PD Presentation: |
X6172 X16,7,17,8 X4,17,1,18 X10,6,11,5 X8493 X22,14,5,13 X20,12,21,11 X12,22,13,21 X14,20,15,19 X18,10,19,9 X2,16,3,15 |
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, 4]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 4]] |
Out[4]= | PD[X[6, 1, 7, 2], X[16, 7, 17, 8], X[4, 17, 1, 18], X[10, 6, 11, 5],
> X[8, 4, 9, 3], X[22, 14, 5, 13], X[20, 12, 21, 11], X[12, 22, 13, 21],
> X[14, 20, 15, 19], X[18, 10, 19, 9], X[2, 16, 3, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -11, 5, -3}, {4, -1, 2, -5, 10, -4, 7, -8, 6, -9, 11, -2, 3, -10,
> 9, -7, 8, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(3/2) 4 3/2 5/2 7/2 9/2
q - ------- + 7 Sqrt[q] - 14 q + 18 q - 22 q + 22 q -
Sqrt[q]
11/2 13/2 15/2 17/2 19/2
> 19 q + 15 q - 9 q + 4 q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -4 2 2 4 6 8 10 12 14 16 18 20
-q + -- + 2 q + 6 q - q + 6 q - q - q + q - 5 q + 3 q - 3 q +
2
q
24 26 28
> 2 q - 2 q + q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 4]][a, z] |
Out[8]= | 3 3 3 3 5
1 3 2 z 2 z 2 z z 2 z 3 z 2 z 2 z z
---- - ---- + --- - -- + --- - --- + - - ---- + ---- + ---- - ---- - -- +
5 3 a z 7 5 3 a 7 5 3 a 7
a z a z a a a a a a a
5 5 5 7 7
3 z 3 z z z z
> ---- + ---- - -- + -- + --
5 3 a 5 3
a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 4]][a, z] |
Out[9]= | 2 2 2
-6 3 3 1 3 2 2 z 4 z 3 z z 2 z 5 z 5 z
-a - -- - -- + ---- + ---- + --- - --- - --- - --- - - - ---- + ---- + ---- +
4 2 5 3 a z 7 5 3 a 10 6 4
a a a z a z a a a a a a
2 3 3 3 3 3 4 4 4
2 z z 6 z 9 z 6 z 8 z 4 5 z 3 z 10 z
> ---- + --- - ---- + ---- - ---- - ---- + 2 z + ---- - ---- - ----- -
2 11 9 5 3 a 10 8 6
a a a a a a a a
4 4 5 5 5 5 5 5 6
13 z 9 z z 12 z 8 z 10 z 6 z 11 z 6 4 z
> ----- - ---- - --- + ----- + ---- - ----- + ---- + ----- - z - ---- +
4 2 11 9 7 5 3 a 10
a a a a a a a a
6 6 6 6 7 7 7 7 8 8
11 z 21 z 21 z 14 z 8 z 17 z 5 z 4 z 9 z 11 z
> ----- + ----- + ----- + ----- - ---- + ----- + ---- - ---- - ---- - ----- -
8 6 4 2 9 5 3 a 8 6
a a a a a a a a a
8 8 9 9 9 10 10
8 z 6 z 6 z 11 z 5 z 2 z 2 z
> ---- - ---- - ---- - ----- - ---- - ----- - -----
4 2 7 5 3 6 4
a a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2
2 4 1 -2 3 4 3 q 4 6 6 2
10 q + 6 q + ----- + t + ----- + - + ---- + 10 q t + 8 q t + 12 q t +
4 3 2 2 t t
q t q t
8 2 8 3 10 3 10 4 12 4 12 5
> 10 q t + 10 q t + 12 q t + 9 q t + 10 q t + 6 q t +
14 5 14 6 16 6 16 7 18 7 20 8
> 9 q t + 3 q t + 6 q t + q t + 3 q t + q t |