PD Presentation: |
X6172 X5,14,6,15 X3849 X2,16,3,15 X16,7,17,8 X9,18,10,19 X17,1,18,4 X19,13,20,22 X13,10,14,11 X21,5,22,12 X11,21,12,20 |
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, NonAlternating, 321]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 321]] |
Out[4]= | PD[X[6, 1, 7, 2], X[5, 14, 6, 15], X[3, 8, 4, 9], X[2, 16, 3, 15],
> X[16, 7, 17, 8], X[9, 18, 10, 19], X[17, 1, 18, 4], X[19, 13, 20, 22],
> X[13, 10, 14, 11], X[21, 5, 22, 12], X[11, 21, 12, 20]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -4, -3, 7}, {-2, -1, 5, 3, -6, 9, -11, 10},
> {-9, 2, 4, -5, -7, 6, -8, 11, -10, 8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -6 2 4 6 9 8 2 3
9 + q - -- + -- - -- + -- - - - 6 q + 5 q - 2 q
5 4 3 2 q
q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -18 2 2 4 2 4 5 2 6 10
3 + q + --- + --- + -- + -- + -- + -- + 5 q + q - 2 q
14 12 8 6 4 2
q q q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 321]][a, z] |
Out[8]= | 2 4 2
2 2 4 -2 2 a a 2 2 z 2 2 4 2
8 - -- - 9 a + 3 a + z - ---- + -- + 9 z - ---- - 11 a z + 3 a z +
2 2 2 2
a z z a
4 2 4 4 4 2 6
> 3 z - 5 a z + a z - a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 321]][a, z] |
Out[9]= | 2 4 3
3 2 4 6 -2 2 a a 2 a 2 a 2 z 7 z
11 + -- + 11 a + 3 a - a - z - ---- - -- + --- + ---- - --- - --- -
2 2 2 z z 3 a
a z z a
2
3 5 2 7 z 2 2 4 2 6 2
> 12 a z - 8 a z - a z - 24 z - ---- - 23 a z - 2 a z + 4 a z +
2
a
3 3 4
3 z 11 z 3 3 3 5 3 4 4 z 2 4
> ---- + ----- + 15 a z + 13 a z + 6 a z + 22 z + ---- + 24 a z +
3 a 2
a a
5 6
4 4 6 4 6 z 5 3 5 5 5 6 z
> 2 a z - 4 a z - ---- - 9 a z - 10 a z - 7 a z - 9 z + -- -
a 2
a
7
2 6 4 6 6 6 3 z 7 3 7 5 7 8
> 16 a z - 5 a z + a z + ---- + 2 a z + a z + 2 a z + 3 z +
a
2 8 4 8 9 3 9
> 5 a z + 2 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 6 1 1 1 3 2 4 2 5
- + 6 q + ------ + ------ + ----- + ----- + ----- + ----- + ----- + ----- +
q 13 6 11 5 9 5 9 4 7 4 7 3 5 3 5 2
q t q t q t q t q t q t q t q t
4 3 5 3 3 2 5 2 7 3
> ----- + ---- + --- + 3 q t + 3 q t + 2 q t + 3 q t + 2 q t
3 2 3 q t
q t q t |