PD Presentation: |
X6172 X12,3,13,4 X18,13,19,14 X22,17,11,18 X16,7,17,8 X8,22,9,21 X20,10,21,9 X10,15,5,16 X14,19,15,20 X2536 X4,11,1,12 |
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, 422]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 422]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[18, 13, 19, 14], X[22, 17, 11, 18],
> X[16, 7, 17, 8], X[8, 22, 9, 21], X[20, 10, 21, 9], X[10, 15, 5, 16],
> X[14, 19, 15, 20], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 5, -6, 7, -8},
> {11, -2, 3, -9, 8, -5, 4, -3, 9, -7, 6, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | -11 3 8 14 19 23 22 21 14 10 4
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 5 -26 -24 2 7 -18 8 6 3
1 - q - q - --- + q + q - --- + --- + q + --- + --- + --- +
28 22 20 16 14 12
q q q q q q
8 2 3 -4 2
> --- - -- + -- + q - --
10 8 6 2
q q q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 422]][a, z] |
Out[8]= | 4 6 8 10
4 6 8 10 2 a 5 a 4 a a 2 2 4 2
7 a - 14 a + 9 a - 2 a + ---- - ---- + ---- - --- + a z + 6 a z -
2 2 2 2
z z z z
6 2 8 2 10 2 2 4 6 4 8 4 4 6 6 6
> 13 a z + 8 a z - a z + a z - 7 a z + 3 a z - a z - 2 a z |
In[9]:= | Kauffman[Link[11, Alternating, 422]][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
9 a + 21 a + 18 a + 5 a - ---- - ---- - ---- - --- + ---- + ---- + ---- +
2 2 2 2 z z z
z z z z
11
a 5 7 9 11 13 2 2 4 2
> --- - 13 a z - 29 a z - 21 a z - 4 a z + a z + a z - 14 a z -
z
6 2 8 2 10 2 12 2 3 3 5 3 7 3
> 47 a z - 44 a z - 11 a z + a z + 3 a z + 13 a z + 34 a z +
9 3 11 3 13 3 2 4 4 4 6 4 8 4
> 33 a z + 7 a z - 2 a z - 2 a z + 18 a z + 67 a z + 65 a z +
10 4 12 4 3 5 5 5 7 5 9 5 11 5
> 14 a z - 4 a z - 8 a z - 5 a z - 7 a z - 20 a z - 9 a z +
13 5 2 6 4 6 6 6 8 6 10 6 12 6
> a z + a z - 20 a z - 56 a z - 51 a z - 13 a z + 3 a z +
3 7 5 7 7 7 11 7 4 8 6 8 8 8
> 4 a z - 10 a z - 20 a z + 6 a z + 8 a z + 16 a z + 16 a z +
10 8 5 9 7 9 9 9 6 10 8 10
> 8 a z + 7 a z + 13 a z + 6 a z + 2 a z + 2 a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 4 7 1 2 1 6 2 8 6
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
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
11 8 12 12 11 11 10 13 6
> ------ + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ---- +
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
8 t 3 t 2
> ---- + -- + --- + q t
5 3 q
q t q |