PD Presentation: |
X10,1,11,2 X12,4,13,3 X22,12,9,11 X2,9,3,10 X20,17,21,18 X6,14,7,13 X14,8,15,7 X8,16,1,15 X4,20,5,19 X18,6,19,5 X16,21,17,22 |
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, 310]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 310]] |
Out[4]= | PD[X[10, 1, 11, 2], X[12, 4, 13, 3], X[22, 12, 9, 11], X[2, 9, 3, 10],
> X[20, 17, 21, 18], X[6, 14, 7, 13], X[14, 8, 15, 7], X[8, 16, 1, 15],
> X[4, 20, 5, 19], X[18, 6, 19, 5], X[16, 21, 17, 22]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -4, 2, -9, 10, -6, 7, -8},
> {4, -1, 3, -2, 6, -7, 8, -11, 5, -10, 9, -5, 11, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(5/2) 3 6 3/2 5/2 7/2
-q + ---- - ------- + 10 Sqrt[q] - 14 q + 15 q - 16 q +
3/2 Sqrt[q]
q
9/2 11/2 13/2 15/2 17/2
> 14 q - 11 q + 6 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -8 -4 -2 2 4 8 10 12 18 20 22
-3 + q - q + q + q + 2 q + 5 q - 2 q + 2 q + 4 q - q + q -
26
> q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 310]][a, z] |
Out[8]= | 3 3 3 3
1 1 2 z 5 z 7 z 4 z z 6 z 7 z 6 z
-(----) + ---- + --- - --- + --- - --- + 2 a z + -- - ---- + ---- - ---- +
5 3 7 5 3 a 7 5 3 a
a z a z a a a a a a
5 5 5 7
3 2 z 4 z 2 z z
> a z - ---- + ---- - ---- + --
5 3 a 3
a a a |
In[9]:= | Kauffman[Link[11, Alternating, 310]][a, z] |
Out[9]= | 2 2
-4 1 1 z z 8 z 7 z 3 z 2 z z
a - ---- - ---- - -- + -- + --- + --- + --- + 2 a z + 6 z + --- - -- +
5 3 9 7 5 3 a 10 8
a z a z a a a a a a
2 2 3 3 3 3 3 4
6 z 10 z 3 z 6 z 21 z 16 z 9 z 3 4 z
> ---- + ----- + ---- - ---- - ----- - ----- - ---- - 5 a z - 15 z - --- +
4 2 9 7 5 3 a 10
a a a a a a a
4 4 4 4 5 5 5 5 5
4 z 5 z 28 z 33 z 3 z 9 z 21 z 7 z 2 z 5
> ---- - ---- - ----- - ----- - ---- + ---- + ----- + ---- + ---- + 4 a z +
8 6 4 2 9 7 5 3 a
a a a a a a a a
6 6 6 6 7 7 7 7
6 5 z 10 z 35 z 32 z 7 z 2 z 13 z 7 z 7
> 12 z - ---- + ----- + ----- + ----- - ---- - ---- + ----- + ---- - a z -
8 6 4 2 7 5 3 a
a a a a a a a
8 8 8 9 9 9 10 10
8 7 z 11 z 7 z 4 z 7 z 3 z z z
> 3 z - ---- - ----- - ---- - ---- - ---- - ---- - --- - ---
6 4 2 5 3 a 4 2
a a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2
2 4 1 2 1 2 4 6 4 q 4 6
8 q + 7 q + ----- + ----- + ----- + -- + ----- + - + ---- + 8 q t + 7 q t +
6 4 4 3 2 3 2 2 2 t t
q t q t q t t q t
6 2 8 2 8 3 10 3 10 4 12 4 12 5
> 8 q t + 8 q t + 6 q t + 8 q t + 5 q t + 7 q t + 2 q t +
14 5 14 6 16 6 18 7
> 4 q t + q t + 2 q t + q t |