PD Presentation: |
X6172 X14,3,15,4 X12,15,5,16 X8,17,9,18 X16,7,17,8 X18,9,19,10 X22,19,13,20 X20,12,21,11 X10,22,11,21 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, Alternating, 440]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 440]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 3, 15, 4], X[12, 15, 5, 16], X[8, 17, 9, 18],
> X[16, 7, 17, 8], X[18, 9, 19, 10], X[22, 19, 13, 20], X[20, 12, 21, 11],
> X[10, 22, 11, 21], X[2, 5, 3, 6], X[4, 13, 1, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 5, -4, 6, -9, 8, -3},
> {11, -2, 3, -5, 4, -6, 7, -8, 9, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -11 3 6 10 13 17 15 14 10 7 3
1 - q + --- - -- + -- - -- + -- - -- + -- - -- + -- - -
10 9 8 7 6 5 4 3 2 q
q q q q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -34 -32 -30 -28 3 3 -22 6 -18 5 3
1 - q - q + q - q + --- + --- + q + --- + q + --- + --- +
26 24 20 16 14
q q q q q
-12 5 -8 2 -2
> q + --- - q + -- - q
10 6
q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 440]][a, z] |
Out[8]= | 4 6 8
4 6 8 10 a 2 a a 2 2 4 2 6 2
5 a - 9 a + 6 a - 2 a + -- - ---- + -- + 2 a z + 5 a z - 12 a z +
2 2 2
z z z
8 2 10 2 2 4 4 4 6 4 8 4 4 6 6 6
> 9 a z - a z + a z - a z - 8 a z + 3 a z - a z - 2 a z |
In[9]:= | Kauffman[Link[11, Alternating, 440]][a, z] |
Out[9]= | 4 6 8 5 7
4 6 8 12 a 2 a a 2 a 2 a 5 7
6 a + 13 a + 9 a - a - -- - ---- - -- + ---- + ---- - 5 a z - 8 a z -
2 2 2 z z
z z z
9 11 13 2 2 4 2 6 2 8 2
> 3 a z + a z + a z + 2 a z - 14 a z - 38 a z - 23 a z +
10 2 12 2 3 3 5 3 7 3 9 3 11 3
> 2 a z + 3 a z + 4 a z + 3 a z + 7 a z + 9 a z - a z -
13 3 2 4 4 4 6 4 8 4 10 4 12 4
> 2 a z - 3 a z + 16 a z + 54 a z + 38 a z - 3 a z - 6 a z -
3 5 5 5 7 5 9 5 11 5 13 5 2 6
> 8 a z + 2 a z + 9 a z - 7 a z - 5 a z + a z + a z -
4 6 6 6 8 6 10 6 12 6 3 7 5 7
> 15 a z - 37 a z - 27 a z - 3 a z + 3 a z + 3 a z - 8 a z -
7 7 11 7 4 8 6 8 8 8 10 8 5 9
> 15 a z + 4 a z + 5 a z + 9 a z + 8 a z + 4 a z + 4 a z +
7 9 9 9 6 10 8 10
> 7 a z + 3 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 5 1 2 1 4 2 6 4
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
5 3 23 9 21 8 19 8 19 7 17 7 17 6 15 6
q q q t q t q t q t q t q t q t
7 6 10 10 8 7 6 8 4
> ------ + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ---- +
15 5 13 5 13 4 11 4 11 3 9 3 9 2 7 2 7
q t q t q t q t q t q t q t q t q t
6 t 2 t 2
> ---- + -- + --- + q t
5 3 q
q t q |