PD Presentation: |
X6172 X10,4,11,3 X12,8,13,7 X18,16,19,15 X16,9,17,10 X8,17,9,18 X20,14,5,13 X14,20,15,19 X2536 X4,12,1,11 |
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, 10]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 10]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 4, 11, 3], X[12, 8, 13, 7], X[18, 16, 19, 15],
> X[16, 9, 17, 10], X[8, 17, 9, 18], X[20, 14, 5, 13], X[14, 20, 15, 19],
> X[2, 5, 3, 6], X[4, 12, 1, 11]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 2, -10}, {9, -1, 3, -6, 5, -2, 10, -3, 7, -8, 4, -5, 6, -4,
> 8, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(7/2) 2 5 7 3/2 5/2 7/2
-q + ---- - ---- + ------- - 10 Sqrt[q] + 11 q - 10 q + 8 q -
5/2 3/2 Sqrt[q]
q q
9/2 11/2 13/2
> 6 q + 3 q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -12 -10 3 -4 2 6 8 10 12 14 16
3 + q + q + -- + q - 2 q - 2 q - q + 2 q - q + 3 q + q -
6
q
18 20
> q + q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 10]][a, z] |
Out[8]= | 3 3 3 3
1 2 1 a a z 3 z 3 z 2 z z
-(----) + ---- - --- - - + -- - -- + --- - 3 a z + a z - -- + ---- + -- -
5 3 a z z z 5 3 5 3 a
a z a z a a a a
5 5
3 z z
> 2 a z + -- + --
3 a
a |
In[9]:= | Kauffman[Link[10, Alternating, 10]][a, z] |
Out[9]= | 3
-4 3 2 1 2 1 a a 5 z 13 z 6 z
-2 - a - -- - a - ---- - ---- - --- + - + -- + --- + ---- + --- - 5 a z -
2 5 3 a z z z 5 3 a
a a z a z a a
2 2 2 3 3 3 3
3 2 z 4 z 11 z 2 2 2 z 11 z 27 z 10 z
> 3 a z + 5 z - -- + ---- + ----- - a z + ---- - ----- - ----- - ----- +
6 4 2 7 5 3 a
a a a a a a
4 4 4 5 5
3 3 3 4 6 z 9 z 20 z 2 4 z 13 z
> 7 a z + 3 a z - z + ---- - ---- - ----- + 4 a z - -- + ----- +
6 4 2 7 5
a a a a a
5 5 6 6 6 7 7
21 z 8 z 3 5 6 3 z 9 z 15 z 2 6 5 z 6 z
> ----- + ---- - a z + z - ---- + ---- + ----- - 2 a z - ---- - ---- -
3 a 6 4 2 5 3
a a a a a a
7 8 8 9 9
3 z 7 8 4 z 6 z z z
> ---- - 2 a z - 2 z - ---- - ---- - -- - --
a 4 2 3 a
a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 1 1 1 4 1 4 3 2 4
7 + 5 q + ----- + ----- + ----- + ----- + ----- + - + ---- + 6 q t + 5 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
> 4 q t + 6 q t + 4 q t + 4 q t + 2 q t + 4 q t + q t +
12 5 14 6
> 2 q t + q t |