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, 499]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 499]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 4, 13, 3], X[16, 8, 17, 7], X[22, 17, 19, 18],
> X[20, 12, 21, 11], X[10, 20, 11, 19], X[18, 21, 5, 22], X[14, 10, 15, 9],
> X[8, 16, 9, 15], X[2, 5, 3, 6], X[4, 14, 1, 13]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {6, -5, 7, -4},
> {10, -1, 3, -9, 8, -6, 5, -2, 11, -8, 9, -3, 4, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -3 2 7 2 3 4 5 6 7 8
-11 + q - -- + - + 16 q - 17 q + 19 q - 16 q + 12 q - 7 q + 3 q - q
2 q
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -10 -8 -6 6 2 2 4 6 10 12 14
3 + q + q + q + -- + -- + 6 q - q + 5 q + 2 q + 3 q - 2 q +
4 2
q q
16 18 20 22 24
> 4 q - 2 q - 2 q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 499]][a, z] |
Out[8]= | 2 2 2 2
2 4 2 2 1 a 2 2 z 6 z z 2 2
-4 - -- + -- + 2 a - -- + ----- + -- - 4 z - ---- + ---- - -- + a z -
6 4 2 2 2 2 6 4 2
a a z a z 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, 499]][a, z] |
Out[9]= | 2
4 8 2 2 1 a 2 2 a 4 z 8 z 8 z
-7 + -- + -- - 4 a + -- + ----- + -- - --- - --- - --- - --- + --- + 4 a z +
6 4 2 2 2 2 a z z 7 5 a
a a z a z z a a
2 2 2 3 3 3 3
2 14 z 36 z 16 z 2 2 2 z 11 z 21 z 3 z
> 12 z - ----- - ----- - ----- + 6 a z - ---- + ----- + ----- - ---- -
6 4 2 9 7 5 3
a a a a a a a
3 4 4 4 4 5 5 5
11 z 4 5 z 27 z 62 z 27 z 2 4 z 13 z 9 z
> ----- - 7 z - ---- + ----- + ----- + ----- - 4 a z + -- - ----- - ---- +
a 8 6 4 2 9 7 5
a a a a a a a
5 6 6 6 6 7 7
9 z 5 6 3 z 21 z 46 z 26 z 2 6 6 z 4 z
> ---- - 4 a z - 3 z + ---- - ----- - ----- - ----- + a z + ---- - ---- -
3 8 6 4 2 7 5
a a a a a a a
7 7 8 8 8 9 9 9
14 z 2 z 7 8 8 z 14 z 9 z 5 z 8 z 3 z
> ----- - ---- + 2 a z + 3 z + ---- + ----- + ---- + ---- + ---- + ---- +
3 a 6 4 2 5 3 a
a a a a a a
10 10
z z
> --- + ---
4 2
a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 1 1 1 6 1 5 6 q 3
11 q + 9 q + ----- + ----- + ----- + ----- + ---- + --- + --- + 10 q t +
7 4 5 3 3 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 + 9 q t + 10 q t + 7 q t + 9 q t + 5 q t + 7 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 |