PD Presentation: |
X6172 X14,3,15,4 X11,20,12,21 X7,18,8,19 X17,22,18,13 X9,17,10,16 X15,11,16,10 X19,12,20,5 X21,8,22,9 X2536 X4,13,1,14 |
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, 348]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 348]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 3, 15, 4], X[11, 20, 12, 21], X[7, 18, 8, 19],
> X[17, 22, 18, 13], X[9, 17, 10, 16], X[15, 11, 16, 10], X[19, 12, 20, 5],
> X[21, 8, 22, 9], X[2, 5, 3, 6], X[4, 13, 1, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, -4, 9, -6, 7, -3, 8},
> {11, -2, -7, 6, -5, 4, -8, 3, -9, 5}] |
In[6]:= | Jones[L][q] |
Out[6]= | -10 2 2 2 -6 2 2 3 2
1 - q + -- - -- + -- + q + -- - -- + -- - -
9 8 7 4 3 2 q
q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -32 -30 -28 3 3 4 5 3 5 -12 2 -8
1 - q - q + q + --- + --- + --- + --- + --- + --- + q + --- + q
24 22 20 18 16 14 10
q q q q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 348]][a, z] |
Out[8]= | 4 6 8
2 4 6 8 10 a 2 a a 2 2 4 2 8 2
a + a - 3 a + 2 a - a + -- - ---- + -- + 3 a z - 2 a z + 2 a z +
2 2 2
z z z
2 4 4 4 4 6
> a z - 4 a z - a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 348]][a, z] |
Out[9]= | 4 6 8 5 7
2 4 6 8 10 a 2 a a 2 a 2 a 3
-a + 3 a + 11 a + 11 a + 3 a - -- - ---- - -- + ---- + ---- - a z -
2 2 2 z z
z z z
5 7 9 11 2 2 4 2 6 2
> 8 a z - 12 a z - 7 a z - 2 a z + 4 a z - a z - 24 a z -
8 2 10 2 3 3 5 3 7 3 9 3
> 29 a z - 10 a z + 6 a z + 14 a z + 16 a z + 14 a z +
11 3 2 4 4 4 6 4 8 4 10 4 3 5
> 6 a z - 4 a z - a z + 27 a z + 40 a z + 16 a z - 8 a z -
5 5 7 5 9 5 11 5 2 6 4 6 6 6
> 11 a z - a z - 3 a z - 5 a z + a z - 3 a z - 14 a z -
8 6 10 6 3 7 5 7 7 7 9 7 11 7
> 21 a z - 11 a z + 2 a z + 2 a z - 5 a z - 4 a z + a z +
4 8 6 8 8 8 10 8 7 9 9 9
> a z + 2 a z + 3 a z + 2 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 2 1 1 1 1 1 2 1
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
5 3 21 9 19 8 17 8 17 7 15 7 15 6 13 6
q q q t q t q t q t q t q t q t
1 1 2 3 5 2 2 2
> ------ + ------ + ------ + ------ + ------ + ----- + ------ + ----- +
15 5 13 5 11 5 13 4 11 4 9 4 11 3 9 3
q t q t q t q t q t q t q t q t
1 2 2 1 1 2 t t 2
> ----- + ----- + ----- + ----- + ---- + ---- + -- + - + q t
7 3 9 2 7 2 5 2 7 5 3 q
q t q t q t q t q t q t q |