PD Presentation: |
X10,1,11,2 X18,11,19,12 X20,5,9,6 X14,7,15,8 X12,4,13,3 X16,14,17,13 X6,15,7,16 X8,9,1,10 X4,19,5,20 X2,18,3,17 |
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[10, Alternating, 106]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 106]] |
Out[4]= | PD[X[10, 1, 11, 2], X[18, 11, 19, 12], X[20, 5, 9, 6], X[14, 7, 15, 8],
> X[12, 4, 13, 3], X[16, 14, 17, 13], X[6, 15, 7, 16], X[8, 9, 1, 10],
> X[4, 19, 5, 20], X[2, 18, 3, 17]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 5, -9, 3, -7, 4, -8},
> {8, -1, 2, -5, 6, -4, 7, -6, 10, -2, 9, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(17/2) 3 6 11 13 14 13 11 7
q - ----- + ----- - ----- + ---- - ---- + ---- - ---- + ------- -
15/2 13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q q
3/2
> 4 Sqrt[q] + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -26 -22 -20 4 -14 2 2 4 2 2 -2 2
-1 - q + q - q + --- + q + --- - --- + -- - -- + -- + q + 2 q -
18 12 10 8 6 4
q q q q q q
4
> q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 106]][a, z] |
Out[8]= | 3 5
a a 3 5 7 3 3 3 5 3 7 3
-(--) + -- - 5 a z + 5 a z - 2 a z + 2 a z - 6 a z + 6 a z - a z +
z z
5 3 5 5 5 3 7
> a z - 4 a z + 2 a z - a z |
In[9]:= | Kauffman[Link[10, Alternating, 106]][a, z] |
Out[9]= | 3 5
4 a a 3 5 7 9 2 2 2 4 2
a - -- - -- + a z + 9 a z + 10 a z + a z - a z - z - a z + a z -
z z
6 2 8 2 10 2 3 3 3 5 3 7 3 9 3
> a z - a z + a z - 8 a z - 27 a z - 30 a z - 8 a z + 3 a z +
4 2 4 4 4 6 4 8 4 10 4 5
> 2 z - 3 a z - 12 a z - 2 a z + 4 a z - a z + 11 a z +
3 5 5 5 7 5 9 5 6 2 6 4 6
> 31 a z + 33 a z + 10 a z - 3 a z - z + 11 a z + 24 a z +
6 6 8 6 7 3 7 5 7 7 7 2 8
> 7 a z - 5 a z - 4 a z - 7 a z - 10 a z - 7 a z - 5 a z -
4 8 6 8 3 9 5 9
> 11 a z - 6 a z - 2 a z - 2 a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 5 7 1 2 1 4 2 7 5
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 2 18 7 16 6 14 6 14 5 12 5 12 4 10 4
q q q t q t q t q t q t q t q t
7 6 7 7 6 7 3 t 2 2 2
> ------ + ----- + ----- + ----- + ---- + ---- + 4 t + --- + t + 3 q t +
10 3 8 3 8 2 6 2 6 4 2
q t q t q t q t q t q t q
4 3
> q t |