PD Presentation: |
X8192 X12,4,13,3 X22,10,7,9 X16,11,17,12 X10,15,11,16 X2738 X20,17,21,18 X6,14,1,13 X4,20,5,19 X18,6,19,5 X14,21,15,22 |
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, 243]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 243]] |
Out[4]= | PD[X[8, 1, 9, 2], X[12, 4, 13, 3], X[22, 10, 7, 9], X[16, 11, 17, 12],
> X[10, 15, 11, 16], X[2, 7, 3, 8], X[20, 17, 21, 18], X[6, 14, 1, 13],
> X[4, 20, 5, 19], X[18, 6, 19, 5], X[14, 21, 15, 22]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -6, 2, -9, 10, -8},
> {6, -1, 3, -5, 4, -2, 8, -11, 5, -4, 7, -10, 9, -7, 11, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(13/2) 4 9 16 21 24 25
-q + ----- - ---- + ---- - ---- + ---- - ------- + 20 Sqrt[q] -
11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q
3/2 5/2 7/2 9/2
> 16 q + 9 q - 4 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -20 -18 -16 3 5 -10 4 5 2 2 6 8
7 + q - q - q + --- - --- + q - -- + -- - -- + 2 q + 5 q - 3 q +
14 12 6 4 2
q q q q q
10 12 14
> q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 243]][a, z] |
Out[8]= | 3 3 3
-2 3 a a z 3 z 3 5 z 4 z 3
--- + --- - -- + -- - --- + 5 a z - 3 a z + a z + -- - ---- + 5 a z -
a z z z 3 a 3 a
a a
5
3 3 5 3 2 z 5 3 5 7
> 4 a z + a z - ---- + 3 a z - 2 a z + a z
a |
In[9]:= | Kauffman[Link[11, Alternating, 243]][a, z] |
Out[9]= | 3
2 4 2 3 a a 2 z 6 z 3 5 2
3 + 3 a + a - --- - --- - -- + --- + --- + 5 a z + 2 a z + a z + 2 z -
a z z z 3 a
a
2 3 3
z 2 2 6 2 7 z 15 z 3 3 3 5 3
> -- + 3 a z - 2 a z - ---- - ----- - 12 a z - 11 a z - 6 a z +
4 3 a
a a
4 4 5 5
7 3 4 2 z 7 z 2 4 4 4 6 4 9 z 15 z
> a z - 24 z + ---- - ---- - 26 a z - 6 a z + 5 a z + ---- + ----- +
4 2 3 a
a a a
6 6
5 3 5 5 5 7 5 6 z 14 z 2 6
> 10 a z + 16 a z + 11 a z - a z + 39 z - -- + ----- + 41 a z +
4 2
a a
7 7
4 6 6 6 4 z 3 z 7 3 7 5 7 8
> 13 a z - 4 a z - ---- + ---- + 14 a z - a z - 8 a z - 15 z -
3 a
a
8 9
7 z 2 8 4 8 6 z 9 3 9 10 2 10
> ---- - 18 a z - 10 a z - ---- - 13 a z - 7 a z - 2 z - 2 a z
2 a
a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 12 1 3 1 6 3 10 6 11
14 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ----- +
2 14 6 12 5 10 5 10 4 8 4 8 3 6 3 6 2
q q t q t q t q t q t q t q t q t
10 13 11 2 2 2 4 2 4 3
> ----- + ---- + ---- + 9 t + 11 q t + 7 q t + 10 q t + 3 q t +
4 2 4 2
q t q t q t
6 3 6 4 8 4 10 5
> 6 q t + q t + 3 q t + q t |