PD Presentation: |
X6172 X10,3,11,4 X16,13,17,14 X14,7,15,8 X8,15,9,16 X18,11,5,12 X12,17,13,18 X2536 X4,9,1,10 |
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[9, Alternating, 7]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[9, Alternating, 7]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 3, 11, 4], X[16, 13, 17, 14], X[14, 7, 15, 8],
> X[8, 15, 9, 16], X[18, 11, 5, 12], X[12, 17, 13, 18], X[2, 5, 3, 6],
> X[4, 9, 1, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -8, 2, -9}, {8, -1, 4, -5, 9, -2, 6, -7, 3, -4, 5, -3, 7, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(21/2) 2 4 5 5 7 5 4 2 -(3/2)
q - ----- + ----- - ----- + ----- - ----- + ---- - ---- + ---- - q
19/2 17/2 15/2 13/2 11/2 9/2 7/2 5/2
q q q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -34 2 -28 -26 2 -22 3 3 2 2 -12 -10
-q - --- - q - q + --- + q + --- + --- + --- + --- - q + q +
32 24 20 18 16 14
q q q q q q
-8 -6 -4
> q - q + q |
In[8]:= | HOMFLYPT[Link[9, Alternating, 7]][a, z] |
Out[8]= | 5 9 11
a 2 a a 3 5 7 9 3 3 5 3 7 3
-(--) + ---- - --- - a z - 2 a z - 2 a z + 3 a z - a z - 2 a z - 2 a z
z z z |
In[9]:= | Kauffman[Link[9, Alternating, 7]][a, z] |
Out[9]= | 5 9 11
6 8 10 12 a 2 a a 3 5 7 9
-a + 3 a + 5 a + 2 a + -- - ---- - --- + a z - 3 a z - a z + 5 a z +
z z z
11 4 2 6 2 8 2 10 2 12 2 3 3
> 2 a z + a z + a z - 10 a z - 15 a z - 5 a z - a z +
5 3 7 3 9 3 11 3 4 4 6 4 8 4
> 3 a z - 2 a z - 12 a z - 6 a z - 2 a z + 2 a z + 13 a z +
10 4 12 4 5 5 7 5 9 5 11 5 6 6
> 13 a z + 4 a z - 3 a z + 5 a z + 15 a z + 7 a z - 3 a z -
8 6 10 6 12 6 7 7 9 7 11 7 8 8 10 8
> 3 a z - a z - a z - 3 a z - 5 a z - 2 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -4 -2 1 1 1 3 1 2 3
q + q + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
22 9 20 8 18 8 18 7 16 7 16 6 14 6
q t q t q t q t q t q t q t
3 2 4 4 2 3 2 2 2
> ------ + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ----
14 5 12 5 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 q t q t |