PD Presentation: |
X10,1,11,2 X12,3,13,4 X5,14,6,15 X16,7,17,8 X20,15,21,16 X13,18,14,19 X6,22,7,21 X22,18,9,17 X19,5,20,4 X2,9,3,10 X8,11,1,12 |
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, 200]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 200]] |
Out[4]= | PD[X[10, 1, 11, 2], X[12, 3, 13, 4], X[5, 14, 6, 15], X[16, 7, 17, 8],
> X[20, 15, 21, 16], X[13, 18, 14, 19], X[6, 22, 7, 21], X[22, 18, 9, 17],
> X[19, 5, 20, 4], X[2, 9, 3, 10], X[8, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, 9, -3, -7, 4, -11},
> {10, -1, 11, -2, -6, 3, 5, -4, 8, 6, -9, -5, 7, -8}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(17/2) 2 3 5 6 5 6 4 3
-q + ----- - ----- + ----- - ---- + ---- - ---- + ---- - ------- +
15/2 13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q q
> Sqrt[q] |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -26 2 -16 -14 2 3 -8 2 2
1 + q - --- + q + q + --- + --- + q + -- - q
18 12 10 6
q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 200]][a, z] |
Out[8]= | 3 5
a a 3 5 7 3 3 3 5 3
-(--) + -- + a z - 3 a z - 2 a z + 2 a z + a z - 3 a z - 3 a z +
z z
7 3 3 5 5 5
> a z - a z - a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 200]][a, z] |
Out[9]= | 3 5
4 a a 3 5 9 2 2 2 4 2 6 2
a - -- - -- + a z + 2 a z - a z + 2 a z - z - a z + a z + 8 a z +
z z
8 2 3 3 3 5 3 7 3 9 3 4 4
> 7 a z - 3 a z - 3 a z + a z - 6 a z - 7 a z - 3 a z -
6 4 8 4 3 5 5 5 7 5 9 5 2 6
> 18 a z - 15 a z + 4 a z + 3 a z + 4 a z + 5 a z - a z +
4 6 6 6 8 6 3 7 5 7 7 7 9 7
> 5 a z + 16 a z + 10 a z - 2 a z + a z + 2 a z - a z -
4 8 6 8 8 8 5 9 7 9
> 2 a z - 4 a z - 2 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 1 1 1 2 1 3 2
2 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
2 18 8 16 7 14 7 14 6 12 6 12 5 10 5
q q t q t q t q t q t q t q t
3 4 3 2 3 3 1 3 2
> ------ + ----- + ----- + ----- + ----- + ----- + ---- + ---- + q t
10 4 8 4 8 3 6 3 6 2 4 2 4 2
q t q t q t q t q t q t q t q t |