PD Presentation: |
X6172 X16,7,17,8 X17,1,18,4 X5,14,6,15 X3849 X9,18,10,19 X11,20,12,21 X13,22,14,5 X19,10,20,11 X21,12,22,13 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, 45]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 45]] |
Out[4]= | PD[X[6, 1, 7, 2], X[16, 7, 17, 8], X[17, 1, 18, 4], X[5, 14, 6, 15],
> X[3, 8, 4, 9], X[9, 18, 10, 19], X[11, 20, 12, 21], X[13, 22, 14, 5],
> X[19, 10, 20, 11], X[21, 12, 22, 13], X[2, 16, 3, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -11, -5, 3}, {-4, -1, 2, 5, -6, 9, -7, 10, -8, 4, 11, -2, -3, 6,
> -9, 7, -10, 8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(23/2) -(21/2) 2 3 4 4 3 3 -(7/2)
q - q + ----- - ----- + ----- - ----- + ----- - ---- + q -
19/2 17/2 15/2 13/2 11/2 9/2
q q q q q q
2
> ----
5/2
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -34 -32 2 2 -26 -24 -22 2 3 3 4 2 2
-q - q - --- - --- - q - q + q + --- + --- + --- + --- + --- + --
30 28 18 16 14 12 10 8
q q q q q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 45]][a, z] |
Out[8]= | 5 7 9
-4 a 7 a 3 a 5 7 9 5 3 7 3
----- + ---- - ---- - 13 a z + 20 a z - 7 a z - 10 a z + 18 a z -
z z z
9 3 5 5 7 5 9 5 7 7
> 5 a z - 2 a z + 7 a z - a z + a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 45]][a, z] |
Out[9]= | 5 7 9
6 8 14 4 a 7 a 3 a 5 7 9
-7 a - 7 a - a + ---- + ---- + ---- - 16 a z - 26 a z - 10 a z +
z z z
6 2 8 2 12 2 14 2 5 3 7 3 9 3
> 19 a z + 23 a z - a z + 3 a z + 14 a z + 36 a z + 16 a z -
11 3 13 3 6 4 8 4 10 4 12 4 14 4
> 4 a z + 2 a z - 15 a z - 24 a z - 6 a z + 2 a z - a z -
5 5 7 5 9 5 11 5 13 5 6 6 8 6
> 3 a z - 22 a z - 15 a z + 3 a z - a z + 6 a z + 11 a z +
10 6 12 6 7 7 9 7 11 7 6 8 8 8 10 8
> 4 a z - a z + 7 a z + 6 a z - a z - a z - 2 a z - a z -
7 9 9 9
> a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 2 1 1 2 1 2 3 1
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
6 4 24 9 20 8 20 7 18 6 16 6 16 5 14 5
q q q t q t q t q t q t q t q t
1 3 2 1 1 2 1
> ------ + ------ + ------ + ------ + ------ + ----- + ----
14 4 12 4 12 3 10 3 10 2 8 2 6
q t q t q t q t q t q t q t |