PD Presentation: |
X12,1,13,2 X16,7,17,8 X10,5,1,6 X6374 X4,9,5,10 X20,14,21,13 X22,17,11,18 X18,21,19,22 X14,20,15,19 X2,11,3,12 X8,15,9,16 |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Length[Skeleton[L]] |
Out[2]= | 2 |
In[3]:= | Show[DrawMorseLink[Link[11, Alternating, 342]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 342]] |
Out[4]= | PD[X[12, 1, 13, 2], X[16, 7, 17, 8], X[10, 5, 1, 6], X[6, 3, 7, 4],
> X[4, 9, 5, 10], X[20, 14, 21, 13], X[22, 17, 11, 18], X[18, 21, 19, 22],
> X[14, 20, 15, 19], X[2, 11, 3, 12], X[8, 15, 9, 16]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 4, -5, 3, -4, 2, -11, 5, -3},
> {10, -1, 6, -9, 11, -2, 7, -8, 9, -6, 8, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(21/2) 3 7 13 17 20 20 18 13 8
q - ----- + ----- - ----- + ----- - ----- + ---- - ---- + ---- - ---- +
19/2 17/2 15/2 13/2 11/2 9/2 7/2 5/2 3/2
q q q q q q q q q
3
> ------- - Sqrt[q]
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -34 2 -30 -28 -26 6 -20 2 4 3 2
-1 - q - --- + q + q - q + --- - q + --- - --- + --- - --- +
32 24 18 16 14 12
q q q q q q
2 4 3 4 2
> --- + -- - -- + -- + q
10 8 6 4
q q q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 342]][a, z] |
Out[8]= | 3 5 7 9 11
-2 a 5 a 6 a 4 a a 3 5 7 9
----- + ---- - ---- + ---- - --- - a z - 4 a z + 10 a z - 11 a z + 4 a z -
z z z z z
3 3 3 5 3 7 3 3 5 5 5
> a z - a z + 8 a z - 6 a z + a z + 3 a z |
In[9]:= | Kauffman[Link[11, Alternating, 342]][a, z] |
Out[9]= | 3 5 7 9 11
4 6 8 10 12 2 a 5 a 6 a 4 a a 3
a + a + 3 a + 3 a + a - ---- - ---- - ---- - ---- - --- - a z + 7 a z +
z z z z z
5 7 9 11 2 2 8 2 10 2
> 23 a z + 29 a z + 18 a z + 4 a z - a z - 7 a z - 9 a z -
12 2 3 3 3 5 3 7 3 9 3 11 3
> 3 a z + 2 a z - 10 a z - 41 a z - 52 a z - 31 a z - 8 a z +
2 4 4 4 6 4 8 4 10 4 12 4 5
> 4 a z - 5 a z - 15 a z - 4 a z + 5 a z + 3 a z - a z +
3 5 5 5 7 5 9 5 11 5 2 6 4 6
> 10 a z + 33 a z + 41 a z + 27 a z + 8 a z - 3 a z + 9 a z +
6 6 8 6 10 6 12 6 3 7 5 7 7 7
> 28 a z + 22 a z + 5 a z - a z - 6 a z - 8 a z - 4 a z -
9 7 11 7 4 8 6 8 8 8 10 8 5 9
> 5 a z - 3 a z - 7 a z - 14 a z - 11 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 6 1 2 1 5 2 8 5
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 2 22 9 20 8 18 8 18 7 16 7 16 6 14 6
q q q t q t q t q t q t q t q t
9 8 11 10 10 10 8 10 5
> ------ + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ---- +
14 5 12 5 12 4 10 4 10 3 8 3 8 2 6 2 6
q t q t q t q t q t q t q t q t q t
8 t 2 2
> ---- + 2 t + -- + q t
4 2
q t q |