6
> 8 a z + 3 a z + 12 a z + 36 a z + 33 a z + 9 a z - z +
2 6 4 6 6 6 8 6 7 3 7 5 7
> 9 a z + 15 a z + 4 a z - a z - 4 a z - 9 a z - 8 a z -
7 7 2 8 4 8 6 8 3 9 5 9
> 3 a z - 4 a z - 7 a z - 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 4 1 2 1 4 2 5 4 5
6 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
2 16 7 14 6 12 6 12 5 10 5 10 4 8 4 8 3
q q t q t q t q t q t q t q t q t
5 6 5 4 6 2 4 2
> ----- + ----- + ----- + ---- + ---- + 2 t + 2 q t + 2 q t
6 3 6 2 4 2 4 2
q t q t q t q t q t |