PD Presentation: |
X8192 X2,9,3,10 X10,3,11,4 X14,5,15,6 X15,20,16,21 X11,18,12,19 X19,12,20,13 X17,22,18,7 X21,16,22,17 X6718 X4,13,5,14 |
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, NonAlternating, 169]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 169]] |
Out[4]= | PD[X[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[14, 5, 15, 6],
> X[15, 20, 16, 21], X[11, 18, 12, 19], X[19, 12, 20, 13], X[17, 22, 18, 7],
> X[21, 16, 22, 17], X[6, 7, 1, 8], X[4, 13, 5, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -11, 4, -10},
> {10, -1, 2, -3, -6, 7, 11, -4, -5, 9, -8, 6, -7, 5, -9, 8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(29/2) 2 3 4 4 3 2 -(15/2)
q - ----- + ----- - ----- + ----- - ----- + ----- - q -
27/2 25/2 23/2 21/2 19/2 17/2
q q q q q q
-(13/2) -(9/2)
> q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -2 -40 -36 -34 -32 -30 -28 2 2 3 2 -18
--- - q + q - q + q - q + q + --- + --- + --- + --- + q +
44 26 24 22 20
q q q q q
-16
> q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 169]][a, z] |
Out[8]= | 9 11 13
-3 a 5 a 2 a 9 11 13 9 3 11 3
----- + ----- - ----- - 20 a z + 22 a z - 5 a z - 37 a z + 24 a z -
z z z
13 3 9 5 11 5 9 7 11 7 9 9
> 2 a z - 28 a z + 9 a z - 9 a z + a z - a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 169]][a, z] |
Out[9]= | 9 11 13
10 12 16 3 a 5 a 2 a 9 11 13
-5 a - 5 a + a + ---- + ----- + ----- - 20 a z - 26 a z - 5 a z -
z z z
17 10 2 12 2 14 2 16 2 18 2 9 3
> a z + 22 a z + 24 a z - 3 a z - 3 a z + 2 a z + 37 a z +
11 3 13 3 15 3 17 3 10 4 12 4
> 45 a z + 3 a z - a z + 4 a z - 24 a z - 26 a z +
14 4 16 4 18 4 9 5 11 5 13 5 15 5
> 3 a z + 4 a z - a z - 28 a z - 33 a z - 2 a z + a z -
17 5 10 6 12 6 14 6 16 6 9 7
> 2 a z + 9 a z + 9 a z - 2 a z - 2 a z + 9 a z +
11 7 15 7 10 8 12 8 9 9 11 9
> 10 a z - a z - a z - a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -10 -8 1 1 1 2 1 2 2
q + q + ------- + ------- + ------- + ------ + ------ + ------ + ------ +
30 11 28 10 26 10 26 9 24 9 24 8 22 8
q t q t q t q t q t q t q t
2 2 2 3 1 2 1 1
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
22 7 20 7 20 6 18 6 20 5 18 5 16 5 16 4
q t q t q t q t q t q t q t q t
2 1 1
> ------ + ------ + ------
14 4 16 3 12 2
q t q t q t |