PD Presentation: |
X6172 X16,7,17,8 X17,1,18,4 X5,12,6,13 X3849 X13,22,14,5 X21,14,22,15 X9,18,10,19 X11,20,12,21 X19,10,20,11 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, NonAlternating, 20]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 20]] |
Out[4]= | PD[X[6, 1, 7, 2], X[16, 7, 17, 8], X[17, 1, 18, 4], X[5, 12, 6, 13],
> X[3, 8, 4, 9], X[13, 22, 14, 5], X[21, 14, 22, 15], X[9, 18, 10, 19],
> X[11, 20, 12, 21], X[19, 10, 20, 11], X[2, 16, 3, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -11, -5, 3}, {-4, -1, 2, 5, -8, 10, -9, 4, -6, 7, 11, -2, -3, 8,
> -10, 9, -7, 6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(21/2) -(19/2) 3 5 6 7 6 6 3 2
q - q + ----- - ----- + ----- - ----- + ---- - ---- + ---- - ----
17/2 15/2 13/2 11/2 9/2 7/2 5/2 3/2
q q q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -32 -30 2 3 -22 -20 3 2 4 -12 2 2 2
-q - q - --- - --- - q + q + --- + --- + --- + q + --- + -- + --
28 26 18 16 14 10 8 4
q q q q q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 20]][a, z] |
Out[8]= | 3 5 7 9
a a 4 a 2 a 3 7 9 3 3 5 3
-(--) - -- + ---- - ---- - 4 a z + 7 a z - 3 a z - 2 a z + 2 a z +
z z z z
7 3 9 3 5 5 7 5
> 4 a z - a z + a z + a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 20]][a, z] |
Out[9]= | 3 5 7 9
4 6 8 10 12 a a 4 a 2 a 3 5
a - 5 a - 6 a + a + 2 a - -- + -- + ---- + ---- + 5 a z - a z -
z z z z
7 9 11 4 2 6 2 8 2 10 2
> 13 a z - 8 a z - a z - a z + 15 a z + 21 a z - 2 a z -
12 2 3 3 5 3 7 3 9 3 11 3 6 4
> 7 a z - 3 a z - 5 a z + 16 a z + 17 a z - a z - 17 a z -
8 4 10 4 12 4 5 5 7 5 9 5 11 5
> 21 a z + a z + 5 a z + 4 a z - 10 a z - 11 a z + 3 a z -
4 6 6 6 8 6 10 6 12 6 5 7 7 7
> a z + 7 a z + 11 a z + 2 a z - a z - 2 a z + 3 a z +
9 7 11 7 6 8 8 8 10 8 7 9 9 9
> 4 a z - a z - 2 a z - 3 a z - a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 2 1 1 3 2 3 4 2
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 2 22 9 18 8 18 7 16 6 14 6 14 5 12 5
q q q t q t q t q t q t q t q t
3 4 3 3 3 3 3
> ------ + ------ + ------ + ----- + ----- + ----- + ----
12 4 10 4 10 3 8 3 8 2 6 2 4
q t q t q t q t q t q t q t |