PD Presentation: |
X6172 X14,4,15,3 X8,18,9,17 X16,8,17,7 X18,10,19,9 X10,14,11,13 X20,11,21,12 X22,19,13,20 X12,21,5,22 X2536 X4,16,1,15 |
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, 447]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 447]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 4, 15, 3], X[8, 18, 9, 17], X[16, 8, 17, 7],
> X[18, 10, 19, 9], X[10, 14, 11, 13], X[20, 11, 21, 12], X[22, 19, 13, 20],
> X[12, 21, 5, 22], X[2, 5, 3, 6], X[4, 16, 1, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 4, -3, 5, -6, 7, -9},
> {6, -2, 11, -4, 3, -5, 8, -7, 9, -8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -4 3 6 10 2 3 4 5 6 7
-11 - q + -- - -- + -- + 15 q - 14 q + 13 q - 9 q + 6 q - 3 q + q
3 2 q
q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -12 -6 3 -2 2 4 6 10 12 16 18 20
5 - q - q + -- + q + 5 q + 2 q + 6 q + 4 q + q + 2 q - q + q
4
q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 447]][a, z] |
Out[8]= | 2 2
3 9 2 -2 1 2 2 5 z 16 z 2 2
8 + -- - -- - 2 a + z + ----- - ----- + 13 z + ---- - ----- - 3 a z +
4 2 4 2 2 2 4 2
a a a z a z a a
4 4 6 6 8
4 4 z 14 z 2 4 6 z 6 z z
> 9 z + ---- - ----- - a z + 2 z + -- - ---- - --
4 2 4 2 2
a a a a a |
In[9]:= | Kauffman[Link[11, Alternating, 447]][a, z] |
Out[9]= | -6 3 11 2 -2 1 2 2 2 z 8 z
11 - a + -- + -- + 3 a - z - ----- - ----- + ---- + --- - -- - --- -
4 2 4 2 2 2 3 a z 5 3
a a a z a z a z a a
2 2 2 2 3
12 z 3 2 z 3 z 5 z 32 z 2 2 3 z
> ---- - 7 a z - 2 a z - 32 z - -- + ---- - ---- - ----- - 9 a z - ---- +
a 8 6 4 2 7
a a a a a
3 3 3 4 4 4
5 z 16 z 18 z 3 3 3 4 z 6 z 8 z
> ---- + ----- + ----- + 15 a z + 5 a z + 52 z + -- - ---- + ---- +
5 3 a 8 6 4
a a a a a
4 5 5 5 6
52 z 2 4 3 z 8 z 10 z 5 3 5 6 5 z
> ----- + 15 a z + ---- - ---- - ----- - 5 a z - 4 a z - 38 z + ---- -
2 7 5 3 6
a a a a a
6 6 7 7 7
10 z 41 z 2 6 6 z 3 z 17 z 7 3 7 8
> ----- - ----- - 12 a z + ---- - ---- - ----- - 7 a z + a z + 7 z +
4 2 5 3 a
a a a a
8 8 9 9 10
6 z 10 z 2 8 4 z 7 z 9 10 z
> ---- + ----- + 3 a z + ---- + ---- + 3 a z + z + ---
4 2 3 a 2
a a a a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 1 2 1 4 2 6 4 5
10 q + 8 q + ----- + ----- + ----- + ----- + ----- + ----- + ---- + --- +
9 5 7 4 5 4 5 3 3 3 3 2 2 q t
q t q t q t q t q t q t q t
6 q 3 5 5 2 7 2 7 3 9 3 9 4
> --- + 7 q t + 7 q t + 6 q t + 7 q t + 3 q t + 6 q t + 3 q t +
t
11 4 11 5 13 5 15 6
> 4 q t + q t + 2 q t + q t |