PD Presentation: |
X6172 X5,12,6,13 X8493 X2,14,3,13 X14,7,15,8 X9,18,10,19 X17,11,18,22 X11,21,12,20 X21,17,22,16 X4,15,1,16 X19,10,20,5 |
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, 280]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 280]] |
Out[4]= | PD[X[6, 1, 7, 2], X[5, 12, 6, 13], X[8, 4, 9, 3], X[2, 14, 3, 13],
> X[14, 7, 15, 8], X[9, 18, 10, 19], X[17, 11, 18, 22], X[11, 21, 12, 20],
> X[21, 17, 22, 16], X[4, 15, 1, 16], X[19, 10, 20, 5]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -4, 3, -10}, {-2, -1, 5, -3, -6, 11},
> {-8, 2, 4, -5, 10, 9, -7, 6, -11, 8, -9, 7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -6 3 6 6 9 7 2 3
8 + q - -- + -- - -- + -- - - - 5 q + 2 q - q
5 4 3 2 q
q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -18 -16 2 3 4 9 6 7 3 4 6 8 10
q - q + --- + --- + --- + -- + -- + -- + -- - 4 q - q - q - q
14 12 10 8 6 4 2
q q q q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 280]][a, z] |
Out[8]= | 2 4 2
2 2 4 4 1 5 a 2 a 2 z 2 2
8 - -- - 8 a + 2 a + -- - ----- - ---- + ---- + 6 z - -- - 7 a z +
2 2 2 2 2 2 2
a z a z z z a
4 2 4 2 4 4 4 2 6
> 2 a z + 2 z - 4 a z + a z - a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 280]][a, z] |
Out[9]= | 2 4
-2 2 4 6 4 1 5 a 2 a 1 5 9 a
7 + a + 10 a + 4 a - a - -- - ----- - ---- - ---- + ---- + --- + --- +
2 2 2 2 2 3 a z z
z a z z z a z
3 2
5 a 2 z 11 z 3 2 2 z 2 2 4 2
> ---- - --- - ---- - 21 a z - 12 a z - 9 z - ---- - 11 a z - a z +
z 3 a 2
a a
3 3 4
6 2 z 11 z 3 3 3 5 3 4 2 z
> 3 a z + -- + ----- + 23 a z + 18 a z + 5 a z + 14 z + ---- +
3 a 2
a a
5
2 4 6 4 3 z 5 3 5 5 5 6
> 15 a z - 3 a z - ---- - 11 a z - 17 a z - 9 a z - 7 z -
a
7
2 6 4 6 6 6 z 7 3 7 5 7 8
> 15 a z - 7 a z + a z + -- + a z + 3 a z + 3 a z + 2 z +
a
2 8 4 8 9 3 9
> 5 a z + 3 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -3 6 1 2 1 4 4 4 2
q + - + 4 q + ------ + ------ + ----- + ----- + ----- + ----- + ----- +
q 13 6 11 5 9 5 9 4 7 4 7 3 5 3
q t q t q t q t q t q t q t
5 4 3 5 3 3 2 5 2 7 3
> ----- + ----- + ---- + --- + q t + 4 q t + q t + q t + q t
5 2 3 2 3 q t
q t q t q t |