PD Presentation: |
X10,1,11,2 X2,11,3,12 X12,3,13,4 X18,8,19,7 X16,9,17,10 X22,15,9,16 X21,5,22,4 X5,14,6,15 X13,20,14,21 X8,18,1,17 X6,20,7,19 |
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, NonAlternating, 223]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 223]] |
Out[4]= | PD[X[10, 1, 11, 2], X[2, 11, 3, 12], X[12, 3, 13, 4], X[18, 8, 19, 7],
> X[16, 9, 17, 10], X[22, 15, 9, 16], X[21, 5, 22, 4], X[5, 14, 6, 15],
> X[13, 20, 14, 21], X[8, 18, 1, 17], X[6, 20, 7, 19]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, 7, -8, -11, 4, -10},
> {5, -1, 2, -3, -9, 8, 6, -5, 10, -4, 11, 9, -7, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(17/2) 2 4 7 8 8 7 6 3
q - ----- + ----- - ----- + ---- - ---- + ---- - ---- + ------- -
15/2 13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q q
> 2 Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -26 -20 2 -16 -10 3 3 2 2
1 - q - q + --- - q - q + -- + -- + -- + 2 q
18 8 4 2
q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 223]][a, z] |
Out[8]= | 3 5
-2 a 3 a a 3 7 3 3 3 5 3
---- + ---- - -- - 5 a z + 7 a z - 2 a z - 2 a z + 7 a z + 2 a z -
z z z
7 3 3 5 5 5
> a z + 2 a z + a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 223]][a, z] |
Out[9]= | 3 5
2 4 6 2 a 3 a a 3 7 2 2
-3 a - 3 a - a + --- + ---- + -- - 9 a z - 13 a z + 4 a z + 6 a z +
z z z
4 2 6 2 8 2 10 2 3 3 3 5 3
> 16 a z + 5 a z - 3 a z + 2 a z + 10 a z + 21 a z - 7 a z -
7 3 9 3 2 4 4 4 6 4 8 4 10 4
> 15 a z + 3 a z - 2 a z - 20 a z - 12 a z + 5 a z - a z -
5 3 5 5 5 7 5 9 5 2 6 4 6
> 3 a z - 10 a z + 6 a z + 11 a z - 2 a z + 2 a z + 13 a z +
6 6 8 6 3 7 5 7 7 7 2 8 4 8 6 8
> 8 a z - 3 a z + 3 a z - a z - 4 a z - a z - 4 a z - 3 a z -
3 9 5 9
> a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 5 1 1 1 3 1 4 3
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 2 18 7 16 6 14 6 14 5 12 5 12 4 10 4
q q q t q t q t q t q t q t q t
4 4 4 4 3 4 2 t 2 2
> ------ + ----- + ----- + ----- + ---- + ---- + t + --- + 2 q t
10 3 8 3 8 2 6 2 6 4 2
q t q t q t q t q t q t q |