PD Presentation: |
X6172 X12,4,13,3 X14,12,15,11 X22,15,5,16 X16,7,17,8 X20,17,21,18 X18,10,19,9 X8,20,9,19 X10,21,11,22 X2536 X4,14,1,13 |
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, 77]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 77]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 4, 13, 3], X[14, 12, 15, 11], X[22, 15, 5, 16],
> X[16, 7, 17, 8], X[20, 17, 21, 18], X[18, 10, 19, 9], X[8, 20, 9, 19],
> X[10, 21, 11, 22], X[2, 5, 3, 6], X[4, 14, 1, 13]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 5, -8, 7, -9, 3, -2, 11, -3, 4, -5, 6, -7,
> 8, -6, 9, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(13/2) 3 7 12 16 19 20
-q + ----- - ---- + ---- - ---- + ---- - ------- + 16 Sqrt[q] -
11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q
3/2 5/2 7/2 9/2
> 13 q + 8 q - 4 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -20 3 3 -10 4 3 2 2 6 8 10 12
5 + q + --- - --- + q - -- + -- - -- + 2 q + 4 q - 2 q + q + q -
14 12 6 4 2
q q q q q
14
> q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 77]][a, z] |
Out[8]= | 3 5 3 3
-2 4 a 3 a a z 4 z 3 5 z 5 z
--- + --- - ---- + -- + -- - --- + 8 a z - 7 a z + 2 a z + -- - ---- +
a z z z z 3 a 3 a
a a
5
3 3 3 5 3 2 z 5 3 5 7
> 8 a z - 6 a z + a z - ---- + 4 a z - 2 a z + a z
a |
In[9]:= | Kauffman[Link[11, Alternating, 77]][a, z] |
Out[9]= | 3 5
2 4 6 2 4 a 3 a a 2 z 9 z 3
2 + 3 a + 3 a + a - --- - --- - ---- - -- + --- + --- + 17 a z + 13 a z +
a z z z z 3 a
a
2 2 3 3
5 7 2 z z 2 2 4 2 6 2 7 z 23 z
> 2 a z - a z - z - -- - -- - 5 a z - 7 a z - 3 a z - ---- - ----- -
4 2 3 a
a a a
4 4
3 3 3 5 3 7 3 4 2 z 5 z 2 4
> 36 a z - 26 a z - 4 a z + 2 a z - 15 z + ---- - ---- - 7 a z +
4 2
a a
5 5
4 4 6 4 10 z 22 z 5 3 5 5 5 7 5
> 6 a z + 5 a z + ----- + ----- + 29 a z + 25 a z + 7 a z - a z +
3 a
a
6 6 7 7
6 z 13 z 2 6 4 6 6 6 4 z z 3 7
> 29 z - -- + ----- + 20 a z + 2 a z - 3 a z - ---- - -- - 8 a z -
4 2 3 a
a a a
8 9
5 7 8 6 z 2 8 4 8 4 z 9 3 9
> 5 a z - 12 z - ---- - 11 a z - 5 a z - ---- - 7 a z - 3 a z -
2 a
a
10 2 10
> z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 10 1 2 1 5 2 7 5 9
12 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ----- +
2 14 6 12 5 10 5 10 4 8 4 8 3 6 3 6 2
q q t q t q t q t q t q t q t q t
7 10 9 2 2 2 4 2 4 3
> ----- + ---- + ---- + 8 t + 8 q t + 5 q t + 8 q t + 3 q t +
4 2 4 2
q t q t q t
6 3 6 4 8 4 10 5
> 5 q t + q t + 3 q t + q t |