PD Presentation: |
X10,1,11,2 X12,4,13,3 X20,12,9,11 X2,9,3,10 X4,17,5,18 X18,5,19,6 X6,14,7,13 X14,8,15,7 X8,16,1,15 X16,19,17,20 |
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, 103]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 103]] |
Out[4]= | PD[X[10, 1, 11, 2], X[12, 4, 13, 3], X[20, 12, 9, 11], X[2, 9, 3, 10],
> X[4, 17, 5, 18], X[18, 5, 19, 6], X[6, 14, 7, 13], X[14, 8, 15, 7],
> X[8, 16, 1, 15], X[16, 19, 17, 20]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -4, 2, -5, 6, -7, 8, -9},
> {4, -1, 3, -2, 7, -8, 9, -10, 5, -6, 10, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(9/2) 3 5 9 11 3/2 5/2
q - ---- + ---- - ---- + ------- - 12 Sqrt[q] + 11 q - 10 q +
7/2 5/2 3/2 Sqrt[q]
q q q
7/2 9/2 11/2
> 6 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -14 -10 4 2 4 8 10 12 14 16
1 - q + q + -- - 2 q + 4 q + 3 q + q - 2 q + q - q
6
q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 103]][a, z] |
Out[8]= | 3 3 5
1 a 3 z 8 z 3 3 z 10 z 3 3 3 z
-(---) + - + --- - --- + 7 a z - 2 a z + ---- - ----- + 7 a z - a z + -- -
a z z 3 a 3 a 3
a a a
5 7
5 z 5 z
> ---- + 2 a z - --
a a |
In[9]:= | Kauffman[Link[10, Alternating, 103]][a, z] |
Out[9]= | 2 2 2
1 a z 2 z 10 z 3 z 2 z 3 z 2 2
1 - --- - - - -- + --- + ---- + 10 a z + 3 a z + -- - ---- - ---- - 2 a z -
a z z 5 3 a 6 4 2
a a a a a
3 3 3 4 4
4 2 3 z 6 z 26 z 3 3 3 4 z 5 z
> 2 a z + ---- - ---- - ----- - 27 a z - 10 a z - 4 z - -- + ---- +
5 3 a 6 4
a a a a
4 5 5 5 6
5 z 4 4 3 z 8 z 28 z 5 3 5 6 5 z
> ---- + 3 a z - ---- + ---- + ----- + 27 a z + 10 a z + 13 z - ---- +
2 5 3 a 4
a a a a
6 7 7 8
z 2 6 4 6 6 z 10 z 7 3 7 8 4 z
> -- + 6 a z - a z - ---- - ----- - 7 a z - 3 a z - 7 z - ---- -
2 3 a 2
a a a
9
2 8 z 9
> 3 a z - -- - a z
a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 1 2 1 3 2 6 3 6 5
7 + 7 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + - + ---- +
10 5 8 4 6 4 6 3 4 3 4 2 2 2 t 2
q t q t q t q t q t q t q t q t
2 4 4 2 6 2 6 3 8 3 8 4
> 6 q t + 5 q t + 4 q t + 6 q t + 2 q t + 4 q t + q t +
10 4 12 5
> 2 q t + q t |