PD Presentation: |
X12,1,13,2 X20,9,11,10 X14,3,15,4 X16,5,17,6 X4,15,5,16 X8,17,9,18 X18,7,19,8 X6,19,7,20 X2,11,3,12 X10,13,1,14 |
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, 115]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 115]] |
Out[4]= | PD[X[12, 1, 13, 2], X[20, 9, 11, 10], X[14, 3, 15, 4], X[16, 5, 17, 6],
> X[4, 15, 5, 16], X[8, 17, 9, 18], X[18, 7, 19, 8], X[6, 19, 7, 20],
> X[2, 11, 3, 12], X[10, 13, 1, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 3, -5, 4, -8, 7, -6, 2, -10},
> {9, -1, 10, -3, 5, -4, 6, -7, 8, -2}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(25/2) -(23/2) 3 5 6 7 7 5 4
-q + q - ----- + ----- - ----- + ----- - ----- + ----- - ---- +
21/2 19/2 17/2 15/2 13/2 11/2 9/2
q q q q q q q
2 -(5/2)
> ---- - q
7/2
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -38 -36 -34 2 -28 -24 -22 -20 2 -16 -12
q + q + q + --- + q - q + q - q + --- + q + q -
32 18
q q
-10 -8
> q + q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 115]][a, z] |
Out[8]= | 9 11
a a 5 7 9 11 5 3 7 3 9 3
-(--) + --- - a z - 5 a z - 2 a z + 3 a z - 3 a z - 7 a z - 3 a z +
z z
11 3 5 5 7 5 9 5
> a z - a z - 2 a z - a z |
In[9]:= | Kauffman[Link[10, Alternating, 115]][a, z] |
Out[9]= | 9 11
10 a a 5 7 9 11 15 6 2
-a + -- + --- - a z + 5 a z - 4 a z - 6 a z - 4 a z - a z +
z z
10 2 12 2 5 3 7 3 9 3 11 3 13 3
> 7 a z + 6 a z + 3 a z - 11 a z + 2 a z + 13 a z + a z +
15 3 6 4 8 4 10 4 12 4 14 4 5 5
> 4 a z + 5 a z - 4 a z - 16 a z - 5 a z + 2 a z - a z +
7 5 9 5 11 5 13 5 15 5 6 6 8 6
> 10 a z - 3 a z - 12 a z + a z - a z - 2 a z + 5 a z +
10 6 12 6 14 6 7 7 9 7 11 7 13 7
> 10 a z + 2 a z - a z - 3 a z + 2 a z + 4 a z - a z -
8 8 10 8 12 8 9 9 11 9
> 2 a z - 3 a z - a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -6 -4 1 1 1 2 1 3 2
q + q + ------- + ------- + ------ + ------ + ------ + ------ + ------ +
26 10 24 10 24 9 22 8 20 8 20 7 18 7
q t q t q t q t q t q t q t
3 3 4 3 3 4 2 3
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
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
2 2 2
> ------ + ----- + ----
10 2 8 2 6
q t q t q t |