PD Presentation: |
X6172 X12,3,13,4 X22,14,11,13 X8,16,9,15 X14,8,15,7 X18,10,19,9 X20,18,21,17 X16,22,17,21 X10,20,5,19 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]= | 3 |
In[3]:= | Show[DrawMorseLink[Link[11, Alternating, 407]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 407]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[22, 14, 11, 13], X[8, 16, 9, 15],
> X[14, 8, 15, 7], X[18, 10, 19, 9], X[20, 18, 21, 17], X[16, 22, 17, 21],
> X[10, 20, 5, 19], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 5, -4, 6, -9},
> {11, -2, 3, -5, 4, -8, 7, -6, 9, -7, 8, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -3 2 7 2 3 4 5 6 7 8
-10 + q - -- + - + 16 q - 18 q + 19 q - 17 q + 13 q - 8 q + 4 q - q
2 q
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -10 -8 -6 6 3 2 4 6 8 12 14
4 + q + q + q + -- + -- + 7 q - q + 4 q - q + 2 q - 3 q +
4 2
q q
16 18 20 22 24
> 4 q - q - q + 2 q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 407]][a, z] |
Out[8]= | 2 2 2 2 4
-4 2 2 1 a 2 z 2 z z 2 2 4 z
-3 + a + 2 a - -- + ----- + -- - 4 z - -- + ---- - -- + a z - 2 z - -- +
2 2 2 2 6 4 2 6
z a z z a a a a
4 4 6 6
2 z z z z
> ---- + -- + -- + --
4 2 4 2
a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 407]][a, z] |
Out[9]= | 2
-6 -4 3 2 2 1 a 2 2 a 2 z 6 z
-6 - a - a - -- - 4 a + -- + ----- + -- - --- - --- - --- - --- + 4 a z +
2 2 2 2 2 a z z 5 3
a z a z z a a
2 2 2 2 3 3 3 3
2 2 z 4 z 9 z 9 z 2 2 z 5 z 8 z 16 z
> 8 z + ---- + ---- + ---- + ---- + 6 a z - -- + ---- + ---- + ----- +
8 6 4 2 9 7 5 3
a a a a a a a a
3 4 4 4 4 5 5 5
14 z 4 6 z 2 z 5 z 8 z 2 4 z 11 z 14 z
> ----- - 3 z - ---- - ---- - ---- - ---- - 4 a z + -- - ----- - ----- -
a 8 6 4 2 9 7 5
a a a a a a a
5 5 6 6 6 6 7
17 z 19 z 5 6 4 z 7 z 13 z 7 z 2 6 7 z
> ----- - ----- - 4 a z - 4 z + ---- - ---- - ----- - ---- + a z + ---- +
3 a 8 6 4 2 7
a a a a a a
7 7 8 8 8 9 9 9
4 z 5 z 7 8 7 z 10 z 6 z 4 z 6 z 2 z
> ---- + ---- + 2 a z + 3 z + ---- + ----- + ---- + ---- + ---- + ---- +
5 a 6 4 2 5 3 a
a a a a a a
10 10
z z
> --- + ---
4 2
a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 1 1 2 5 2 5 5 q 3
11 q + 6 q + ----- + ----- + ----- + ----- + ---- + --- + --- + 8 q t +
7 4 5 4 5 3 3 2 2 q t t
q t q t q t q t q t
5 5 2 7 2 7 3 9 3 9 4 11 4
> 10 q t + 11 q t + 10 q t + 8 q t + 9 q t + 5 q t + 8 q t +
11 5 13 5 13 6 15 6 17 7
> 3 q t + 5 q t + q t + 3 q t + q t |