PD Presentation: |
X10,1,11,2 X16,7,9,8 X12,3,13,4 X6,13,7,14 X14,5,15,6 X4,15,5,16 X2,9,3,10 X8,11,1,12 |
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[8, Alternating, 13]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[8, Alternating, 13]] |
Out[4]= | PD[X[10, 1, 11, 2], X[16, 7, 9, 8], X[12, 3, 13, 4], X[6, 13, 7, 14],
> X[14, 5, 15, 6], X[4, 15, 5, 16], X[2, 9, 3, 10], X[8, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -7, 3, -6, 5, -4, 2, -8}, {7, -1, 8, -3, 4, -5, 6, -2}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(19/2) -(17/2) 3 4 4 4 4 2 -(3/2)
-q + q - ----- + ----- - ----- + ---- - ---- + ---- - q
15/2 13/2 11/2 9/2 7/2 5/2
q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -30 -28 -26 3 -22 -16 -14 -10 -8 -6 -4
q + q + q + --- + q - q + q + q + q - q + q
24
q |
In[8]:= | HOMFLYPT[Link[8, Alternating, 13]][a, z] |
Out[8]= | 7 9
a a 3 5 7 9 3 3 5 3 7 3
-(--) + -- - a z - 3 a z - a z + a z - a z - 2 a z - a z
z z |
In[9]:= | Kauffman[Link[8, Alternating, 13]][a, z] |
Out[9]= | 7 9
8 a a 3 5 7 9 11 4 2 8 2
a - -- - -- + a z - 3 a z + 3 a z + 3 a z - 4 a z + a z - a z -
z z
3 3 5 3 7 3 9 3 11 3 4 4 6 4 8 4
> a z + 4 a z - a z - 2 a z + 4 a z - 2 a z + a z + 5 a z +
10 4 5 5 9 5 11 5 6 6 8 6 10 6
> 2 a z - 3 a z + 2 a z - a z - 2 a z - 3 a z - a z -
7 7 9 7
> a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -4 -2 1 1 1 2 1 2 2
q + q + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
20 8 18 8 18 7 16 6 14 6 14 5 12 5
q t q t q t q t q t q t q t
2 2 2 2 2 2 2
> ------ + ------ + ------ + ----- + ----- + ----- + ----
12 4 10 4 10 3 8 3 8 2 6 2 4
q t q t q t q t q t q t q t |