PD Presentation: |
X6172 X14,3,15,4 X16,8,17,7 X18,10,19,9 X8,18,9,17 X22,20,5,19 X20,11,21,12 X10,21,11,22 X12,16,13,15 X2536 X4,13,1,14 |
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, 105]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 105]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 3, 15, 4], X[16, 8, 17, 7], X[18, 10, 19, 9],
> X[8, 18, 9, 17], X[22, 20, 5, 19], X[20, 11, 21, 12], X[10, 21, 11, 22],
> X[12, 16, 13, 15], X[2, 5, 3, 6], X[4, 13, 1, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -5, 4, -8, 7, -9, 11, -2, 9, -3, 5, -4,
> 6, -7, 8, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(11/2) 2 6 9 13 15 3/2
-q + ---- - ---- + ---- - ---- + ------- - 16 Sqrt[q] + 15 q -
9/2 7/2 5/2 3/2 Sqrt[q]
q q q q
5/2 7/2 9/2 11/2
> 11 q + 7 q - 4 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -18 2 -14 3 2 -8 2 3 2 4 6 8
1 + q + --- + q + --- + --- - q + -- - -- - 2 q + 3 q - 3 q + 2 q +
16 12 10 6 4
q q q q q
10 12 14 16
> q - q + 2 q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 105]][a, z] |
Out[8]= | 3 5 3 3
1 3 a 4 a 2 a 4 z 3 5 2 z 6 z
-(---) + --- - ---- + ---- - --- + 9 a z - 8 a z + a z + ---- - ---- +
a z z z z a 3 a
a
5 5 7
3 3 3 z 4 z 5 z
> 10 a z - 3 a z + -- - ---- + 3 a z - --
3 a a
a |
In[9]:= | Kauffman[Link[11, Alternating, 105]][a, z] |
Out[9]= | 3 5
-2 2 4 1 3 a 4 a 2 a z 3 z 3
3 + a + 3 a + 2 a - --- - --- - ---- - ---- - -- + --- + 13 a z + 16 a z +
a z z z z 3 a
a
2 2 3 3 3
5 2 2 z 7 z 2 2 4 2 3 z z 11 z
> 7 a z - 7 z - ---- - ---- - 3 a z - a z + ---- + -- - ----- -
4 2 5 3 a
a a a a
4 4 4
3 3 3 5 3 4 z 7 z 7 z 2 4
> 25 a z - 25 a z - 9 a z - 7 z - -- + ---- + ---- - 12 a z -
6 4 2
a a a
5 5 5
4 4 4 z 7 z 16 z 5 3 5 5 5 6
> 6 a z - ---- + ---- + ----- + 13 a z + 13 a z + 5 a z + 23 z -
5 3 a
a a
6 6 7 7
7 z 5 z 2 6 4 6 8 z 2 z 7 3 7 5 7
> ---- + ---- + 18 a z + 7 a z - ---- - ---- + 9 a z + 2 a z - a z -
4 2 3 a
a a a
8 9
8 7 z 2 8 4 8 4 z 9 3 9 10 2 10
> 9 z - ---- - 4 a z - 2 a z - ---- - 6 a z - 2 a z - z - a z
2 a
a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 1 1 1 5 2 5 4 8
9 + 8 q + ------ + ------ + ----- + ----- + ----- + ----- + ----- + ----- +
12 6 10 5 8 5 8 4 6 4 6 3 4 3 4 2
q t q t q t q t q t q t q t q t
5 8 7 2 4 4 2 6 2 6 3
> ----- + - + ---- + 7 q t + 8 q t + 4 q t + 7 q t + 3 q t +
2 2 t 2
q t q t
8 3 8 4 10 4 12 5
> 4 q t + q t + 3 q t + q t |