PD Presentation: |
X12,1,13,2 X16,7,17,8 X10,5,1,6 X6374 X4,9,5,10 X20,17,11,18 X18,13,19,14 X14,19,15,20 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[10, Alternating, 108]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 108]] |
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, 17, 11, 18], X[18, 13, 19, 14], X[14, 19, 15, 20],
> X[2, 11, 3, 12], X[8, 15, 9, 16]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 4, -5, 3, -4, 2, -10, 5, -3},
> {9, -1, 7, -8, 10, -2, 6, -7, 8, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(25/2) 3 6 11 13 14 14 10 8
-q + ----- - ----- + ----- - ----- + ----- - ----- + ----- - ---- +
23/2 21/2 19/2 17/2 15/2 13/2 11/2 9/2
q q q q q q q q
3 -(5/2)
> ---- - q
7/2
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -40 2 -36 2 -32 6 -28 -24 6 -20 6 -16
q + --- - q - --- - q - --- - q + q + --- + q + --- + q +
38 34 30 22 18
q q q q q
3 2 -8
> --- - --- + q
12 10
q q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 108]][a, z] |
Out[8]= | 7 9 11 13
-4 a 8 a 5 a a 5 7 9 11 5 3
----- + ---- - ----- + --- - a z - 11 a z + 14 a z - 4 a z - 2 a z -
z z z z
7 3 9 3 5 5 7 5
> 10 a z + 6 a z - a z - 3 a z |
In[9]:= | Kauffman[Link[10, Alternating, 108]][a, z] |
Out[9]= | 7 9 11 13
8 10 12 14 4 a 8 a 5 a a 5 7
8 a + 14 a + 9 a + 2 a - ---- - ---- - ----- - --- - a z + 12 a z +
z z z z
9 11 13 15 6 2 8 2 10 2
> 22 a z + 9 a z - a z - a z - a z - 19 a z - 35 a z -
12 2 14 2 5 3 7 3 9 3 11 3 13 3
> 22 a z - 5 a z + 2 a z - 15 a z - 32 a z - 16 a z + a z +
15 3 6 4 8 4 10 4 12 4 14 4 5 5
> 2 a z + 4 a z + 18 a z + 29 a z + 21 a z + 6 a z - a z +
7 5 9 5 11 5 13 5 15 5 6 6 8 6
> 13 a z + 32 a z + 23 a z + 4 a z - a z - 3 a z - 2 a z -
10 6 12 6 14 6 7 7 9 7 11 7 13 7
> a z - 5 a z - 3 a z - 6 a z - 13 a z - 11 a z - 4 a z -
8 8 10 8 12 8 9 9 11 9
> 4 a z - 7 a z - 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -6 -4 1 2 1 4 2 7 4
q + q + ------- + ------ + ------ + ------ + ------ + ------ + ------ +
26 10 24 9 22 9 22 8 20 8 20 7 18 7
q t q t q t q t q t q t q t
6 7 8 6 6 9 5 5
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
18 6 16 6 16 5 14 5 14 4 12 4 12 3 10 3
q t q t q t q t q t q t q t q t
3 5 3
> ------ + ----- + ----
10 2 8 2 6
q t q t q t |