PD Presentation: |
X8192 X2,9,3,10 X10,3,11,4 X20,12,21,11 X14,6,15,5 X4,21,5,22 X16,7,17,8 X22,15,7,16 X18,14,19,13 X6,18,1,17 X12,20,13,19 |
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, 175]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 175]] |
Out[4]= | PD[X[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[20, 12, 21, 11],
> X[14, 6, 15, 5], X[4, 21, 5, 22], X[16, 7, 17, 8], X[22, 15, 7, 16],
> X[18, 14, 19, 13], X[6, 18, 1, 17], X[12, 20, 13, 19]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -6, 5, -10},
> {7, -1, 2, -3, 4, -11, 9, -5, 8, -7, 10, -9, 11, -4, 6, -8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(15/2) 3 6 9 12 13 13 11
-q + ----- - ----- + ---- - ---- + ---- - ---- + ------- - 9 Sqrt[q] +
13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q
3/2 5/2 7/2
> 5 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -22 -20 -18 -16 3 2 -8 -6 -4 3 2 4 8
q - q + q + q + --- - --- + q - q - q + -- + 3 q + q + q -
12 10 2
q q q
10
> q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 175]][a, z] |
Out[8]= | 3 5 3
1 2 a 2 a a z 3 5 3 z 3 3 3
-(---) + --- - ---- + -- + - - 4 a z + 2 a z + ---- - 4 a z - 5 a z +
a z z z z a a
5
5 3 z 5 3 5 5 5 7 3 7
> 3 a z + -- - 4 a z - 4 a z + a z - a z - a z
a |
In[9]:= | Kauffman[Link[11, Alternating, 175]][a, z] |
Out[9]= | 3 5
2 1 2 a 2 a a z 3 5 7 2
-a - --- - --- - ---- - -- - - + 4 a z + 10 a z + 4 a z - a z + 10 z +
a z z z z a
2 3
4 z 2 2 4 2 6 2 17 z 3 3 3
> ---- + 13 a z + 4 a z - 3 a z + ----- + 12 a z - 22 a z -
2 a
a
4
5 3 7 3 9 3 4 8 z 2 4 4 4
> 12 a z + 4 a z - a z - 22 z - ---- - 43 a z - 14 a z +
2
a
5
6 4 8 4 28 z 5 3 5 5 5 7 5
> 12 a z - 3 a z - ----- - 45 a z + 12 a z + 23 a z - 6 a z +
a
6 7
6 5 z 2 6 4 6 6 6 16 z 7 3 7
> 7 z + ---- + 36 a z + 25 a z - 9 a z + ----- + 38 a z + 11 a z -
2 a
a
8 9
5 7 8 z 2 8 4 8 3 z 9 3 9
> 11 a z + 5 z - -- - 4 a z - 10 a z - ---- - 9 a z - 6 a z -
2 a
a
10 2 10
> 2 z - 2 a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 6 8 1 2 1 4 2 5 4 7
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
4 2 16 6 14 5 12 5 12 4 10 4 10 3 8 3 8 2
q q q t q t q t q t q t q t q t q t
6 7 6 6 t 2 2 2 2 3 4 3
> ----- + ---- + ---- + 5 t + --- + 3 t + 6 q t + 2 q t + 3 q t +
6 2 6 4 2
q t q t q t q
4 4 6 4 8 5
> q t + 2 q t + q t |