PD Presentation: |
X6172 X12,4,13,3 X14,8,15,7 X18,10,19,9 X22,16,5,15 X16,22,17,21 X20,12,21,11 X8,18,9,17 X10,20,11,19 X2536 X4,14,1,13 |
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, 64]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 64]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 4, 13, 3], X[14, 8, 15, 7], X[18, 10, 19, 9],
> X[22, 16, 5, 15], X[16, 22, 17, 21], X[20, 12, 21, 11], X[8, 18, 9, 17],
> X[10, 20, 11, 19], X[2, 5, 3, 6], X[4, 14, 1, 13]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -8, 4, -9, 7, -2, 11, -3, 5, -6, 8, -4,
> 9, -7, 6, -5}] |
In[6]:= | Jones[L][q] |
Out[6]= | 3/2 5/2 7/2 9/2 11/2 13/2
-Sqrt[q] + 2 q - 5 q + 7 q - 12 q + 13 q - 14 q +
15/2 17/2 19/2 21/2 23/2
> 13 q - 10 q + 7 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | 2 6 8 12 14 16 18 20 22 24 26
q + q + 2 q + 5 q + q + 4 q + 3 q - q + 2 q - 4 q - q -
28 30 32 34
> 2 q - 2 q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 64]][a, z] |
Out[8]= | 3 3 3 3 5
2 4 1 1 3 z 7 z 4 z 3 z 6 z 4 z 4 z z
---- - ---- + ---- + ---- + --- - --- + --- + ---- - ---- - ---- + ---- + -- -
9 7 5 3 9 7 3 9 7 5 3 9
a z a z a z a z a a a a a a a a
5 5 5 7 7
4 z 4 z z z z
> ---- - ---- + -- - -- - --
7 5 3 7 5
a a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 64]][a, z] |
Out[9]= | 2 -10 6 5 -4 2 4 1 1 z 8 z 13 z
--- + a - -- - -- + a + ---- + ---- + ---- - ---- - --- - --- - ---- -
12 8 6 9 7 5 3 11 9 7
a a a a z a z a z a z a a a
2 2 2 2 2 3 3 3
z 5 z z 6 z 4 z 19 z 16 z 2 z 4 z 15 z
> -- + --- + --- - ---- - ---- + ----- + ----- + ---- - ---- + ----- +
5 3 14 12 10 8 6 13 11 9
a a a a a a a a a a
3 3 3 4 4 4 4 4 5 5
24 z 5 z 8 z z 8 z 24 z 23 z 8 z 3 z 9 z
> ----- - ---- - ---- - --- + ---- - ----- - ----- - ---- - ---- + ---- -
7 5 3 14 12 8 6 4 13 11
a a a a a a a a a a
5 5 5 5 6 6 6 6 6 7
9 z 25 z z 5 z 6 z 7 z 21 z 16 z 8 z 7 z
> ---- - ----- + -- + ---- - ---- + ---- + ----- + ----- + ---- - ---- +
9 7 5 3 12 10 8 6 4 11
a a a a a a a a a a
7 7 7 7 8 8 8 8 9 9 9
6 z 19 z 5 z z 6 z 6 z 2 z 2 z 4 z 6 z 2 z
> ---- + ----- + ---- - -- - ---- - ---- - ---- - ---- - ---- - ---- - ---- -
9 7 5 3 10 8 6 4 9 7 5
a a a a a a a a a a a
10 10
z z
> --- - ---
8 6
a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 4
4 6 -2 q q 6 8 8 2 10 2 10 3
4 q + 3 q + t + -- + -- + 5 q t + 2 q t + 7 q t + 5 q t + 6 q t +
t t
12 3 12 4 14 4 14 5 16 5 16 6
> 7 q t + 8 q t + 6 q t + 5 q t + 8 q t + 5 q t +
18 6 18 7 20 7 20 8 22 8 24 9
> 5 q t + 2 q t + 5 q t + q t + 2 q t + q t |