PD Presentation: |
X10,1,11,2 X2,11,3,12 X12,3,13,4 X14,5,15,6 X6,9,7,10 X18,7,19,8 X20,16,9,15 X16,20,17,19 X8,17,1,18 X4,13,5,14 |
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, 97]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 97]] |
Out[4]= | PD[X[10, 1, 11, 2], X[2, 11, 3, 12], X[12, 3, 13, 4], X[14, 5, 15, 6],
> X[6, 9, 7, 10], X[18, 7, 19, 8], X[20, 16, 9, 15], X[16, 20, 17, 19],
> X[8, 17, 1, 18], X[4, 13, 5, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -10, 4, -5, 6, -9},
> {5, -1, 2, -3, 10, -4, 7, -8, 9, -6, 8, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(21/2) 2 4 5 6 6 6 4 3 2
-q + ----- - ----- + ----- - ----- + ----- - ---- + ---- - ---- + ---- -
19/2 17/2 15/2 13/2 11/2 9/2 7/2 5/2 3/2
q q q q q q q q q
1
> -------
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -32 -30 -26 2 -20 -18 2 -14 -12 -10 -2
q + q + q + --- + q + q + --- - q + q - q + q
22 16
q q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 97]][a, z] |
Out[8]= | 7 9
a a 3 5 7 9 3 3 5 3 7 3
-(--) + -- - 3 a z + 3 a z - 7 a z + 3 a z - 4 a z + 7 a z - 8 a z +
z z
9 3 3 5 5 5 7 5 5 7
> a z - a z + 5 a z - 2 a z + a z |
In[9]:= | Kauffman[Link[10, Alternating, 97]][a, z] |
Out[9]= | 7 9
8 a a 3 5 7 9 11 13 4 2
a - -- - -- + 3 a z + 2 a z + 7 a z + 5 a z - 2 a z + a z + 5 a z +
z z
6 2 8 2 10 2 12 2 3 3 5 3 7 3
> 5 a z - 2 a z - a z + a z - 7 a z - 9 a z - 12 a z -
9 3 11 3 13 3 4 4 6 4 8 4 10 4
> 6 a z + 3 a z - a z - 14 a z - 17 a z + 2 a z + 3 a z -
12 4 3 5 5 5 7 5 9 5 11 5 4 6
> 2 a z + 5 a z + 5 a z + 9 a z + 6 a z - 3 a z + 10 a z +
6 6 8 6 10 6 3 7 5 7 9 7 4 8
> 16 a z + 3 a z - 3 a z - a z + 2 a z - 3 a z - 2 a z -
6 8 8 8 5 9 7 9
> 4 a z - 2 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 2 1 1 2 2 2 3 2
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
6 4 22 8 20 8 20 7 18 6 16 6 16 5 14 5
q q q t q t q t q t q t q t q t
3 3 3 3 3 3 1 3 t
> ------ + ------ + ------ + ------ + ------ + ----- + ---- + ---- + -- +
14 4 12 4 12 3 10 3 10 2 8 2 8 6 4
q t q t q t q t q t q t q t q t q
t 2
> -- + t
2
q |