PD Presentation: |
X6172 X12,3,13,4 X13,21,14,20 X7,17,8,16 X19,9,20,8 X9,19,10,18 X17,11,18,10 X15,5,16,22 X21,15,22,14 X2536 X4,11,1,12 |
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[11, NonAlternating, 99]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 99]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[13, 21, 14, 20], X[7, 17, 8, 16],
> X[19, 9, 20, 8], X[9, 19, 10, 18], X[17, 11, 18, 10], X[15, 5, 16, 22],
> X[21, 15, 22, 14], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, -4, 5, -6, 7, 11, -2, -3, 9, -8, 4, -7, 6,
> -5, 3, -9, 8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(5/2) -(3/2) 2 3/2 11/2 13/2 15/2
-q + q - ------- + Sqrt[q] - 2 q + q - q + q
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -8 -6 -4 -2 2 4 6 8 10 12 14
2 + q + q + q + q + 3 q + 3 q + 4 q + 2 q - q - 2 q - 3 q -
16 18 24
> q - q - q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 99]][a, z] |
Out[8]= | 3 3
2 4 1 a z 2 z 6 z 2 z 5 z 4 z 3
---- - ---- + --- + - + -- + --- - --- - --- + 3 a z - ---- - ---- + a z -
5 3 a z z 7 5 3 a 3 a
a z a z a a a a
5 5
z z
> -- - --
3 a
a |
In[9]:= | Kauffman[Link[11, NonAlternating, 99]][a, z] |
Out[9]= | 2 -6 6 5 2 4 1 a 6 z 16 z 5 z
1 + -- + a - -- - -- + ---- + ---- + --- - - - --- - ---- - --- + 5 a z -
8 4 2 5 3 a z z 5 3 a
a a a a z a z a a
2 2 2 2 3 3 3 3
2 6 z 7 z 19 z 19 z 5 z 4 z 29 z 10 z 3
> z - ---- - ---- + ----- + ----- - ---- + ---- + ----- + ----- - 10 a z -
8 6 4 2 7 5 3 a
a a a a a a a
4 4 4 4 5 5 5
4 5 z 6 z 19 z 25 z 5 z 22 z 11 z 5 6
> 5 z + ---- + ---- - ----- - ----- + ---- - ----- - ----- + 6 a z + 5 z -
8 6 4 2 7 3 a
a a a a a a
6 6 6 6 7 7 7 8 8 9 9
z z 8 z 13 z z 8 z 6 z 7 8 z 2 z z z
> -- - -- + ---- + ----- - -- + ---- + ---- - a z - z - -- - ---- - -- - --
8 6 4 2 7 3 a 4 2 3 a
a a a a a a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2
2 4 1 1 1 -2 1 1 q 2 6
1 + 3 q + q + ----- + ----- + ----- + t + ----- + - + -- + q t + 2 q t +
6 4 4 4 4 3 2 2 t t
q t q t q t q t
4 2 6 2 6 3 8 3 10 3 8 4 10 4 12 5
> q t + 3 q t + q t + q t + 2 q t + q t + q t + q t +
12 6 16 7
> q t + q t |