PD Presentation: |
X6172 X12,3,13,4 X20,13,21,14 X16,7,17,8 X8,19,9,20 X18,9,19,10 X10,17,11,18 X22,15,5,16 X14,21,15,22 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, 73]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 73]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[20, 13, 21, 14], X[16, 7, 17, 8],
> X[8, 19, 9, 20], X[18, 9, 19, 10], X[10, 17, 11, 18], X[22, 15, 5, 16],
> X[14, 21, 15, 22], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 4, -5, 6, -7, 11, -2, 3, -9, 8, -4, 7, -6,
> 5, -3, 9, -8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(27/2) 2 6 10 13 16 16 15 10
q - ----- + ----- - ----- + ----- - ----- + ----- - ----- + ----- -
25/2 23/2 21/2 19/2 17/2 15/2 13/2 11/2
q q q q q q q q
7 3 -(5/2)
> ---- + ---- - q
9/2 7/2
q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -42 2 -38 4 -34 3 5 -26 -24 3 -20 5
-q - --- - q - --- - q + --- + --- + q + q + --- - q + --- +
40 36 32 28 22 18
q q q q q q
2 2 -8
> --- - --- + q
12 10
q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 73]][a, z] |
Out[8]= | 7 9 11 13
a a 4 a 2 a 7 9 11 13 5 3
-(--) - -- + ----- - ----- - 7 a z - a z + 7 a z - a z - 2 a z -
z z z z
7 3 9 3 11 3 5 5 7 5 9 5
> 9 a z - 4 a z + 3 a z - a z - 3 a z - 2 a z |
In[9]:= | Kauffman[Link[11, Alternating, 73]][a, z] |
Out[9]= | 7 9 11 13
8 10 12 14 16 a a 4 a 2 a 7 9
a - 5 a - 6 a + a + 2 a - -- + -- + ----- + ----- + 7 a z - 2 a z -
z z z z
11 13 15 10 2 12 2 14 2 16 2
> 17 a z - 9 a z - a z + 22 a z + 25 a z - 2 a z - 5 a z +
5 3 7 3 9 3 11 3 13 3 15 3 6 4
> 2 a z - 15 a z - 4 a z + 31 a z + 16 a z - 2 a z + 5 a z -
8 4 10 4 12 4 14 4 16 4 5 5 7 5
> 9 a z - 41 a z - 32 a z - a z + 4 a z - a z + 15 a z +
9 5 11 5 13 5 15 5 6 6 8 6 10 6
> a z - 29 a z - 9 a z + 5 a z - 3 a z + 12 a z + 30 a z +
12 6 14 6 16 6 7 7 9 7 11 7 13 7
> 22 a z + 6 a z - a z - 6 a z + 4 a z + 18 a z + 6 a z -
15 7 8 8 10 8 12 8 14 8 9 9 11 9
> 2 a z - 6 a z - 9 a z - 6 a z - 3 a z - 4 a z - 7 a z -
13 9 10 10 12 10
> 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -6 -4 1 1 1 5 1 5 5
q + q + ------- + ------- + ------- + ------ + ------ + ------ + ------ +
28 11 26 10 24 10 24 9 22 9 22 8 20 8
q t q t q t q t q t q t q t
8 5 8 8 8 8 7 9
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
20 7 18 7 18 6 16 6 16 5 14 5 14 4 12 4
q t q t q t q t q t q t q t q t
4 6 3 4 3
> ------ + ------ + ------ + ----- + ----
12 3 10 3 10 2 8 2 6
q t q t q t q t q t |