PD Presentation: |
X6172 X12,3,13,4 X22,13,5,14 X14,7,15,8 X20,18,21,17 X10,15,11,16 X8,19,9,20 X18,9,19,10 X16,22,17,21 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]= | 2 |
In[3]:= | Show[DrawMorseLink[Link[11, Alternating, 62]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 62]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[22, 13, 5, 14], X[14, 7, 15, 8],
> X[20, 18, 21, 17], X[10, 15, 11, 16], X[8, 19, 9, 20], X[18, 9, 19, 10],
> X[16, 22, 17, 21], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 4, -7, 8, -6, 11, -2, 3, -4, 6, -9, 5, -8,
> 7, -5, 9, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(21/2) 3 7 12 16 20 20 18 13 9
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
4
> ------- - Sqrt[q]
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -34 2 -30 2 5 4 2 3 2 -10 4 3
-2 - q - --- + q - --- + --- + --- - --- + --- - --- + q + -- - -- +
32 26 24 18 16 14 12 8 6
q q q q q q q q q
4 2
> -- + q
4
q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 62]][a, z] |
Out[8]= | 3 5 7 9 11
a 2 a 3 a 3 a a 3 5 7 9 3
-(--) + ---- - ---- + ---- - --- - 3 a z + 4 a z - 7 a z + 4 a z - a z -
z z z z z
3 3 5 3 7 3 3 5 5 5
> a z + 3 a z - 5 a z + a z + 2 a z |
In[9]:= | Kauffman[Link[11, Alternating, 62]][a, z] |
Out[9]= | 3 5 7 9 11
6 10 12 a 2 a 3 a 3 a a 3 5
-2 a + 2 a + a - -- - ---- - ---- - ---- - --- + 4 a z + 10 a z +
z z z z z
7 9 11 4 2 6 2 8 2 10 2
> 16 a z + 13 a z + 3 a z + 4 a z + 13 a z + 6 a z - 6 a z -
12 2 3 3 3 5 3 7 3 9 3 11 3
> 3 a z + a z - 8 a z - 24 a z - 31 a z - 23 a z - 7 a z +
2 4 4 4 6 4 8 4 10 4 12 4 5
> 5 a z - 12 a z - 38 a z - 21 a z + 3 a z + 3 a z - a z +
3 5 5 5 7 5 9 5 11 5 2 6 4 6
> 14 a z + 22 a z + 20 a z + 21 a z + 8 a z - 4 a z + 16 a z +
6 6 8 6 10 6 12 6 3 7 5 7 7 7
> 41 a z + 28 a z + 6 a z - a z - 8 a z - 3 a z + 5 a z -
9 7 11 7 4 8 6 8 8 8 10 8 5 9
> 3 a z - 3 a z - 9 a z - 16 a z - 11 a z - 4 a z - 5 a z -
7 9 9 9 6 10 8 10
> 8 a z - 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 4 6 1 2 1 5 2 7 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 7 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
> ---- + 3 t + -- + q t
4 2
q t q |