PD Presentation: |
X8192 X2,9,3,10 X10,3,11,4 X16,5,17,6 X14,7,15,8 X18,11,19,12 X20,15,7,16 X12,17,13,18 X4,13,5,14 X6,19,1,20 |
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, 77]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 77]] |
Out[4]= | PD[X[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[16, 5, 17, 6],
> X[14, 7, 15, 8], X[18, 11, 19, 12], X[20, 15, 7, 16], X[12, 17, 13, 18],
> X[4, 13, 5, 14], X[6, 19, 1, 20]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -9, 4, -10},
> {5, -1, 2, -3, 6, -8, 9, -5, 7, -4, 8, -6, 10, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(25/2) 3 6 10 12 13 13 9 7
-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]= | -38 -36 -34 -32 3 -28 4 5 -16 2 2 -8
q - q - q + q - --- + q + --- + --- + q + --- - --- + q
30 22 18 12 10
q q q q q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 77]][a, z] |
Out[8]= | 7 9 11
-2 a 3 a a 7 9 11 5 3 7 3 11 3
----- + ---- - --- - 9 a z + 5 a z + a z - 2 a z - 10 a z + a z -
z z z
5 5 7 5 9 5
> a z - 3 a z - a z |
In[9]:= | Kauffman[Link[10, Alternating, 77]][a, z] |
Out[9]= | 7 9 11
8 10 12 2 a 3 a a 7 9 13 15
3 a + 3 a + a - ---- - ---- - --- + 9 a z + 9 a z - a z - a z -
z z z
8 2 10 2 12 2 14 2 5 3 7 3 9 3
> 4 a z + 2 a z + 3 a z - 3 a z + 2 a z - 17 a z - 19 a z -
11 3 13 3 15 3 6 4 8 4 10 4 12 4
> a z + a z + 2 a z + 5 a z - 4 a z - 18 a z - 3 a z +
14 4 5 5 7 5 9 5 11 5 13 5 15 5
> 6 a z - a z + 16 a z + 16 a z + 5 a z + 5 a z - a z -
6 6 8 6 10 6 12 6 14 6 7 7 9 7
> 3 a z + 9 a z + 20 a z + 5 a z - 3 a z - 6 a z - 4 a z -
11 7 13 7 8 8 10 8 12 8 9 9 11 9
> 2 a z - 4 a z - 5 a z - 9 a z - 4 a z - 2 a z - 2 a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -6 -4 1 2 1 4 2 6 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 5 5 8 4 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 4 3
> ------ + ----- + ----
10 2 8 2 6
q t q t q t |