PD Presentation: |
X6172 X16,7,17,8 X4,17,1,18 X14,10,15,9 X8493 X10,5,11,6 X20,12,21,11 X22,20,5,19 X18,13,19,14 X12,22,13,21 X2,16,3,15 |
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, 3]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 3]] |
Out[4]= | PD[X[6, 1, 7, 2], X[16, 7, 17, 8], X[4, 17, 1, 18], X[14, 10, 15, 9],
> X[8, 4, 9, 3], X[10, 5, 11, 6], X[20, 12, 21, 11], X[22, 20, 5, 19],
> X[18, 13, 19, 14], X[12, 22, 13, 21], X[2, 16, 3, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -11, 5, -3}, {6, -1, 2, -5, 4, -6, 7, -10, 9, -4, 11, -2, 3, -9,
> 8, -7, 10, -8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(9/2) 4 9 15 20 3/2 5/2
q - ---- + ---- - ---- + ------- - 25 Sqrt[q] + 24 q - 22 q +
7/2 5/2 3/2 Sqrt[q]
q q q
7/2 9/2 11/2 13/2
> 16 q - 10 q + 5 q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -14 -12 -10 3 4 2 -2 2 4 8 10
5 - q + q + q - -- + -- - -- - q - 2 q + 7 q + 3 q + 3 q -
8 6 4
q q q
12 14 16 18 20
> 5 q + 2 q - 2 q - 2 q + q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 3]][a, z] |
Out[8]= | 3 3 3
1 3 2 z 3 z 3 z 4 z 3 3 3
---- - ---- + --- - -- + 2 a z - a z - -- + ---- - ---- + 4 a z - a z +
5 3 a z 3 5 3 a
a z a z a a a
5 5 7
2 z 3 z 5 z
> ---- - ---- + 2 a z - --
3 a a
a |
In[9]:= | Kauffman[Link[11, Alternating, 3]][a, z] |
Out[9]= | 2
-6 3 3 1 3 2 z z 3 2 3 z
-a - -- - -- + ---- + ---- + --- - -- + - + 4 a z + 2 a z + 7 z + ---- +
4 2 5 3 a z 3 a 4
a a a z a z a a
2 3 3 3
7 z 2 2 4 2 5 z 15 z 20 z 3 3 3 4
> ---- + 2 a z - a z - ---- - ----- - ----- - 16 a z - 6 a z - 32 z +
2 5 3 a
a a a
4 4 4 5 5 5 5
5 z z 27 z 2 4 4 4 z 14 z 26 z 16 z
> ---- - -- - ----- - 9 a z + 2 a z - -- + ----- + ----- + ----- +
6 4 2 7 5 3 a
a a a a a a
6 6 6
5 3 5 6 5 z 12 z 43 z 2 6 4 6
> 14 a z + 9 a z + 42 z - ---- + ----- + ----- + 15 a z - a z -
6 4 2
a a a
7 7 7 8 8
10 z 5 z 13 z 7 3 7 8 11 z 19 z 2 8
> ----- - ---- + ----- + 4 a z - 4 a z - 15 z - ----- - ----- - 7 a z -
5 3 a 4 2
a a a a
9 9 10
7 z 13 z 9 10 2 z
> ---- - ----- - 6 a z - 2 z - -----
3 a 2
a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 1 3 1 6 3 9 6 9
14 + 13 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + - +
10 5 8 4 6 4 6 3 4 3 4 2 2 2 t
q t q t q t q t q t q t q t
11 2 4 4 2 6 2 6 3 8 3
> ---- + 12 q t + 12 q t + 10 q t + 12 q t + 6 q t + 10 q t +
2
q t
8 4 10 4 10 5 12 5 14 6
> 4 q t + 6 q t + q t + 4 q t + q t |