PD Presentation: |
X8192 X12,3,13,4 X16,6,17,5 X22,13,7,14 X18,15,19,16 X14,21,15,22 X20,10,21,9 X4,18,5,17 X10,20,11,19 X2738 X6,11,1,12 |
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, 217]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 217]] |
Out[4]= | PD[X[8, 1, 9, 2], X[12, 3, 13, 4], X[16, 6, 17, 5], X[22, 13, 7, 14],
> X[18, 15, 19, 16], X[14, 21, 15, 22], X[20, 10, 21, 9], X[4, 18, 5, 17],
> X[10, 20, 11, 19], X[2, 7, 3, 8], X[6, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -8, 3, -11},
> {10, -1, 7, -9, 11, -2, 4, -6, 5, -3, 8, -5, 9, -7, 6, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(15/2) 4 9 15 19 23 22 19
q - ----- + ----- - ---- + ---- - ---- + ---- - ------- + 14 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 + 3 q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -24 3 3 2 4 4 4 -8 -6 2 3 2
5 - q + --- - --- + --- + --- - --- + --- - q + q + -- - -- - 3 q +
20 18 16 14 12 10 4 2
q q q q q q q q
6 8 12
> 4 q - 2 q + q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 217]][a, z] |
Out[8]= | 3 5 3
1 2 a 2 a a z z 3 5 7 2 z
-(---) + --- - ---- + -- - -- - - + 5 a z - 5 a z + 2 a z - a z + ---- +
a z z z z 3 a a
a
3 3 3 5 3 5 3 5
> 3 a z - 3 a z + 3 a z - a z - 2 a z |
In[9]:= | Kauffman[Link[11, Alternating, 217]][a, z] |
Out[9]= | 3 5
2 1 2 a 2 a a z 4 z 3 5 7
-a - --- - --- - ---- - -- - -- + --- + 12 a z + 10 a z + 5 a z + 2 a z +
a z z z z 3 a
a
2 3 3
2 z 2 2 4 2 6 2 8 2 2 z 7 z 3
> 7 z - -- + 13 a z + 8 a z + 2 a z - a z + ---- - ---- - 23 a z -
2 3 a
a a
4
3 3 5 3 7 3 4 4 z 2 4 4 4
> 22 a z - 14 a z - 6 a z - 13 z + ---- - 37 a z - 30 a z -
2
a
5 5
6 4 8 4 z 9 z 5 3 5 5 5 7 5
> 8 a z + 2 a z - -- + ---- + 15 a z + 9 a z + 13 a z + 9 a z +
3 a
a
6 7
6 3 z 2 6 4 6 6 6 8 6 6 z 7
> 13 z - ---- + 39 a z + 39 a z + 15 a z - a z - ---- + a z +
2 a
a
3 7 5 7 7 7 8 2 8 4 8 6 8
> 16 a z + 5 a z - 4 a z - 8 z - 14 a z - 13 a z - 7 a z -
9 3 9 5 9 2 10 4 10
> 6 a z - 12 a z - 6 a z - 2 a z - 2 a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 9 1 3 1 6 3 9 6 10
11 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
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
9 13 11 10 12 2 2 2 4 2
> ----- + ----- + ----- + ---- + ---- + 6 t + 8 q t + 2 q t + 6 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 + 2 q t + q t |