PD Presentation: |
X6172 X14,3,15,4 X16,8,17,7 X22,12,5,11 X8,22,9,21 X18,9,19,10 X20,17,21,18 X10,19,11,20 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, 113]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 113]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 3, 15, 4], X[16, 8, 17, 7], X[22, 12, 5, 11],
> X[8, 22, 9, 21], X[18, 9, 19, 10], X[20, 17, 21, 18], X[10, 19, 11, 20],
> 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, 6, -8, 4, -9, 11, -2, 9, -3, 7, -6,
> 8, -7, 5, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(15/2) 3 7 13 16 20 20 18
q - ----- + ----- - ---- + ---- - ---- + ---- - ------- + 13 Sqrt[q] -
13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q
3/2 5/2 7/2
> 8 q + 4 q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -24 -22 -20 2 -16 5 6 -8 2 4 2 4
4 - q - q + q - --- + q + --- + --- + q + -- - -- - 3 q - q +
18 14 10 4 2
q q q q q
6 8 10
> 2 q - 2 q + q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 113]][a, z] |
Out[8]= | 3 5 7 3
a 4 a 4 a a z 3 5 7 2 z 3
- - ---- + ---- - -- - - + 4 a z - 10 a z + 6 a z - a z - ---- + 7 a z -
z z z z a a
5
3 3 5 3 z 5 3 5 7
> 9 a z + 3 a z - -- + 4 a z - 3 a z + a z
a |
In[9]:= | Kauffman[Link[11, Alternating, 113]][a, z] |
Out[9]= | 3 5 7
2 4 6 8 a 4 a 4 a a z 3
1 + 4 a + 7 a + 4 a + a - - - ---- - ---- - -- + - + 4 a z + 14 a z +
z z z z a
2
5 7 2 2 z 2 2 4 2 6 2 8 2
> 15 a z + 4 a z - 4 z - ---- - 10 a z - 16 a z - 11 a z - 3 a z +
2
a
3 3 4
z 6 z 3 3 3 5 3 7 3 4 6 z
> -- - ---- - 17 a z - 27 a z - 25 a z - 8 a z + 3 z + ---- -
3 a 2
a a
5 5
2 4 4 4 6 4 8 4 z 11 z 5 3 5
> 3 a z + 3 a z + 6 a z + 3 a z - -- + ----- + 23 a z + 26 a z +
3 a
a
6
5 5 7 5 6 4 z 2 6 4 6 6 6 8 6
> 23 a z + 8 a z + 6 z - ---- + 22 a z + 18 a z + 5 a z - a z -
2
a
7
7 z 7 3 7 5 7 7 7 8 2 8 4 8
> ---- - 7 a z - a z - 4 a z - 3 a z - 7 z - 13 a z - 10 a z -
a
6 8 9 3 9 5 9 2 10 4 10
> 4 a z - 4 a z - 7 a z - 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 9 1 2 1 5 2 8 6 9
10 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
2 16 7 14 6 12 6 12 5 10 5 10 4 8 4 8 3
q q t q t q t q t q t q t q t q t
7 11 9 9 11 2 2 2 4 2
> ----- + ----- + ----- + ---- + ---- + 5 t + 8 q t + 3 q t + 5 q t +
6 3 6 2 4 2 4 2
q t q t q t q t q t
4 3 6 3 8 4
> q t + 3 q t + q t |