PD Presentation: |
X8192 X2,9,3,10 X10,3,11,4 X7,16,8,17 X13,20,14,21 X15,22,16,7 X19,1,20,6 X18,11,19,12 X5,12,6,13 X21,14,22,15 X4,18,5,17 |
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[11, NonAlternating, 154]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 154]] |
Out[4]= | PD[X[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[7, 16, 8, 17],
> X[13, 20, 14, 21], X[15, 22, 16, 7], X[19, 1, 20, 6], X[18, 11, 19, 12],
> X[5, 12, 6, 13], X[21, 14, 22, 15], X[4, 18, 5, 17]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -11, -9, 7},
> {-4, -1, 2, -3, 8, 9, -5, 10, -6, 4, 11, -8, -7, 5, -10, 6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(23/2) 2 4 6 7 7 6 5 2 2
q - ----- + ----- - ----- + ----- - ----- + ----- - ---- + ---- - ----
21/2 19/2 17/2 15/2 13/2 11/2 9/2 7/2 5/2
q q q q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -34 2 -28 -24 2 -20 2 2 2 4 -10 2
-q - --- - q - q + --- - q + --- + --- + --- + --- + q + --
30 22 18 16 14 12 8
q q q q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 154]][a, z] |
Out[8]= | 5 7 9
-3 a 5 a 2 a 5 7 9 5 3 7 3
----- + ---- - ---- - 11 a z + 15 a z - 5 a z - 9 a z + 14 a z -
z z z
9 3 5 5 7 5 9 5 7 7
> 4 a z - 2 a z + 6 a z - a z + a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 154]][a, z] |
Out[9]= | 5 7 9
6 8 12 3 a 5 a 2 a 5 7 9
-5 a - 5 a + a + ---- + ---- + ---- - 13 a z - 20 a z - 5 a z +
z z z
11 6 2 8 2 12 2 14 2 5 3 7 3
> 2 a z + 13 a z + 20 a z - 5 a z + 2 a z + 12 a z + 30 a z +
9 3 11 3 13 3 6 4 8 4 10 4 12 4
> 6 a z - 9 a z + 3 a z - 9 a z - 21 a z - 5 a z + 6 a z -
14 4 5 5 7 5 9 5 11 5 13 5 6 6
> a z - 3 a z - 17 a z - 5 a z + 7 a z - 2 a z + 4 a z +
8 6 10 6 12 6 7 7 9 7 11 7 6 8
> 11 a z + 4 a z - 3 a z + 5 a z + 2 a z - 3 a z - a z -
8 8 10 8 7 9 9 9
> 3 a z - 2 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -6 2 1 1 1 3 1 3 3
q + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 24 9 22 8 20 8 20 7 18 7 18 6 16 6
q q t q t q t q t q t q t q t
4 3 3 4 3 3 2 4
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ----- +
16 5 14 5 14 4 12 4 12 3 10 3 10 2 8 2
q t q t q t q t q t q t q t q t
1 1
> ---- + ----
8 6
q t q t |