PD Presentation: |
X6172 X14,7,15,8 X4,15,1,16 X5,12,6,13 X3849 X9,16,10,17 X17,19,18,22 X11,20,12,21 X19,10,20,11 X21,5,22,18 X13,2,14,3 |
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, 385]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 385]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 7, 15, 8], X[4, 15, 1, 16], X[5, 12, 6, 13],
> X[3, 8, 4, 9], X[9, 16, 10, 17], X[17, 19, 18, 22], X[11, 20, 12, 21],
> X[19, 10, 20, 11], X[21, 5, 22, 18], X[13, 2, 14, 3]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, 11, -5, -3}, {-9, 8, -10, 7},
> {-4, -1, 2, 5, -6, 9, -8, 4, -11, -2, 3, 6, -7, 10}] |
In[6]:= | Jones[L][q] |
Out[6]= | -10 -9 -8 2 2 3 -4 3 -2 1
-q + q - q + -- - -- + -- - q + -- - q + -
7 6 5 3 q
q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -34 2 2 -26 2 2 5 5 6 5 4 2 -6
-q - --- - --- - q + --- + --- + --- + --- + --- + --- + --- + -- + q +
30 28 22 20 18 16 14 12 10 8
q q q q q q q q q q
-4
> q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 385]][a, z] |
Out[8]= | 4 6 8 10
4 6 8 10 2 a 5 a 4 a a 4 2 6 2
8 a - 16 a + 10 a - 2 a + ---- - ---- + ---- - --- + 11 a z - 21 a z +
2 2 2 2
z z z z
8 2 10 2 4 4 6 4 8 4 4 6 6 6
> 11 a z - a z + 6 a z - 17 a z + 6 a z + a z - 7 a z +
8 6 6 8
> a z - a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 385]][a, z] |
Out[9]= | 4 6 8 10 5 7 9
4 6 8 10 2 a 5 a 4 a a 5 a 9 a 5 a
10 a + 22 a + 17 a + 4 a - ---- - ---- - ---- - --- + ---- + ---- + ---- +
2 2 2 2 z z z
z z z z
11
a 5 7 9 11 13 4 2 6 2
> --- - 15 a z - 29 a z - 17 a z - 2 a z + a z - 19 a z - 47 a z -
z
8 2 10 2 12 2 5 3 7 3 9 3 11 3
> 36 a z - 7 a z + a z + 12 a z + 30 a z + 19 a z + a z +
4 4 6 4 8 4 10 4 5 5 7 5 9 5
> 17 a z + 54 a z + 39 a z + 2 a z + 3 a z - 8 a z - 11 a z -
4 6 6 6 8 6 5 7 7 7 9 7 4 8
> 7 a z - 26 a z - 19 a z - 5 a z - 3 a z + 2 a z + a z +
6 8 8 8 5 9 7 9
> 4 a z + 3 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 3 1 1 1 2 1 2 1
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
7 5 21 7 19 7 19 6 17 6 15 6 17 5 15 5
q q q t q t q t q t q t q t q t
1 1 4 2 3 2 1 3
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ----- +
13 5 15 4 13 4 11 4 13 3 11 3 11 2 9 2
q t q t q t q t q t q t q t q t
2
1 1 1 t t
> ----- + ---- + ---- + -- + --
7 2 9 7 5 q
q t q t q t q |