PD Presentation: |
X6172 X14,3,15,4 X20,10,21,9 X16,8,17,7 X18,12,19,11 X22,16,13,15 X12,18,5,17 X10,20,11,19 X8,22,9,21 X2536 X4,13,1,14 |
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, 451]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 451]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 3, 15, 4], X[20, 10, 21, 9], X[16, 8, 17, 7],
> X[18, 12, 19, 11], X[22, 16, 13, 15], X[12, 18, 5, 17], X[10, 20, 11, 19],
> X[8, 22, 9, 21], X[2, 5, 3, 6], X[4, 13, 1, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 4, -9, 3, -8, 5, -7},
> {11, -2, 6, -4, 7, -5, 8, -3, 9, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -4 2 5 7 2 3 4 5 6 7
9 + q - -- + -- - - - 10 q + 11 q - 8 q + 7 q - 4 q + 3 q - q
3 2 q
q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -14 -12 -10 2 -6 2 2 2 4 6 8 10
q + q - q + -- + q - -- + -- + 2 q + 4 q + 4 q + 6 q + 2 q +
8 4 2
q q q
12 14 16 18 20 22
> 2 q + 3 q - q + q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 451]][a, z] |
Out[8]= | 2 2 2 4
2 3 4 -2 1 2 2 z z 2 z 2 2 4 z
-- - -- + a + z + ----- - ----- - z - -- + -- - ---- - 2 a z + z + -- +
4 2 4 2 2 2 6 4 2 4
a a a z a z a a a a
4
z
> --
2
a |
In[9]:= | Kauffman[Link[11, Alternating, 451]][a, z] |
Out[9]= | 8 13 4 -2 1 2 2 2 11 z 11 z 2
5 + -- + -- + a - z - ----- - ----- + ---- + --- - ---- - ---- - 9 z -
4 2 4 2 2 2 3 a z 3 a
a a a z a z a z a
2 2 2 3 3 3 3
7 z 23 z 28 z 2 2 4 2 3 z z 8 z 14 z
> ---- - ----- - ----- + a z - 2 a z + ---- - -- + ---- + ----- -
6 4 2 7 5 3 a
a a a a a a
4 4 4 5 5
3 3 4 18 z 35 z 29 z 2 4 4 4 4 z 11 z
> 2 a z + 8 z + ----- + ----- + ----- - 3 a z + a z - ---- + ----- +
6 4 2 7 5
a a a a a
5 5 6 6 6
12 z 7 z 5 3 5 6 14 z 22 z 16 z 2 6
> ----- - ---- - 2 a z + 2 a z - 5 z - ----- - ----- - ----- + 3 a z +
3 a 6 4 2
a a a a
7 7 7 7 8 8 8 9
z 12 z 17 z z 7 8 3 z 2 z 2 z 3 z
> -- - ----- - ----- - -- + 3 a z + 3 z + ---- + ---- + ---- + ---- +
7 5 3 a 6 4 2 5
a a a a a a a
9 9 10 10
5 z 2 z z z
> ---- + ---- + --- + ---
3 a 4 2
a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 5 1 1 2 3 2 4 3 3
- + 5 q + ----- + ----- + ----- + ----- + ----- + ---- + --- + 6 q t + 4 q t +
q 9 4 7 4 7 3 5 2 3 2 3 q t
q t q t q t q t q t q t
3 2 5 2 5 3 7 3 7 4 9 4 9 5
> 5 q t + 6 q t + 3 q t + 5 q t + 4 q t + 5 q t + 2 q t +
11 5 11 6 13 6 15 7
> 2 q t + q t + 2 q t + q t |