PD Presentation: |
X6172 X5,14,6,15 X3849 X2,16,3,15 X16,7,17,8 X9,18,10,19 X11,21,12,20 X19,22,20,13 X13,12,14,5 X17,1,18,4 X21,11,22,10 |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Length[Skeleton[L]] |
Out[2]= | 3 |
In[3]:= | Show[DrawMorseLink[Link[11, NonAlternating, 324]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 324]] |
Out[4]= | PD[X[6, 1, 7, 2], X[5, 14, 6, 15], X[3, 8, 4, 9], X[2, 16, 3, 15],
> X[16, 7, 17, 8], X[9, 18, 10, 19], X[11, 21, 12, 20], X[19, 22, 20, 13],
> X[13, 12, 14, 5], X[17, 1, 18, 4], X[21, 11, 22, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -4, -3, 10}, {-2, -1, 5, 3, -6, 11, -7, 9},
> {-9, 2, 4, -5, -10, 6, -8, 7, -11, 8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -8 2 3 6 7 8 6 6
-3 - q + -- - -- + -- - -- + -- - -- + - + 2 q
7 6 5 4 3 2 q
q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -24 -20 3 -14 4 3 3 4 -4 4 2 4
2 - q - q + --- + q + --- + --- + -- + -- + q + -- + 2 q + 2 q
16 12 10 8 6 2
q q q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 324]][a, z] |
Out[8]= | 2 4
2 4 6 -2 2 a a 2 2 2 4 2
4 - 9 a + 7 a - 2 a + z - ---- + -- + 2 z - 10 a z + 10 a z -
2 2
z z
6 2 2 4 4 4 6 4 4 6
> 3 a z - 3 a z + 5 a z - a z + a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 324]][a, z] |
Out[9]= | 2 4 3
2 4 8 -2 2 a a 2 a 2 a 3
6 + 13 a + 9 a - a - z - ---- - -- + --- + ---- - 5 a z - 8 a z -
2 2 z z
z z
5 7 9 2 2 2 4 2 6 2 8 2
> 3 a z + a z + a z - 8 z - 31 a z - 26 a z + a z + 4 a z +
3 3 3 5 3 9 3 4 2 4 4 4 6 4
> a z + 6 a z + 8 a z - 3 a z + 3 z + 25 a z + 32 a z + 4 a z -
8 4 5 3 5 5 5 7 5 9 5 2 6 4 6
> 6 a z - a z + 2 a z - 2 a z - 4 a z + a z - 9 a z - 16 a z -
6 6 8 6 7 3 7 5 7 7 7 2 8 4 8
> 5 a z + 2 a z + a z - 2 a z - a z + 2 a z + 2 a z + 4 a z +
6 8 3 9 5 9
> 2 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 4 5 1 1 1 2 1 4 3 4
-- + - + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
3 q 17 7 15 6 13 6 13 5 11 5 11 4 9 4 9 3
q q t q t q t q t q t q t q t q t
3 4 4 2 4 2 t 3 2
> ----- + ----- + ----- + ---- + ---- + --- + q t + 2 q t
7 3 7 2 5 2 5 3 q
q t q t q t q t q t |