PD Presentation: |
X10,1,11,2 X12,3,13,4 X14,6,15,5 X16,13,17,14 X18,8,19,7 X20,17,9,18 X4,16,5,15 X6,20,7,19 X2,9,3,10 X8,11,1,12 |
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[10, Alternating, 95]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 95]] |
Out[4]= | PD[X[10, 1, 11, 2], X[12, 3, 13, 4], X[14, 6, 15, 5], X[16, 13, 17, 14],
> X[18, 8, 19, 7], X[20, 17, 9, 18], X[4, 16, 5, 15], X[6, 20, 7, 19],
> X[2, 9, 3, 10], X[8, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 2, -7, 3, -8, 5, -10},
> {9, -1, 10, -2, 4, -3, 7, -4, 6, -5, 8, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(13/2) 3 5 9 12 11 12 3/2
-q + ----- - ---- + ---- - ---- + ---- - ------- + 9 Sqrt[q] - 6 q +
11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q
5/2 7/2
> 3 q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -20 -18 -14 4 -10 -8 -6 4 6 8 12
4 + q - q + q - --- + q + q + q + -- + 2 q - 2 q + q
12 4
q q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 95]][a, z] |
Out[8]= | 3
1 a z z 3 5 2 z 3 3 5 3 5
-(---) + - - -- + - + 2 a z - 3 a z + a z + ---- - 2 a z + a z - a z -
a z z 3 a a
a
3 5
> a z |
In[9]:= | Kauffman[Link[10, Alternating, 95]][a, z] |
Out[9]= | 2
1 a z 2 z 3 5 2 3 z 2 2
1 - --- - - - -- + --- + 10 a z + 10 a z + 3 a z - 4 z - ---- - 5 a z -
a z z 3 a 2
a a
3 3
4 2 6 2 2 z 2 z 3 3 3 5 3 7 3
> 8 a z - 4 a z + ---- - ---- - 17 a z - 21 a z - 6 a z + 2 a z +
3 a
a
4 5 5
4 6 z 2 4 4 4 6 4 z 6 z 5 3 5
> 7 z + ---- + a z + 7 a z + 7 a z - -- + ---- + 17 a z + 19 a z +
2 3 a
a a
6 7
5 5 7 5 3 z 2 6 4 6 6 6 4 z 7
> 8 a z - a z - ---- + 7 a z + a z - 3 a z - ---- - 7 a z -
2 a
a
3 7 5 7 8 2 8 4 8 9 3 9
> 7 a z - 4 a z - 3 z - 6 a z - 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 7 1 2 1 3 2 6 3 6
7 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ----- +
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
6 5 6 2 2 2 4 2 4 3 6 3
> ----- + ---- + ---- + 4 t + 5 q t + 2 q t + 4 q t + q t + 2 q t +
4 2 4 2
q t q t q t
8 4
> q t |