PD Presentation: |
X6172 X12,3,13,4 X16,8,17,7 X18,10,19,9 X8,18,9,17 X19,22,20,5 X13,20,14,21 X21,14,22,15 X10,16,11,15 X2536 X4,11,1,12 |
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, 97]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 97]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[16, 8, 17, 7], X[18, 10, 19, 9],
> X[8, 18, 9, 17], X[19, 22, 20, 5], X[13, 20, 14, 21], X[21, 14, 22, 15],
> X[10, 16, 11, 15], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -5, 4, -9, 11, -2, -7, 8, 9, -3, 5, -4,
> -6, 7, -8, 6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(11/2) 4 5 8 9 9 3/2 5/2
q - ---- + ---- - ---- + ---- - ------- + 7 Sqrt[q] - 5 q + 3 q -
9/2 7/2 5/2 3/2 Sqrt[q]
q q q q
7/2
> q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | 3 -12 3 2 -6 2 2 2 4 6 8 10
2 + --- + q + --- + -- - q + -- - -- - q - q + q - q + q
14 10 8 4 2
q q q q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 97]][a, z] |
Out[8]= | 3 5 3 5
a a 2 z 3 3 z 3 3 3 z 5
-(--) + -- - --- + 3 a z - 3 a z - ---- + 8 a z - 3 a z - -- + 5 a z -
z z a a a
3 5 7
> a z + a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 97]][a, z] |
Out[9]= | 3 5 2
4 a a 2 z 5 2 2 z 2 2 4 2 6 2
a - -- - -- + --- + a z + a z + z - ---- + 4 a z + 2 a z + a z +
z z a 2
a
3 3 4
2 z 7 z 3 3 3 5 3 4 7 z 2 4
> ---- - ---- - 9 a z + 6 a z + 6 a z - 4 z + ---- - 13 a z -
3 a 2
a a
5 5 6
4 4 6 4 z 10 z 5 3 5 5 5 6 3 z
> 3 a z - a z - -- + ----- + 8 a z - 7 a z - 4 a z + 6 z - ---- +
3 a 2
a a
7
2 6 4 6 4 z 7 3 7 8 2 8 4 8
> 10 a z + a z - ---- - 2 a z + 2 a z - 3 z - 4 a z - a z -
a
9 3 9
> a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 5 1 3 2 3 2 5 3 4
5 + -- + ------ + ------ + ----- + ----- + ----- + ----- + ----- + ---- +
2 12 5 10 4 8 4 8 3 6 3 6 2 4 2 4
q q t q t q t q t q t q t q t q t
5 2 2 2 4 2 4 3 6 3 8 4
> ---- + 3 t + 4 q t + 2 q t + 3 q t + q t + 2 q t + q t
2
q t |