PD Presentation: |
X8192 X10,3,11,4 X12,17,13,18 X14,5,15,6 X4,13,5,14 X18,11,19,12 X22,19,7,20 X20,15,21,16 X16,21,17,22 X2738 X6,9,1,10 |
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, 152]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 152]] |
Out[4]= | PD[X[8, 1, 9, 2], X[10, 3, 11, 4], X[12, 17, 13, 18], X[14, 5, 15, 6],
> X[4, 13, 5, 14], X[18, 11, 19, 12], X[22, 19, 7, 20], X[20, 15, 21, 16],
> X[16, 21, 17, 22], X[2, 7, 3, 8], X[6, 9, 1, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -5, 4, -11},
> {10, -1, 11, -2, 6, -3, 5, -4, 8, -9, 3, -6, 7, -8, 9, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(27/2) 3 7 12 16 19 19 17 12
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
8 3 -(5/2)
> ---- + ---- - q
9/2 7/2
q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -42 -40 -38 3 3 2 4 -24 3 2 5 -16
-q - q + q - --- + --- - --- + --- + q + --- - --- + --- - q +
36 32 30 28 22 20 18
q q q q q q q
3 2 -8
> --- - --- + q
12 10
q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 152]][a, z] |
Out[8]= | 7 11 13
a 2 a a 5 7 11 13 5 3 7 3
-(--) + ----- - --- - a z - 6 a z + 5 a z - a z - 2 a z - 8 a z -
z z z
9 3 11 3 5 5 7 5 9 5
> 3 a z + 3 a z - a z - 3 a z - 2 a z |
In[9]:= | Kauffman[Link[11, Alternating, 152]][a, z] |
Out[9]= | 7 11 13
8 10 12 14 a 2 a a 5 7 9
a - 3 a - 5 a - 2 a - -- + ----- + --- - a z + 7 a z + 3 a z -
z z z
11 13 15 6 2 8 2 10 2 12 2
> 6 a z + a z + 2 a z - a z - 4 a z + 13 a z + 25 a z +
14 2 16 2 5 3 7 3 9 3 11 3 13 3
> 7 a z - 2 a z + 2 a z - 11 a z - 11 a z + a z - 7 a z -
15 3 6 4 8 4 10 4 12 4 14 4
> 6 a z + 4 a z + 3 a z - 30 a z - 44 a z - 12 a z +
16 4 5 5 7 5 9 5 13 5 15 5 6 6
> 3 a z - a z + 11 a z + 14 a z + 6 a z + 8 a z - 3 a z +
8 6 10 6 12 6 14 6 16 6 7 7 9 7
> 5 a z + 32 a z + 38 a z + 13 a z - a z - 6 a z - 3 a z +
11 7 13 7 15 7 8 8 10 8 12 8
> 10 a z + 4 a z - 3 a z - 6 a z - 13 a z - 12 a z -
14 8 9 9 11 9 13 9 10 10 12 10
> 5 a z - 4 a z - 8 a z - 4 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -6 -4 1 2 1 5 2 7 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
9 7 10 10 10 9 7 10
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
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
5 7 3 5 3
> ------ + ------ + ------ + ----- + ----
12 3 10 3 10 2 8 2 6
q t q t q t q t q t |