PD Presentation: |
X6172 X10,3,11,4 X16,11,17,12 X14,7,15,8 X8,15,9,16 X20,17,5,18 X18,14,19,13 X12,20,13,19 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[10, Alternating, 11]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 11]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 3, 11, 4], X[16, 11, 17, 12], X[14, 7, 15, 8],
> X[8, 15, 9, 16], X[20, 17, 5, 18], X[18, 14, 19, 13], X[12, 20, 13, 19],
> X[2, 5, 3, 6], X[4, 9, 1, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 2, -10}, {9, -1, 4, -5, 10, -2, 3, -8, 7, -4, 5, -3, 6, -7,
> 8, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(19/2) 3 7 11 13 14 14 10 7
-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
3
> ------- - Sqrt[q]
Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -30 -28 -26 3 -22 3 -18 3 3 -12 2
-1 + q + q - q + --- - q - --- + q - --- + --- + q + --- +
24 20 16 14 10
q q q q q
4 2 3 2
> -- - -- + -- + q
8 6 4
q q q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 11]][a, z] |
Out[8]= | 3 5 7 9
-2 a 4 a 3 a a 3 5 7 9 3
----- + ---- - ---- + -- - a z - 3 a z + 6 a z - 5 a z + a z - a z +
z z z z
5 3 7 3 3 5 5 5
> 5 a z - 3 a z + a z + 2 a z |
In[9]:= | Kauffman[Link[10, Alternating, 11]][a, z] |
Out[9]= | 3 5 7 9
4 6 8 10 2 a 4 a 3 a a 3 5
2 a + 3 a + 3 a + a - ---- - ---- - ---- - -- - a z + 6 a z + 17 a z +
z z z z
7 9 11 2 2 4 2 6 2 8 2
> 14 a z + 3 a z - a z - 2 a z - 6 a z - 9 a z - 8 a z -
10 2 3 3 3 5 3 7 3 9 3 11 3
> 3 a z + 2 a z - 8 a z - 34 a z - 31 a z - 5 a z + 2 a z +
2 4 4 4 6 4 8 4 10 4 5 3 5
> 5 a z + 7 a z + 7 a z + 10 a z + 5 a z - a z + 9 a z +
5 5 7 5 9 5 11 5 2 6 4 6 6 6
> 34 a z + 33 a z + 8 a z - a z - 3 a z + a z + 7 a z -
10 6 3 7 5 7 7 7 9 7 4 8 6 8
> 3 a z - 5 a z - 13 a z - 13 a z - 5 a z - 4 a z - 8 a z -
8 8 5 9 7 9
> 4 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 5 1 2 1 5 2 6 5
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 2 20 8 18 7 16 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
7 7 8 6 6 8 4 6 t
> ------ + ------ + ------ + ----- + ----- + ----- + ---- + ---- + 2 t + -- +
12 4 10 4 10 3 8 3 8 2 6 2 6 4 2
q t q t q t q t q t q t q t q t q
2 2
> q t |