PD Presentation: |
X6172 X12,4,13,3 X14,8,15,7 X20,12,21,11 X22,16,5,15 X16,22,17,21 X8,20,9,19 X18,10,19,9 X10,18,11,17 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, 65]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 65]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 4, 13, 3], X[14, 8, 15, 7], X[20, 12, 21, 11],
> X[22, 16, 5, 15], X[16, 22, 17, 21], X[8, 20, 9, 19], X[18, 10, 19, 9],
> X[10, 18, 11, 17], X[2, 5, 3, 6], X[4, 14, 1, 13]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -7, 8, -9, 4, -2, 11, -3, 5, -6, 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 + 16 q - 17 q +
Sqrt[q]
13/2 15/2 17/2 19/2 21/2
> 14 q - 10 q + 7 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -2 4 6 8 10 12 14 18 20 22
-1 + q + 3 q - 2 q + 4 q + 3 q + q + 5 q + 3 q - q - 3 q +
24 26 28 30 32
> q - 4 q - q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 65]][a, z] |
Out[8]= | 3 3 3 3
1 1 2 2 z z 4 z 3 z z z 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, 65]][a, z] |
Out[9]= | 2
-4 9 4 2 1 1 2 2 5 z 13 z 7 z z 2 z
--- - -- - -- + -- + ---- + ---- - ---- - ---- + --- + ---- + --- - - - ---- +
10 8 6 4 9 7 5 3 7 5 3 a 12
a a a a a z a z a z a z a a a a
2 2 2 2 2 3 3 3 3 3
12 z 31 z 15 z 3 z z 4 z 2 z 14 z 29 z 7 z
> ----- + ----- + ----- - ---- - -- - ---- + ---- - ----- - ----- - ---- +
10 8 6 4 2 11 9 7 5 3
a a a a a a a a a a
3 4 4 4 4 4 5 5 5 5
2 z 3 z 16 z 46 z 32 z 5 z 8 z 4 z 22 z 9 z
> ---- + ---- - ----- - ----- - ----- + ---- + ---- - ---- + ----- + ---- -
a 12 10 8 6 2 11 9 5 3
a a a a a a a a a
5 6 6 6 6 6 6 7 7 7
z z 15 z 34 z 27 z 6 z 3 z 3 z 8 z 12 z
> -- - --- + ----- + ----- + ----- + ---- - ---- - ---- + ---- + ----- -
a 12 10 8 6 4 2 11 9 7
a a a a a a a a a
7 7 8 8 8 8 9 9 9 10 10
4 z 5 z 5 z 9 z 9 z 5 z 4 z 7 z 3 z z z
> ---- - ---- - ---- - ---- - ---- - ---- - ---- - ---- - ---- - --- - ---
5 3 10 8 6 4 9 7 5 8 6
a a a a a a a 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 + 8 q t +
2 2 t t
q t
10 3 10 4 12 4 12 5 14 5 14 6
> 8 q t + 9 q t + 8 q t + 5 q t + 9 q t + 5 q t +
16 6 16 7 18 7 18 8 20 8 22 9
> 5 q t + 2 q t + 5 q t + q t + 2 q t + q t |