PD Presentation: |
X6172 X12,3,13,4 X16,13,17,14 X14,9,15,10 X10,15,11,16 X17,5,18,20 X7,19,8,18 X19,9,20,8 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[10, NonAlternating, 38]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, NonAlternating, 38]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[16, 13, 17, 14], X[14, 9, 15, 10],
> X[10, 15, 11, 16], X[17, 5, 18, 20], X[7, 19, 8, 18], X[19, 9, 20, 8],
> X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 2, -10}, {9, -1, -7, 8, 4, -5, 10, -2, 3, -4, 5, -3, -6, 7,
> -8, 6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(15/2) 2 4 6 5 7 5 4
q - ----- + ----- - ---- + ---- - ---- + ---- - ------- + 2 Sqrt[q]
13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -24 2 -20 2 2 4 4 6 2 2 -4 2 2
-q - --- - q - --- + --- + --- + --- + --- + -- + -- - q - -- - 2 q
22 18 16 14 12 10 8 6 2
q q q q q q q q q |
In[8]:= | HOMFLYPT[Link[10, NonAlternating, 38]][a, z] |
Out[8]= | 3 5 7
2 a 7 a 7 a 2 a 3 5 7 3 3 3
--- - ---- + ---- - ---- + 4 a z - 14 a z + 9 a z - a z + 2 a z - 9 a z +
z z z z
5 3 3 5
> 3 a z - 2 a z |
In[9]:= | Kauffman[Link[10, NonAlternating, 38]][a, z] |
Out[9]= | 3 5 7
2 4 6 8 2 a 7 a 7 a 2 a 3
2 + 8 a + 13 a + 8 a + 2 a - --- - ---- - ---- - ---- + 3 a z + 16 a z +
z z z z
5 7 2 2 2 4 2 6 2 8 2
> 17 a z + 4 a z - 3 z - 17 a z - 29 a z - 20 a z - 5 a z -
3 3 3 5 3 7 3 2 4 4 4 6 4
> 3 a z - 18 a z - 22 a z - 7 a z + 11 a z + 24 a z + 17 a z +
8 4 5 3 5 5 5 7 5 2 6 4 6
> 4 a z - a z + 12 a z + 20 a z + 7 a z - 4 a z - 5 a z -
6 6 8 6 3 7 5 7 7 7 4 8 6 8
> 2 a z - a z - 4 a z - 6 a z - 2 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 1 1 1 3 1 3 4 3
2 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
2 16 7 14 6 12 6 12 5 10 5 10 4 8 4 8 3
q q t q t q t q t q t q t q t q t
2 4 3 1 4 2
> ----- + ----- + ----- + ---- + ---- + 2 q t
6 3 6 2 4 2 4 2
q t q t q t q t q t |