PD Presentation: |
X6172 X14,4,15,3 X16,8,17,7 X20,14,21,13 X22,12,5,11 X12,22,13,21 X8,20,9,19 X18,10,19,9 X10,18,11,17 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, 114]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 114]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 4, 15, 3], X[16, 8, 17, 7], X[20, 14, 21, 13],
> X[22, 12, 5, 11], X[12, 22, 13, 21], X[8, 20, 9, 19], X[18, 10, 19, 9],
> X[10, 18, 11, 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, -7, 8, -9, 5, -6, 4, -2, 11, -3, 9, -8,
> 7, -4, 6, -5}] |
In[6]:= | Jones[L][q] |
Out[6]= | 1 3/2 5/2 7/2 9/2 11/2
-(-------) + 3 Sqrt[q] - 7 q + 10 q - 15 q + 15 q - 15 q +
Sqrt[q]
13/2 15/2 17/2 19/2 21/2
> 13 q - 9 q + 5 q - 2 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -2 4 6 8 10 12 14 16 18 20
-1 + q + 3 q - 2 q + 4 q + 3 q + 2 q + 5 q - q + 2 q - 2 q -
22 24 26 28 32
> 2 q + 2 q - 3 q - q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 114]][a, z] |
Out[8]= | 3 3 3 3
1 1 2 2 2 z 3 z 3 z 3 z z z 2 z 4 z z
---- - ---- - ---- + ---- + --- - --- - --- + --- + - + -- - ---- - ---- + -- -
9 7 5 3 9 7 5 3 a 9 7 5 a
a z a z a z a z a a a a a a a
5 5 5
z 2 z z
> -- - ---- - --
7 5 3
a a a |
In[9]:= | Kauffman[Link[11, Alternating, 114]][a, z] |
Out[9]= | -4 9 4 2 1 1 2 2 2 z z 11 z 7 z z
--- - -- - -- + -- + ---- + ---- - ---- - ---- - --- + -- + ---- + --- - - -
10 8 6 4 9 7 5 3 9 7 5 3 a
a a a a a z a z a z a z a a a a
2 2 2 2 2 2 3 3 3 3
4 z 12 z 34 z 15 z 4 z z 4 z 11 z 3 z 27 z
> ---- + ----- + ----- + ----- - ---- - -- - ---- + ----- - ---- - ----- -
12 10 8 6 4 2 11 9 7 5
a a a a a a a a a a
3 3 4 4 4 4 4 4 5 5
7 z 2 z 4 z 12 z 39 z 27 z z 5 z 6 z 12 z
> ---- + ---- + ---- - ----- - ----- - ----- + -- + ---- + ---- - ----- -
3 a 12 10 8 6 4 2 11 9
a a a a a a a a a
5 5 5 5 6 6 6 6 6 6
8 z 20 z 9 z z z 9 z 22 z 21 z 6 z 3 z
> ---- + ----- + ---- - -- - --- + ---- + ----- + ----- + ---- - ---- -
7 5 3 a 12 10 8 6 4 2
a a a a a a a a a
7 7 7 7 7 8 8 8 8 9
2 z 8 z 12 z 3 z 5 z 3 z 5 z 7 z 5 z 3 z
> ---- + ---- + ----- - ---- - ---- - ---- - ---- - ---- - ---- - ---- -
11 9 7 5 3 10 8 6 4 9
a a a a a a a a a a
9 9 10 10
6 z 3 z z z
> ---- - ---- - --- - ---
7 5 8 6
a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2
2 4 1 2 q 4 6 6 2 8 2 8 3
5 q + 4 q + ----- + - + -- + 7 q t + 3 q t + 8 q t + 7 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 + 5 q t + 8 q t + 4 q t +
16 6 16 7 18 7 18 8 20 8 22 9
> 5 q t + q t + 4 q t + q t + q t + q t |