PD Presentation: |
X6172 X18,7,19,8 X4,19,1,20 X12,6,13,5 X8493 X16,10,17,9 X22,14,5,13 X10,16,11,15 X14,22,15,21 X20,12,21,11 X2,18,3,17 |
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, 10]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 10]] |
Out[4]= | PD[X[6, 1, 7, 2], X[18, 7, 19, 8], X[4, 19, 1, 20], X[12, 6, 13, 5],
> X[8, 4, 9, 3], X[16, 10, 17, 9], X[22, 14, 5, 13], X[10, 16, 11, 15],
> X[14, 22, 15, 21], X[20, 12, 21, 11], X[2, 18, 3, 17]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -11, 5, -3}, {4, -1, 2, -5, 6, -8, 10, -4, 7, -9, 8, -6, 11, -2,
> 3, -10, 9, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(5/2) 4 8 3/2 5/2 7/2 9/2
q - ---- + ------- - 13 Sqrt[q] + 16 q - 20 q + 18 q - 16 q +
3/2 Sqrt[q]
q
11/2 13/2 15/2 17/2
> 12 q - 7 q + 4 q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -8 2 3 2 4 6 8 10 12 14 16 18
4 - q + -- - -- - q + 2 q + 5 q + q + 5 q - q + q + q - 5 q +
6 2
q q
20 22 24 26
> q - q - 2 q + q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 10]][a, z] |
Out[8]= | 3 3 5 5 5
1 2 1 2 z 2 z z 3 z 3 z 2 z z
---- - ---- + --- - --- + --- - -- + ---- - a z + -- + ---- + --
7 5 a z 5 3 7 3 5 3 a
a z a z a a a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 10]][a, z] |
Out[9]= | 2 2
2 5 3 -2 1 2 1 3 z 4 z z 2 3 z 3 z
-- + -- + -- - a - ---- - ---- + --- + --- + --- + - - z + ---- + ---- +
8 6 4 7 5 a z 5 3 a 8 6
a a a a z a z a a a a
2 3 3 3 3 3 4 4
z 2 z 2 z 5 z 19 z 8 z 3 4 16 z 32 z
> -- - ---- + ---- - ---- - ----- - ---- + 2 a z + 7 z - ----- - ----- -
4 9 7 5 3 a 8 6
a a a a a a a
4 4 5 5 5 5 5
25 z z 2 4 3 z 13 z 11 z 24 z 15 z 5 6
> ----- - -- - a z + ---- - ----- - ----- + ----- + ----- - 4 a z - 8 z +
4 2 9 7 5 3 a
a a a a a a
6 6 6 6 7 7 7 7 7 8
15 z 32 z 37 z 12 z z 16 z 27 z z 11 z 4 z
> ----- + ----- + ----- + ----- - -- + ----- + ----- - -- - ----- - ---- -
8 6 4 2 9 7 5 3 a 8
a a a a a a a a a
8 8 8 9 9 9 10 10
5 z 11 z 10 z 5 z 11 z 6 z 2 z 2 z
> ---- - ----- - ----- - ---- - ----- - ---- - ----- - -----
6 4 2 7 5 3 6 4
a a a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 1 3 1 3 5 2 4 4 2
8 + 7 q + ----- + ----- + ----- + - + ---- + 10 q t + 6 q t + 10 q t +
6 3 4 2 2 2 t 2
q t q t q t q t
6 2 6 3 8 3 8 4 10 4 10 5 12 5
> 10 q t + 8 q t + 10 q t + 8 q t + 8 q t + 4 q t + 8 q t +
12 6 14 6 14 7 16 7 18 8
> 3 q t + 4 q t + q t + 3 q t + q t |