PD Presentation: |
X6172 X20,7,21,8 X4,21,1,22 X11,14,12,15 X3849 X5,13,6,12 X13,5,14,22 X15,19,16,18 X9,17,10,16 X17,11,18,10 X19,2,20,3 |
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, 36]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 36]] |
Out[4]= | PD[X[6, 1, 7, 2], X[20, 7, 21, 8], X[4, 21, 1, 22], X[11, 14, 12, 15],
> X[3, 8, 4, 9], X[5, 13, 6, 12], X[13, 5, 14, 22], X[15, 19, 16, 18],
> X[9, 17, 10, 16], X[17, 11, 18, 10], X[19, 2, 20, 3]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, 11, -5, -3}, {-6, -1, 2, 5, -9, 10, -4, 6, -7, 4, -8, 9, -10, 8,
> -11, -2, 3, 7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -2 4 7 8 9 3/2 5/2 7/2
---- + ---- - ---- + ---- - ------- + 8 Sqrt[q] - 7 q + 4 q - 2 q +
9/2 7/2 5/2 3/2 Sqrt[q]
q q q q
9/2
> q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -18 2 -10 2 -6 3 -2 2 6 8 12 14
2 + q + --- + q + -- - q + -- - q + q + 2 q - q - q - q
14 8 4
q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 36]][a, z] |
Out[8]= | 3 5 3 3
1 3 3 a 2 a a 3 z 9 z 3 5 z 8 z
---- - --- + --- - ---- + -- + --- - --- + 8 a z - 5 a z + a z + -- - ---- +
3 a z z z z 3 a 3 a
a z a a
5
3 3 3 2 z 5 3 5 7
> 9 a z - 4 a z - ---- + 5 a z - a z + a z
a |
In[9]:= | Kauffman[Link[11, NonAlternating, 36]][a, z] |
Out[9]= | 3 5
-4 2 2 1 3 3 a 2 a a 4 z 14 z 3
a + -- - 2 a - ---- - --- - --- - ---- - -- + --- + ---- + 15 a z + 9 a z +
2 3 a z z z z 3 a
a a z a
2 2 3 3
5 2 4 z 6 z 2 2 4 2 7 z 21 z 3
> 4 a z + 5 z - ---- - ---- + 9 a z + 2 a z - ---- - ----- - 24 a z -
4 2 3 a
a a a
4 4 5
3 3 5 3 4 4 z 3 z 2 4 4 4 7 z
> 13 a z - 3 a z - 13 z + ---- + ---- - 14 a z - 2 a z + ---- +
4 2 3
a a a
5 6 6 7
15 z 5 3 5 6 z 4 z 2 6 4 6 2 z
> ----- + 15 a z + 7 a z + 14 z - -- + ---- + 8 a z - a z - ---- -
a 4 2 3
a a a
7 8 9
2 z 7 3 7 8 2 z 2 8 z 9
> ---- - 3 a z - 3 a z - 5 z - ---- - 3 a z - -- - a z
a 2 a
a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 5 2 1 3 1 4 3 4 4
5 + -- + ------ + ----- + ----- + ----- + ----- + ----- + ---- + ---- + 4 t +
2 10 4 8 4 8 3 6 3 6 2 4 2 4 2
q q t q t q t q t q t q t q t q t
2 2 2 4 2 4 3 6 3 6 4 8 4 10 5
> 4 q t + 3 q t + 4 q t + q t + 3 q t + q t + q t + q t |