PD Presentation: |
X8192 X10,4,11,3 X22,10,7,9 X2738 X16,14,17,13 X14,5,15,6 X4,15,5,16 X20,17,21,18 X18,11,19,12 X12,19,13,20 X6,22,1,21 |
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, 160]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 160]] |
Out[4]= | PD[X[8, 1, 9, 2], X[10, 4, 11, 3], X[22, 10, 7, 9], X[2, 7, 3, 8],
> X[16, 14, 17, 13], X[14, 5, 15, 6], X[4, 15, 5, 16], X[20, 17, 21, 18],
> X[18, 11, 19, 12], X[12, 19, 13, 20], X[6, 22, 1, 21]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -4, 2, -7, 6, -11},
> {4, -1, 3, -2, 9, -10, 5, -6, 7, -5, 8, -9, 10, -8, 11, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(15/2) 3 7 12 16 20 19 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 3 2 5 2 2 4 3 2
4 - q - q + q - --- + --- - --- + --- + -- + -- + -- - -- - 3 q -
18 14 12 10 8 6 4 2
q q q q q q q q
4 6 8 10
> q + 2 q - 2 q + q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 160]][a, z] |
Out[8]= | 3 5 7 3
-2 a 3 a a z 3 5 7 2 z 3
----- + ---- - -- - - + 4 a z - 9 a z + 6 a z - a z - ---- + 7 a 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, 160]][a, z] |
Out[9]= | 3 5 7
4 6 8 2 a 3 a a 2 z 3 5
3 a + 3 a + a - ---- - ---- - -- + --- + 8 a z + 15 a z + 12 a z +
z z z a
2 3 3
7 2 2 z 2 2 4 2 6 2 8 2 z 6 z
> 3 a z - 4 z - ---- - 2 a z - 4 a z - 7 a z - 3 a z + -- - ---- -
2 3 a
a a
4
3 3 3 5 3 7 3 4 6 z 2 4
> 24 a z - 33 a z - 23 a z - 7 a z + 4 z + ---- - 11 a z -
2
a
5 5
4 4 6 4 8 4 z 11 z 5 3 5 5 5
> 9 a z + 3 a z + 3 a z - -- + ----- + 26 a z + 27 a z + 21 a z +
3 a
a
6 7
7 5 6 4 z 2 6 4 6 6 6 8 6 7 z
> 8 a z + 6 z - ---- + 25 a z + 22 a z + 6 a z - a z - ---- -
2 a
a
7 5 7 7 7 8 2 8 4 8 6 8
> 7 a z - 3 a z - 3 a z - 7 z - 13 a z - 10 a z - 4 a z -
9 3 9 5 9 2 10 4 10
> 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 7 5 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 10 9 10 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 |