PD Presentation: |
X6172 X14,7,15,8 X16,9,17,10 X8,15,9,16 X4,17,1,18 X12,6,13,5 X10,4,11,3 X18,12,5,11 X2,14,3,13 |
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[9, Alternating, 9]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[9, Alternating, 9]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 7, 15, 8], X[16, 9, 17, 10], X[8, 15, 9, 16],
> X[4, 17, 1, 18], X[12, 6, 13, 5], X[10, 4, 11, 3], X[18, 12, 5, 11],
> X[2, 14, 3, 13]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 7, -5}, {6, -1, 2, -4, 3, -7, 8, -6, 9, -2, 4, -3, 5, -8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(11/2) 3 5 7 8 9 3/2 5/2
q - ---- + ---- - ---- + ---- - ------- + 6 Sqrt[q] - 5 q + 3 q -
9/2 7/2 5/2 3/2 Sqrt[q]
q q q q
7/2
> q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -16 -14 -12 -10 -8 -6 3 2 6 8 10
4 - q + q - q + q + q - q + -- + q + q - q + q
4
q |
In[8]:= | HOMFLYPT[Link[9, Alternating, 9]][a, z] |
Out[8]= | 3 5
1 a 2 z 3 3 z 3 3 3 z 5
-(---) + - - --- + 4 a z - 2 a z - ---- + 8 a z - 3 a z - -- + 5 a z -
a z z a a a
3 5 7
> a z + a z |
In[9]:= | Kauffman[Link[9, Alternating, 9]][a, z] |
Out[9]= | 2
1 a 4 z 3 2 2 z 2 2 4 2 6 2
1 - --- - - + --- + 8 a z + 4 a z - 3 z - ---- - 3 a z - a z + a z +
a z z a 2
a
3 3 4
2 z 10 z 3 3 3 5 3 4 7 z 2 4
> ---- - ----- - 24 a z - 8 a z + 4 a z + 4 z + ---- + 3 a z +
3 a 2
a a
5 5 6
4 4 6 4 z 11 z 5 3 5 5 5 6 3 z
> 5 a z - a z - -- + ----- + 22 a z + 7 a z - 3 a z + z - ---- -
3 a 2
a a
7
4 6 4 z 7 3 7 8 2 8
> 4 a z - ---- - 8 a z - 4 a z - 2 z - 2 a z
a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 5 1 2 1 3 2 4 3 4
6 + -- + ------ + ------ + ----- + ----- + ----- + ----- + ----- + ---- +
2 12 5 10 4 8 4 8 3 6 3 6 2 4 2 4
q q t q t q t q t q t q t q t q t
4 2 2 2 4 2 4 3 6 3 8 4
> ---- + 3 t + 3 q t + 2 q t + 3 q t + q t + 2 q t + q t
2
q t |