PD Presentation: |
X12,1,13,2 X2,13,3,14 X14,3,15,4 X18,7,19,8 X8,11,9,12 X20,10,21,9 X22,20,11,19 X10,22,1,21 X4,17,5,18 X16,5,17,6 X6,15,7,16 |
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, 368]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 368]] |
Out[4]= | PD[X[12, 1, 13, 2], X[2, 13, 3, 14], X[14, 3, 15, 4], X[18, 7, 19, 8],
> X[8, 11, 9, 12], X[20, 10, 21, 9], X[22, 20, 11, 19], X[10, 22, 1, 21],
> X[4, 17, 5, 18], X[16, 5, 17, 6], X[6, 15, 7, 16]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -9, 10, -11, 4, -5, 6, -8},
> {5, -1, 2, -3, 11, -10, 9, -4, 7, -6, 8, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(19/2) 2 4 7 10 11 12 10 8
-q + ----- - ----- + ----- - ----- + ---- - ---- + ---- - ---- +
17/2 15/2 13/2 11/2 9/2 7/2 5/2 3/2
q q q q q q q q
5 3/2
> ------- - 3 Sqrt[q] + q
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -28 -24 -22 -20 2 -16 2 2 3 2 -4 2 4
q + q + q - q + --- - q + --- + --- + -- - -- + q + q - q
18 14 12 8 6
q q q q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 368]][a, z] |
Out[8]= | 5 7
a a 3 5 7 3 3 3 5 3
-(--) + -- + a z - a z - 7 a z + 4 a z + 3 a z - 4 a z - 9 a z +
z z
7 3 5 3 5 5 5 7 5 3 7 5 7
> 4 a z + a z - 4 a z - 5 a z + a z - a z - a z |
In[9]:= | Kauffman[Link[11, Alternating, 368]][a, z] |
Out[9]= | 5 7
6 a a 5 7 9 11 2 2 2
-a + -- + -- + a z - 9 a z - 7 a z - a z - 2 a z - z + 2 a z +
z z
4 2 6 2 8 2 10 2 3 3 3 5 3
> 6 a z + 7 a z + a z - 3 a z - 7 a z + a z + 24 a z +
7 3 9 3 11 3 4 2 4 4 4 6 4
> 15 a z + 2 a z + 3 a z + 3 z - 10 a z - 17 a z - 10 a z -
8 4 10 4 5 3 5 5 5 7 5 9 5
> a z + 5 a z + 10 a z - 5 a z - 31 a z - 13 a z + 2 a z -
11 5 6 2 6 4 6 6 6 8 6 10 6 7
> a z - z + 13 a z + 13 a z + 3 a z + 2 a z - 2 a z - 3 a z +
3 7 5 7 7 7 9 7 2 8 4 8 8 8
> 8 a z + 18 a z + 5 a z - 2 a z - 4 a z - 2 a z - 2 a z -
3 9 5 9 7 9 4 10 6 10
> 3 a z - 5 a z - 2 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 4 5 1 1 1 3 2 5 2
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 2 20 8 18 7 16 7 16 6 14 6 14 5 12 5
q q q t q t q t q t q t q t q t
5 5 6 5 6 6 4 6
> ------ + ------ + ------ + ----- + ----- + ----- + ---- + ---- + 3 t +
12 4 10 4 10 3 8 3 8 2 6 2 6 4
q t q t q t q t q t q t q t q t
2 t 2 2 2 4 3
> --- + t + 2 q t + q t
2
q |