PD Presentation: |
X6172 X12,3,13,4 X18,10,19,9 X16,8,17,7 X22,16,11,15 X20,14,21,13 X14,22,15,21 X10,18,5,17 X8,20,9,19 X2536 X4,11,1,12 |
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, 415]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 415]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[18, 10, 19, 9], X[16, 8, 17, 7],
> X[22, 16, 11, 15], X[20, 14, 21, 13], X[14, 22, 15, 21], X[10, 18, 5, 17],
> X[8, 20, 9, 19], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 4, -9, 3, -8},
> {11, -2, 6, -7, 5, -4, 8, -3, 9, -6, 7, -5}] |
In[6]:= | Jones[L][q] |
Out[6]= | -3 2 6 2 3 4 5 6 7 8
-9 + q - -- + - + 14 q - 15 q + 17 q - 14 q + 11 q - 7 q + 3 q - q
2 q
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -10 -8 3 2 4 6 8 10 12 14 16
2 + q + q + -- + 7 q + 3 q + 9 q + 4 q + 3 q + 2 q - 4 q + q -
4
q
18 20 22 24
> 3 q - 2 q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 415]][a, z] |
Out[8]= | 2 2 2
-2 8 8 2 2 1 4 5 2 2 z 6 z 4 z
-- + -- - -- + 2 a + -- - ----- + ----- - ----- - 4 z - ---- + ---- - ---- +
6 4 2 2 6 2 4 2 2 2 6 4 2
a a a z a z a z a z a a a
4 4 4 6 6
2 2 4 z 3 z z z z
> a z - 2 z - -- + ---- + -- + -- + --
6 4 2 4 2
a a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 415]][a, z] |
Out[9]= | 4 17 20 2 2 1 4 5 1 5 9
6 + -- + -- + -- - 2 a - -- - ----- - ----- - ----- + ---- + ---- + ---- +
6 4 2 2 6 2 4 2 2 2 7 5 3
a a a z a z a z a z a z a z a z
2 2 2
5 5 z 21 z 33 z 16 z 2 12 z 33 z 33 z
> --- - --- - ---- - ---- - ---- + a z - 7 z - ----- - ----- - ----- +
a z 7 5 3 a 6 4 2
a a a a a a
3 3 3 3 3 4
2 2 2 z 12 z 30 z 35 z 21 z 3 4 5 z
> 5 a z - ---- + ----- + ----- + ----- + ----- + 2 a z + 6 z - ---- +
9 7 5 3 a 8
a a a a a
4 4 4 5 5 5 5 5
22 z 44 z 27 z 2 4 z 14 z 13 z 9 z 16 z
> ----- + ----- + ----- - 4 a z + -- - ----- - ----- - ---- - ----- -
6 4 2 9 7 5 3 a
a a a a a a a
6 6 6 6 7 7 7
5 6 3 z 18 z 30 z 17 z 2 6 6 z 2 z 8 z
> 5 a z - 7 z + ---- - ----- - ----- - ----- + a z + ---- - ---- - ---- +
8 6 4 2 7 5 3
a a a a a a a
7 8 8 8 9 9 9 10 10
2 z 7 8 7 z 9 z 5 z 4 z 6 z 2 z z z
> ---- + 2 a z + 3 z + ---- + ---- + ---- + ---- + ---- + ---- + --- + ---
a 6 4 2 5 3 a 4 2
a a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 1 1 2 4 2 5 4 q 3
9 q + 6 q + ----- + ----- + ----- + ----- + ---- + --- + --- + 7 q t +
7 4 5 4 5 3 3 2 2 q t t
q t q t q t q t q t
5 5 2 7 2 7 3 9 3 9 4 11 4
> 8 q t + 10 q t + 9 q t + 6 q t + 8 q t + 5 q t + 6 q t +
11 5 13 5 13 6 15 6 17 7
> 2 q t + 5 q t + q t + 2 q t + q t |