PD Presentation: |
X6172 X14,3,15,4 X22,16,13,15 X8,18,9,17 X16,8,17,7 X18,10,19,9 X10,22,11,21 X20,12,21,11 X12,20,5,19 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, 443]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 443]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 3, 15, 4], X[22, 16, 13, 15], X[8, 18, 9, 17],
> X[16, 8, 17, 7], X[18, 10, 19, 9], X[10, 22, 11, 21], X[20, 12, 21, 11],
> X[12, 20, 5, 19], X[2, 5, 3, 6], X[4, 13, 1, 14]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 5, -4, 6, -7, 8, -9},
> {11, -2, 3, -5, 4, -6, 9, -8, 7, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -3 2 6 2 3 4 5 6 7 8
-9 + q - -- + - + 13 q - 14 q + 15 q - 13 q + 10 q - 5 q + 3 q - q
2 q
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -10 -8 3 2 6 8 10 12 14 16 22
1 + q + q + -- + 4 q + 6 q + 2 q + 3 q + 3 q - q + 4 q + q -
4
q
24
> q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 443]][a, z] |
Out[8]= | 2 2 2
3 5 2 -2 1 2 2 2 z 4 z 4 z 2 2
-- - -- + 2 a + z + ----- - ----- - 4 z - ---- + ---- - ---- + a z -
4 2 4 2 2 2 6 4 2
a a a z a z a a a
4 4 4 6 6
4 z 3 z z z z
> 2 z - -- + ---- + -- + -- + --
6 4 2 4 2
a a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 443]][a, z] |
Out[9]= | 2 3 9 2 -2 1 2 2 2 z 8 z 8 z
3 - -- + -- + -- - 2 a - z - ----- - ----- + ---- + --- + -- - --- - --- +
6 4 2 4 2 2 2 3 a z 5 3 a
a a a a z a z a z a a
2 2 2 2 3 3 3
2 4 z 5 z 4 z 14 z 2 2 2 z 3 z z
> a z - 4 z + ---- + ---- - ---- - ----- + 5 a z - ---- + ---- - -- +
8 6 4 2 9 7 5
a a a a a a a
3 3 4 4 4 5 5
5 z 13 z 3 4 7 z 7 z 9 z 2 4 z 7 z
> ---- + ----- + 2 a z + 5 z - ---- + ---- + ---- - 4 a z + -- - ---- +
3 a 8 4 2 9 7
a a a a a a
5 5 5 6 6 6 6
3 z 4 z 12 z 5 6 3 z 5 z 8 z 8 z 2 6
> ---- + ---- - ----- - 5 a z - 7 z + ---- - ---- - ---- - ---- + a z +
5 3 a 8 6 4 2
a a a a a a
7 7 7 7 8 8 8 9
4 z 3 z 8 z z 7 8 4 z 4 z 3 z 3 z
> ---- - ---- - ---- + -- + 2 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]= | 3 1 1 2 4 2 5 4 q 3
8 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
> 7 q t + 8 q t + 7 q t + 5 q t + 8 q t + 5 q t + 7 q t +
11 5 13 5 13 6 15 6 17 7
> 2 q t + 3 q t + q t + 2 q t + q t |