PD Presentation: |
X6172 X16,7,17,8 X4,17,1,18 X12,6,13,5 X8493 X22,14,19,13 X20,10,21,9 X10,20,11,19 X14,22,15,21 X18,12,5,11 X2,16,3,15 |
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, Alternating, 486]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 486]] |
Out[4]= | PD[X[6, 1, 7, 2], X[16, 7, 17, 8], X[4, 17, 1, 18], X[12, 6, 13, 5],
> X[8, 4, 9, 3], X[22, 14, 19, 13], X[20, 10, 21, 9], X[10, 20, 11, 19],
> X[14, 22, 15, 21], X[18, 12, 5, 11], X[2, 16, 3, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -11, 5, -3}, {8, -7, 9, -6},
> {4, -1, 2, -5, 7, -8, 10, -4, 6, -9, 11, -2, 3, -10}] |
In[6]:= | Jones[L][q] |
Out[6]= | -2 4 2 3 4 5 6 7 8 9
-9 - q + - + 17 q - 22 q + 27 q - 25 q + 23 q - 17 q + 10 q - 4 q + q
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -6 2 -2 2 4 6 8 10 12 14 16
-2 - q + -- - q + 6 q - 3 q + 5 q + 5 q + 2 q + 9 q - q + 6 q -
4
q
20 22 24 28
> 3 q + 4 q - 2 q + q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 486]][a, z] |
Out[8]= | 2 2 2 2
-8 2 -4 2 1 2 1 2 z 5 z 4 z z 4
a - -- - a + -- + ----- - ----- + ----- - z + -- - ---- + ---- + -- - z -
6 2 6 2 4 2 2 2 8 6 4 2
a a a z a z a z a a a a
4 4 4 6 6
3 z 5 z z 2 z z
> ---- + ---- + -- + ---- + --
6 4 2 4 2
a a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 486]][a, z] |
Out[9]= | 3 5 2 -2 1 2 1 2 2 2 z 7 z 5 z
-- + -- + -- - a + ----- + ----- + ----- - ---- - ---- - --- - --- - --- -
8 6 4 6 2 4 2 2 2 5 3 9 7 5
a a a a z a z a z a z a z a a a
2 2 2 2 2 3 3 3
z z 2 z 8 z 30 z 27 z 4 z 6 z 20 z 27 z
> -- - - + 2 z + --- - ---- - ----- - ----- - ---- + ---- + ----- + ----- +
3 a 10 8 6 4 2 9 7 5
a a a a a a a a a
3 3 4 4 4 4 4 5
19 z 5 z 3 4 2 z 14 z 62 z 63 z 12 z 8 z
> ----- + ---- - a z - 5 z - ---- + ----- + ----- + ----- + ----- - ---- -
3 a 10 8 6 4 2 9
a a a a a a a
5 5 5 5 6 6 6 6
20 z 23 z 22 z 10 z 5 6 z 17 z 65 z 67 z
> ----- - ----- - ----- - ----- + a z + 4 z + --- - ----- - ----- - ----- -
7 5 3 a 10 8 6 4
a a a a a a a
6 7 7 7 7 7 8 8 8 8
16 z 4 z 3 z 14 z z 8 z 8 z 22 z 25 z 11 z
> ----- + ---- - ---- - ----- + -- + ---- + ---- + ----- + ----- + ----- +
2 9 7 5 3 a 8 6 4 2
a a a a a a a a a
9 9 9 10 10
7 z 15 z 8 z 2 z 2 z
> ---- + ----- + ---- + ----- + -----
7 5 3 6 4
a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 1 3 1 6 3 q 3 5 5 2
11 q + 8 q + ----- + ----- + ---- + --- + --- + 13 q t + 9 q t + 14 q t +
5 3 3 2 2 q t t
q t q t q t
7 2 7 3 9 3 9 4 11 4 11 5
> 13 q t + 11 q t + 14 q t + 12 q t + 13 q t + 7 q t +
13 5 13 6 15 6 15 7 17 7 19 8
> 10 q t + 3 q t + 7 q t + q t + 3 q t + q t |