PD Presentation: |
X8192 X2,9,3,10 X10,3,11,4 X16,5,17,6 X22,18,7,17 X18,12,19,11 X12,22,13,21 X20,14,21,13 X14,20,15,19 X6718 X4,15,5,16 |
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, 201]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 201]] |
Out[4]= | PD[X[8, 1, 9, 2], X[2, 9, 3, 10], X[10, 3, 11, 4], X[16, 5, 17, 6],
> X[22, 18, 7, 17], X[18, 12, 19, 11], X[12, 22, 13, 21], X[20, 14, 21, 13],
> X[14, 20, 15, 19], X[6, 7, 1, 8], X[4, 15, 5, 16]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -11, 4, -10},
> {10, -1, 2, -3, 6, -7, 8, -9, 11, -4, 5, -6, 9, -8, 7, -5}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(15/2) 3 6 8 11 11 11 9
-q + ----- - ----- + ---- - ---- + ---- - ---- + ------- - 7 Sqrt[q] +
13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q
3/2 5/2 7/2
> 4 q - 2 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -22 -20 -18 -16 -14 4 3 2 2 4 6 10
-1 + q - q + q + q + q + --- + -- + -- + q - q - q - q
12 8 2
q q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 201]][a, z] |
Out[8]= | 5 3
1 2 a a 4 z 3 5 4 z 3 3 3
--- - --- + -- + --- - 8 a z - a z + 2 a z + ---- - 9 a z - 4 a z +
a z z z a a
5
5 3 z 5 3 5 5 5 7 3 7
> 3 a z + -- - 5 a z - 4 a z + a z - a z - a z
a |
In[9]:= | Kauffman[Link[11, Alternating, 201]][a, z] |
Out[9]= | 5
2 2 4 1 2 a a 4 z 3 5 7
-5 - -- - 3 a + a + --- + --- - -- - --- - 10 a z + a z + 5 a z - 2 a z +
2 a z z z a
a
2 3
2 9 z 2 2 4 2 6 2 14 z 3 3 3
> 26 z + ---- + 16 a z - 3 a z - 2 a z + ----- + 21 a z - 9 a z -
2 a
a
4
5 3 7 3 9 3 4 12 z 2 4 4 4 6 4
> 10 a z + 5 a z - a z - 39 z - ----- - 41 a z - a z + 10 a z -
2
a
5 6
8 4 20 z 5 3 5 5 5 7 5 6 6 z
> 3 a z - ----- - 35 a z + 9 a z + 18 a z - 6 a z + 18 z + ---- +
a 2
a
7 8
2 6 4 6 6 6 11 z 7 3 7 5 7 z
> 34 a z + 14 a z - 8 a z + ----- + 26 a z + 6 a z - 9 a z - -- -
a 2
a
9
2 8 4 8 2 z 9 3 9 10 2 10
> 6 a z - 7 a z - ---- - 6 a z - 4 a z - z - a z
a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 6 6 1 1 3 3 3 5 3 6
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
4 2 16 6 14 6 14 5 12 4 10 4 10 3 8 3 8 2
q q q t q t q t q t q t q t q t q t
5 5 6 4 t 2 2 2 2 3 4 3
> ----- + ---- + ---- + 5 t + --- + 3 t + 4 q t + q t + 3 q t +
6 2 6 4 2
q t q t q t q
4 4 6 4 8 5
> q t + q t + q t |