PD Presentation: |
X8192 X16,9,17,10 X6718 X20,17,7,18 X10,4,11,3 X14,6,15,5 X4,12,5,11 X18,14,19,13 X12,20,13,19 X2,16,3,15 |
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, 69]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 69]] |
Out[4]= | PD[X[8, 1, 9, 2], X[16, 9, 17, 10], X[6, 7, 1, 8], X[20, 17, 7, 18],
> X[10, 4, 11, 3], X[14, 6, 15, 5], X[4, 12, 5, 11], X[18, 14, 19, 13],
> X[12, 20, 13, 19], X[2, 16, 3, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 5, -7, 6, -3},
> {3, -1, 2, -5, 7, -9, 8, -6, 10, -2, 4, -8, 9, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(7/2) 4 8 11 3/2 5/2 7/2
-q + ---- - ---- + ------- - 15 Sqrt[q] + 15 q - 14 q + 11 q -
5/2 3/2 Sqrt[q]
q q
9/2 11/2 13/2
> 7 q + 3 q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -10 2 2 2 4 6 10 12 14 20
5 + q - -- + -- - 2 q + 3 q - 2 q + 2 q - 2 q + 3 q + q
8 6
q q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 69]][a, z] |
Out[8]= | 3 3 3
1 2 2 a 2 z 6 z 4 z z 6 z 6 z 3
-(----) + ---- - --- + - - --- + --- - --- + a z - -- + ---- - ---- + 2 a z +
5 3 a z z 5 3 a 5 3 a
a z a z a a a a
5 5 7
2 z 4 z 5 z
> ---- - ---- + a z - --
3 a a
a |
In[9]:= | Kauffman[Link[10, Alternating, 69]][a, z] |
Out[9]= | 2 2
-2 1 2 2 a z 3 z 11 z 9 z 2 z 2 z
-a - ---- - ---- - --- - - - -- + --- + ---- + --- + 2 a z - ---- + ---- +
5 3 a z z 7 5 3 a 6 4
a z a z a a a a a
2 3 3 3 3 4 4
5 z 2 2 2 z 5 z 23 z 24 z 3 3 3 5 z 3 z
> ---- - a z + ---- - ---- - ----- - ----- - 7 a z + a z + ---- - ---- -
2 7 5 3 a 6 4
a a a a a a
4 5 5 5 5
14 z 2 4 z 8 z 23 z 28 z 5 3 5 6
> ----- + 6 a z - -- + ---- + ----- + ----- + 13 a z - a z + 7 z -
2 7 5 3 a
a a a a
6 6 6 7 7 7
3 z 6 z 20 z 2 6 5 z 8 z 10 z 7 8
> ---- + ---- + ----- - 4 a z - ---- - ---- - ----- - 7 a z - 6 z -
6 4 2 5 3 a
a a a a a
8 8 9 9
5 z 11 z 2 z 2 z
> ---- - ----- - ---- - ----
4 2 3 a
a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 1 3 1 5 3 5 6 2 4
9 + 7 q + ----- + ----- + ----- + ----- + ----- + - + ---- + 7 q t + 8 q t +
8 4 6 3 4 3 4 2 2 2 t 2
q t q t q t q t q t q t
4 2 6 2 6 3 8 3 8 4 10 4 10 5
> 7 q t + 8 q t + 5 q t + 6 q t + 2 q t + 5 q t + q t +
12 5 14 6
> 2 q t + q t |