PD Presentation: |
X10,1,11,2 X12,4,13,3 X22,12,9,11 X2,9,3,10 X20,15,21,16 X8,14,1,13 X4,20,5,19 X18,8,19,7 X16,6,17,5 X6,18,7,17 X14,21,15,22 |
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, 300]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 300]] |
Out[4]= | PD[X[10, 1, 11, 2], X[12, 4, 13, 3], X[22, 12, 9, 11], X[2, 9, 3, 10],
> X[20, 15, 21, 16], X[8, 14, 1, 13], X[4, 20, 5, 19], X[18, 8, 19, 7],
> X[16, 6, 17, 5], X[6, 18, 7, 17], X[14, 21, 15, 22]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -4, 2, -7, 9, -10, 8, -6},
> {4, -1, 3, -2, 6, -11, 5, -9, 10, -8, 7, -5, 11, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(5/2) 3 6 3/2 5/2 7/2
-q + ---- - ------- + 10 Sqrt[q] - 14 q + 16 q - 18 q +
3/2 Sqrt[q]
q
9/2 11/2 13/2 15/2 17/2
> 15 q - 12 q + 8 q - 4 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -8 -4 -2 2 4 6 8 10 12 14 16
-3 + q - q + q + q + 2 q - q + 5 q - q + 3 q + q - q +
18 20 22 24 26
> 3 q - 2 q + q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 300]][a, z] |
Out[8]= | 3 3 3 3
1 1 z 3 z 6 z 4 z z 5 z 7 z 6 z
-(----) + ---- + -- - --- + --- - --- + 2 a z + -- - ---- + ---- - ---- +
5 3 7 5 3 a 7 5 3 a
a z a z a a a a a a
5 5 5 7
3 2 z 4 z 2 z z
> a z - ---- + ---- - ---- + --
5 3 a 3
a a a |
In[9]:= | Kauffman[Link[11, Alternating, 300]][a, z] |
Out[9]= | 2 2 2
-4 1 1 2 z 7 z 6 z 3 z 2 2 z 2 z 3 z
a - ---- - ---- + --- + --- + --- + --- + 2 a z + 6 z - ---- - ---- + ---- +
5 3 7 5 3 a 8 6 4
a z a z a a a a a a
2 3 3 3 3 3 4 4
9 z 2 z 7 z 23 z 19 z 10 z 3 4 z 8 z
> ---- + ---- - ---- - ----- - ----- - ----- - 5 a z - 15 z - --- + ---- +
2 9 7 5 3 a 10 8
a a a a a a a
4 4 4 5 5 5 5 5
5 z 21 z 32 z 4 z 13 z 30 z 11 z 2 z 5
> ---- - ----- - ----- - ---- + ----- + ----- + ----- + ---- + 4 a z +
6 4 2 9 7 5 3 a
a a a a a a a
6 6 6 6 7 7 7 7
6 8 z 6 z 33 z 31 z 10 z 7 z 11 z 7 z 7
> 12 z - ---- + ---- + ----- + ----- - ----- - ---- + ----- + ---- - a z -
8 6 4 2 7 5 3 a
a a a a a a a
8 8 8 9 9 9 10 10
8 8 z 12 z 7 z 4 z 7 z 3 z z z
> 3 z - ---- - ----- - ---- - ---- - ---- - ---- - --- - ---
6 4 2 5 3 a 4 2
a a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2
2 4 1 2 1 2 4 6 4 q 4 6
8 q + 7 q + ----- + ----- + ----- + -- + ----- + - + ---- + 9 q t + 7 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 + 9 q t + 6 q t + 9 q t + 6 q t + 7 q t + 3 q t +
14 5 14 6 16 6 18 7
> 5 q t + q t + 3 q t + q t |