PD Presentation: |
X8192 X16,6,17,5 X18,10,19,9 X10,20,11,19 X2,11,3,12 X12,3,13,4 X4758 X20,14,21,13 X22,16,7,15 X6,18,1,17 X14,22,15,21 |
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, 224]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 224]] |
Out[4]= | PD[X[8, 1, 9, 2], X[16, 6, 17, 5], X[18, 10, 19, 9], X[10, 20, 11, 19],
> X[2, 11, 3, 12], X[12, 3, 13, 4], X[4, 7, 5, 8], X[20, 14, 21, 13],
> X[22, 16, 7, 15], X[6, 18, 1, 17], X[14, 22, 15, 21]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -5, 6, -7, 2, -10},
> {7, -1, 3, -4, 5, -6, 8, -11, 9, -2, 10, -3, 4, -8, 11, -9}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(5/2) 3 7 3/2 5/2 7/2
-q + ---- - ------- + 10 Sqrt[q] - 15 q + 16 q - 17 q +
3/2 Sqrt[q]
q
9/2 11/2 13/2 15/2 17/2
> 15 q - 11 q + 7 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -6 -4 3 2 4 8 10 12 14 16 18
q - q + -- + 3 q + 4 q + 6 q - 3 q + 2 q - 2 q - 2 q + q -
2
q
20 22 24
> 3 q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 224]][a, z] |
Out[8]= | 3 3 3 5 5
2 5 3 7 z 16 z 8 z 9 z 25 z 9 z 5 z 19 z
---- - ---- + --- + --- - ---- + --- + ---- - ----- + ---- + ---- - ----- +
5 3 a z 5 3 a 5 3 a 5 3
a z a z a a a a a a
5 7 7 7 9
5 z z 7 z z z
> ---- + -- - ---- + -- - --
a 5 3 a 3
a a a |
In[9]:= | Kauffman[Link[11, Alternating, 224]][a, z] |
Out[9]= | 2
-8 5 5 2 5 3 9 z 20 z 9 z 2 z
a - -- - -- + ---- + ---- + --- - --- - ---- - --- + 2 a z + 2 z + --- -
4 2 5 3 a z 5 3 a 10
a a a z a z a a a
2 2 2 3 3 3 3 3
5 z 18 z 14 z 2 z 7 z 15 z 37 z 8 z 3
> ---- + ----- + ----- + ---- - ---- + ----- + ----- + ---- - 5 a z -
8 4 2 9 7 5 3 a
a a a a a a a
4 4 4 4 4 5 5 5 5
4 z 7 z 6 z 27 z 24 z 3 z 11 z 10 z 40 z
> 11 z - --- + ---- - ---- - ----- - ----- - ---- + ----- - ----- - ----- -
10 8 6 4 2 9 7 5 3
a a a a a a a a a
5 6 6 6 6 7 7
12 z 5 6 6 z 12 z 26 z 19 z 8 z 10 z
> ----- + 4 a z + 11 z - ---- + ----- + ----- + ----- - ---- + ----- +
a 8 6 4 2 7 5
a a a a a a
7 7 8 8 8 9 9 9
32 z 13 z 7 8 8 z 6 z z 6 z 10 z 4 z
> ----- + ----- - a z - 3 z - ---- - ---- - -- - ---- - ----- - ---- -
3 a 6 4 2 5 3 a
a a a a a a
10 10
2 z 2 z
> ----- - -----
4 2
a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2
2 4 1 2 1 3 5 6 4 q 4 6
9 q + 7 q + ----- + ----- + ----- + -- + ----- + - + ---- + 8 q t + 8 q t +
6 4 4 3 2 3 2 2 2 t t
q t q t q t t q t
6 2 8 2 8 3 10 3 10 4 12 4 12 5
> 9 q t + 8 q t + 6 q t + 9 q t + 5 q t + 6 q t + 2 q t +
14 5 14 6 16 6 18 7
> 5 q t + q t + 2 q t + q t |