PD Presentation: |
X6172 X5,12,6,13 X3849 X2,14,3,13 X14,7,15,8 X11,18,12,19 X9,21,10,20 X19,5,20,10 X15,1,16,4 X17,22,18,11 X21,16,22,17 |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Length[Skeleton[L]] |
Out[2]= | 3 |
In[3]:= | Show[DrawMorseLink[Link[11, NonAlternating, 289]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 289]] |
Out[4]= | PD[X[6, 1, 7, 2], X[5, 12, 6, 13], X[3, 8, 4, 9], X[2, 14, 3, 13],
> X[14, 7, 15, 8], X[11, 18, 12, 19], X[9, 21, 10, 20], X[19, 5, 20, 10],
> X[15, 1, 16, 4], X[17, 22, 18, 11], X[21, 16, 22, 17]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -4, -3, 9}, {-2, -1, 5, 3, -7, 8},
> {-6, 2, 4, -5, -9, 11, -10, 6, -8, 7, -11, 10}] |
In[6]:= | Jones[L][q] |
Out[6]= | -8 2 4 6 7 8 6 6
-2 - q + -- - -- + -- - -- + -- - -- + - + 2 q
7 6 5 4 3 2 q
q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -24 2 2 2 2 2 4 6 4 7 2 4
4 - q - --- - --- - --- + --- + --- + -- + -- + -- + -- + 3 q + 2 q
20 18 14 12 10 8 6 4 2
q q q q q q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 289]][a, z] |
Out[8]= | 2 4 6
2 4 6 2 5 a 4 a a 2 2 2 4 2
5 - 13 a + 11 a - 3 a + -- - ---- + ---- - -- + 2 z - 11 a z + 11 a z -
2 2 2 2
z z z z
6 2 2 4 4 4 6 4 4 6
> 3 a z - 3 a z + 5 a z - a z + a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 289]][a, z] |
Out[9]= | 2 4 6 3 5 7
2 4 6 2 5 a 4 a a 5 a 9 a 5 a a
9 + 21 a + 18 a + 5 a - -- - ---- - ---- - -- + --- + ---- + ---- + -- -
2 2 2 2 z z z z
z z z z
3 5 7 9 2 2 2 4 2
> 13 a z - 29 a z - 21 a z - 4 a z + a z - 10 z - 37 a z - 40 a z -
6 2 8 2 3 3 3 5 3 7 3 9 3
> 12 a z + a z + 8 a z + 28 a z + 31 a z + 8 a z - 3 a z +
4 2 4 4 4 6 4 8 4 5 3 5
> 3 z + 28 a z + 47 a z + 17 a z - 5 a z - 3 a z - 7 a z -
5 5 7 5 9 5 2 6 4 6 6 6 8 6
> 14 a z - 9 a z + a z - 10 a z - 23 a z - 11 a z + 2 a z +
7 3 7 5 7 7 7 2 8 4 8 6 8 3 9 5 9
> a z - a z + a z + 3 a z + 2 a z + 5 a z + 3 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 5 1 1 1 3 1 3 3 4
-- + - + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
3 q 17 7 15 6 13 6 13 5 11 5 11 4 9 4 9 3
q q t q t q t q t q t q t q t q t
3 4 5 3 3 t 2 3 2
> ----- + ----- + ----- + ---- + ---- + - + q t + q t + 2 q t
7 3 7 2 5 2 5 3 q
q t q t q t q t q t |