PD Presentation: |
X8192 X12,4,13,3 X20,10,21,9 X22,12,7,11 X10,22,11,21 X2738 X18,15,19,16 X6,14,1,13 X4,18,5,17 X16,6,17,5 X14,19,15,20 |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Length[Skeleton[L]] |
Out[2]= | 2 |
In[3]:= | Show[DrawMorseLink[Link[11, Alternating, 219]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 219]] |
Out[4]= | PD[X[8, 1, 9, 2], X[12, 4, 13, 3], X[20, 10, 21, 9], X[22, 12, 7, 11],
> X[10, 22, 11, 21], X[2, 7, 3, 8], X[18, 15, 19, 16], X[6, 14, 1, 13],
> X[4, 18, 5, 17], X[16, 6, 17, 5], X[14, 19, 15, 20]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -6, 2, -9, 10, -8},
> {6, -1, 3, -5, 4, -2, 8, -11, 7, -10, 9, -7, 11, -3, 5, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(5/2) 3 6 3/2 5/2 7/2
-q + ---- - ------- + 10 Sqrt[q] - 14 q + 15 q - 17 q +
3/2 Sqrt[q]
q
9/2 11/2 13/2 15/2 17/2
> 14 q - 11 q + 7 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -8 -4 -2 2 4 8 12 14 16 18 20
-3 + q - q + q + q + 2 q + 6 q + 4 q + q - q + 2 q - 3 q -
26
> q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 219]][a, z] |
Out[8]= | 3 3 3 3
1 3 2 2 z 6 z 7 z 4 z z 6 z 7 z 6 z
---- - ---- + ---- + --- - --- + --- - --- + 2 a z + -- - ---- + ---- - ---- +
7 5 3 7 5 3 a 7 5 3 a
a z a z a z a a a a a a
5 5 5 7
3 2 z 4 z 2 z z
> a z - ---- + ---- - ---- + --
5 3 a 3
a a a |
In[9]:= | Kauffman[Link[11, Alternating, 219]][a, z] |
Out[9]= | -8 3 3 1 3 2 5 z 10 z 5 z 2 z 2
a + -- + -- - ---- - ---- - ---- + --- + ---- + --- + --- + 2 a z + 6 z +
6 4 7 5 3 7 5 3 a
a a a z a z a z a a a
2 2 2 2 2 3 3 3 3 3
z 5 z 7 z 4 z 11 z 2 z 11 z 21 z 12 z 9 z
> --- - ---- - ---- + ---- + ----- + ---- - ----- - ----- - ----- - ---- -
10 8 6 4 2 9 7 5 3 a
a a a a a a a a a
4 4 4 4 4 5 5 5
3 4 z 7 z 3 z 24 z 34 z 3 z 12 z 22 z
> 5 a z - 15 z - --- + ---- + ---- - ----- - ----- - ---- + ----- + ----- +
10 8 6 4 2 9 7 5
a a a a a a a a
5 5 6 6 6 6 7 7
5 z 2 z 5 6 6 z 7 z 33 z 32 z 8 z 3 z
> ---- + ---- + 4 a z + 12 z - ---- + ---- + ----- + ----- - ---- - ---- +
3 a 8 6 4 2 7 5
a a a a a a a
7 7 8 8 8 9 9 9
13 z 7 z 7 8 7 z 11 z 7 z 4 z 7 z 3 z
> ----- + ---- - 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]= | 2
2 4 1 2 1 2 4 6 4 q 4 6
8 q + 7 q + ----- + ----- + ----- + -- + ----- + - + ---- + 8 q t + 7 q t +
6 4 4 3 2 3 2 2 2 t t
q t q t q t t q t
6 2 8 2 8 3 10 3 10 4 12 4 12 5
> 9 q t + 9 q t + 6 q t + 8 q t + 5 q t + 6 q t + 2 q t +
14 5 14 6 16 6 18 7
> 5 q t + q t + 2 q t + q t |