PD Presentation: |
X6172 X2,16,3,15 X3,10,4,11 X5,14,6,15 X11,20,12,13 X13,12,14,5 X19,1,20,4 X8,17,9,18 X16,7,17,8 X18,9,19,10 |
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[10, NonAlternating, 81]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, NonAlternating, 81]] |
Out[4]= | PD[X[6, 1, 7, 2], X[2, 16, 3, 15], X[3, 10, 4, 11], X[5, 14, 6, 15],
> X[11, 20, 12, 13], X[13, 12, 14, 5], X[19, 1, 20, 4], X[8, 17, 9, 18],
> X[16, 7, 17, 8], X[18, 9, 19, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, -3, 7}, {-4, -1, 9, -8, 10, 3, -5, 6},
> {-6, 4, 2, -9, 8, -10, -7, 5}] |
In[6]:= | Jones[L][q] |
Out[6]= | -10 2 5 6 6 6 6 2 2
q - -- + -- - -- + -- - -- + -- - -- + --
9 8 7 6 5 4 3 2
q q q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -30 3 3 -22 2 -18 3 3 4 5 -8 2
q + --- + --- + q + --- - q + --- + --- + --- + --- + q + --
26 24 20 16 14 12 10 6
q q q q q q q q |
In[8]:= | HOMFLYPT[Link[10, NonAlternating, 81]][a, z] |
Out[8]= | 4 6 8
4 6 8 a 2 a a 4 2 6 2 8 2 4 4
7 a - 11 a + 4 a + -- - ---- + -- + 7 a z - 11 a z + 3 a z + 2 a z -
2 2 2
z z z
6 4 8 4 6 6
> 5 a z + a z - a z |
In[9]:= | Kauffman[Link[10, NonAlternating, 81]][a, z] |
Out[9]= | 4 6 8 5 7
4 6 8 12 a 2 a a 2 a 2 a 5 7
8 a + 13 a + 5 a + a - -- - ---- - -- + ---- + ---- - 11 a z - 11 a z -
2 2 2 z z
z z z
4 2 6 2 8 2 10 2 12 2 5 3 7 3
> 9 a z - 20 a z - 7 a z + 2 a z - 2 a z + 9 a z + 9 a z -
9 3 11 3 4 4 6 4 8 4 10 4 12 4
> 2 a z - 2 a z + 3 a z + 12 a z + 4 a z - 4 a z + a z -
5 5 7 5 11 5 6 6 10 6 5 7 7 7
> 3 a z - 5 a z + 2 a z - 3 a z + 3 a z + a z + 3 a z +
9 7 6 8 8 8
> 2 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 2 1 1 2 3 2 3 3
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
5 3 21 8 19 8 19 7 17 6 15 6 15 5 13 5
q q q t q t q t q t q t q t q t
3 4 4 2 2 4 2
> ------ + ------ + ------ + ----- + ----- + ----- + ----
13 4 11 4 11 3 9 3 9 2 7 2 5
q t q t q t q t q t q t q t |