PD Presentation: |
X6172 X10,3,11,4 X14,8,15,7 X20,16,21,15 X18,12,19,11 X12,20,13,19 X22,18,5,17 X16,22,17,21 X8,14,9,13 X2536 X4,9,1,10 |
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, 25]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 25]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 3, 11, 4], X[14, 8, 15, 7], X[20, 16, 21, 15],
> X[18, 12, 19, 11], X[12, 20, 13, 19], X[22, 18, 5, 17], X[16, 22, 17, 21],
> X[8, 14, 9, 13], X[2, 5, 3, 6], X[4, 9, 1, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -9, 11, -2, 5, -6, 9, -3, 4, -8, 7, -5,
> 6, -4, 8, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(5/2) 2 7 3/2 5/2 7/2
-q + ---- - ------- + 10 Sqrt[q] - 15 q + 17 q - 17 q +
3/2 Sqrt[q]
q
9/2 11/2 13/2 15/2 17/2
> 16 q - 12 q + 7 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -8 -6 -4 5 2 4 6 8 10 14 16
1 + q + q + q + -- + 4 q + 3 q - 2 q + 3 q - 5 q - 2 q - 2 q +
2
q
18 20 22 26
> 3 q - 2 q + q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 25]][a, z] |
Out[8]= | 3 3 3 3
1 1 2 2 a 2 z 2 z 5 z z 5 z 2 z 6 z
---- - ---- - --- + --- + --- - --- - --- + 3 a z + -- - ---- + ---- - ---- +
5 3 a z z 7 5 a 7 5 3 a
a z a z a a a a a
5 5 5 7
3 2 z 3 z 2 z z
> a z - ---- + ---- - ---- + --
5 3 a 3
a a a |
In[9]:= | Kauffman[Link[11, Alternating, 25]][a, z] |
Out[9]= | -8 3 1 1 2 2 a 3 z 3 z 4 z 3 z 2
3 + a - -- + ---- + ---- - --- - --- + --- + --- - --- + --- + 7 a z - 4 z +
4 5 3 a z z 7 5 3 a
a a z a z a a a
2 2 2 2 3 3 3 3 3
z 4 z 23 z 14 z 2 z 12 z 22 z z 2 z 3
> --- - ---- + ----- + ----- + ---- - ----- - ----- - -- - ---- - 9 a z -
10 8 4 2 9 7 5 3 a
a a a a a a a a
4 4 4 4 4 5 5 5 5
4 z 6 z 7 z 49 z 38 z 3 z 14 z 25 z z
> 3 z - --- + ---- - ---- - ----- - ----- - ---- + ----- + ----- - -- -
10 8 6 4 2 9 7 5 3
a a a a a a a a a
5 6 6 6 6 7 7 7
4 z 5 6 6 z 14 z 49 z 35 z 9 z 2 z 16 z
> ---- + 5 a z + 6 z - ---- + ----- + ----- + ----- - ---- - ---- + ----- +
a 8 6 4 2 7 5 3
a a a a a a a
7 8 8 8 9 9 9 10 10
8 z 7 8 9 z 15 z 8 z 5 z 8 z 3 z z z
> ---- - a z - 2 z - ---- - ----- - ---- - ---- - ---- - ---- - --- - ---
a 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 1 2 2 5 5 5 q 4
10 q + 6 q + ----- + ----- + ----- + -- + ----- + - + ---- + 8 q t +
6 4 4 4 4 3 2 2 2 t t
q t q t q t t q t
6 6 2 8 2 8 3 10 3 10 4 12 4
> 9 q t + 9 q t + 8 q t + 7 q t + 9 q t + 5 q t + 7 q t +
12 5 14 5 14 6 16 6 18 7
> 2 q t + 5 q t + q t + 2 q t + q t |