PD Presentation: |
X6172 X14,4,15,3 X18,8,19,7 X22,12,5,11 X8,22,9,21 X20,10,21,9 X10,20,11,19 X16,14,17,13 X12,18,13,17 X2536 X4,16,1,15 |
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, 126]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 126]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 4, 15, 3], X[18, 8, 19, 7], X[22, 12, 5, 11],
> X[8, 22, 9, 21], X[20, 10, 21, 9], X[10, 20, 11, 19], X[16, 14, 17, 13],
> X[12, 18, 13, 17], X[2, 5, 3, 6], X[4, 16, 1, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -5, 6, -7, 4, -9, 8, -2, 11, -8, 9, -3,
> 7, -6, 5, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | 1 3/2 5/2 7/2 9/2 11/2
-(-------) + 2 Sqrt[q] - 6 q + 9 q - 14 q + 15 q - 15 q +
Sqrt[q]
13/2 15/2 17/2 19/2 21/2
> 14 q - 10 q + 6 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -2 2 4 6 8 10 14 16 20 22 24
q + q + 4 q - q + 4 q + 3 q + 3 q - 3 q - 2 q - 2 q + 3 q -
26 30 32
> 2 q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 126]][a, z] |
Out[8]= | 3 3 3 3 3 5 5 5
1 2 1 z 3 z 2 z z z 4 z z z z 2 z z
---- - ---- + --- + -- - --- + --- + -- - -- - ---- - -- + -- - -- - ---- - --
7 5 a z 9 5 a 9 7 5 3 a 7 5 3
a z a z a a a a a a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 126]][a, z] |
Out[9]= | 2 2 2
2 5 3 -2 1 2 1 2 z 5 z 3 z 2 z 2 z 3 z
-- + -- + -- - a - ---- - ---- + --- - --- + --- - --- - ---- + ---- - ---- -
8 6 4 7 5 a z 9 5 a 12 10 8
a a a a z a z a a a a a
2 2 3 3 3 3 3 4 4 4
15 z 8 z 7 z 4 z 3 z 11 z 3 z 3 z 7 z 2 z
> ----- - ---- - ---- + ---- + ---- - ----- + ---- + ---- - ---- + ---- +
6 4 11 9 7 5 a 12 10 8
a a a a a a a a a
4 4 4 5 5 5 5 5 5 6 6
15 z 6 z 3 z 9 z z 3 z 11 z 3 z z z 10 z
> ----- + ---- + ---- + ---- - -- - ---- + ----- + ---- - -- - --- + ----- +
6 4 2 11 9 7 5 3 a 12 10
a a a a a a a a a a
6 6 6 7 7 7 7 7 8 8
7 z 2 z 2 z 3 z 4 z 6 z 4 z 3 z 4 z 4 z
> ---- - ---- - ---- - ---- + ---- + ---- - ---- - ---- - ---- - ---- -
8 6 2 11 9 7 5 3 10 8
a a a a a a a a a a
8 8 9 9 9 10 10
3 z 3 z 3 z 5 z 2 z z z
> ---- - ---- - ---- - ---- - ---- - --- - ---
6 4 9 7 5 8 6
a a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2
2 4 1 1 q 4 6 6 2 8 2 8 3
5 q + 3 q + ----- + - + -- + 6 q t + 3 q t + 8 q t + 6 q t + 7 q t +
2 2 t t
q t
10 3 10 4 12 4 12 5 14 5 14 6
> 8 q t + 8 q t + 7 q t + 6 q t + 8 q t + 4 q t +
16 6 16 7 18 7 18 8 20 8 22 9
> 6 q t + 2 q t + 4 q t + q t + 2 q t + q t |