PD Presentation: |
X12,1,13,2 X20,8,21,7 X14,3,15,4 X6,15,7,16 X16,5,17,6 X4,17,5,18 X22,20,11,19 X18,9,19,10 X2,11,3,12 X10,13,1,14 X8,22,9,21 |
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, Alternating, 370]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 370]] |
Out[4]= | PD[X[12, 1, 13, 2], X[20, 8, 21, 7], X[14, 3, 15, 4], X[6, 15, 7, 16],
> X[16, 5, 17, 6], X[4, 17, 5, 18], X[22, 20, 11, 19], X[18, 9, 19, 10],
> X[2, 11, 3, 12], X[10, 13, 1, 14], X[8, 22, 9, 21]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 3, -6, 5, -4, 2, -11, 8, -10},
> {9, -1, 10, -3, 4, -5, 6, -8, 7, -2, 11, -7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(17/2) 2 5 9 13 15 17 15 12
-q + ----- - ----- + ----- - ---- + ---- - ---- + ---- - ------- +
15/2 13/2 11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q q q
3/2 5/2
> 8 Sqrt[q] - 4 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -26 -22 3 2 2 2 2 3 -8 2 -4 2
3 + q + q + --- - --- + --- + --- - --- + --- - q + -- + q - -- -
20 18 16 14 12 10 6 2
q q q q q q q q
2 6 8
> 3 q + 2 q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 370]][a, z] |
Out[8]= | 5 7 3
a a 3 5 7 z 3 3 5 3 7 3
-(--) + -- + a z - 3 a z - 3 a z + 2 a z + -- - 4 a z - 2 a z + a z -
z z a
5 3 5 5 5
> a z - 2 a z - a z |
In[9]:= | Kauffman[Link[11, Alternating, 370]][a, z] |
Out[9]= | 5 7
6 a a 3 5 9 2 2 2 6 2
-a + -- + -- + a z + 3 a z - 2 a z + 4 a z - 2 z - 3 a z + 5 a z +
z z
3
8 2 2 z 3 3 3 5 3 7 3 9 3 4
> 4 a z + ---- - 6 a z - 13 a z - 4 a z - 7 a z - 8 a z + 8 z -
a
4 5
z 2 4 4 4 6 4 8 4 4 z 5 3 5
> -- + 4 a z - 9 a z - 14 a z - 10 a z - ---- + 13 a z + 20 a z +
2 a
a
5 5 7 5 9 5 6 2 6 4 6 6 6
> a z + 3 a z + 5 a z - 8 z + 7 a z + 22 a z + 15 a z +
8 6 7 3 7 5 7 7 7 9 7 2 8
> 8 a z - 10 a z - 4 a z + 11 a z + 4 a z - a z - 8 a z -
4 8 6 8 8 8 3 9 5 9 7 9 4 10 6 10
> 9 a z - 3 a z - 2 a z - 4 a z - 6 a z - 2 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 6 1 1 1 4 2 6 3
7 + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
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
7 6 8 7 9 8 6 9
> ------ + ----- + ----- + ----- + ----- + ----- + ---- + ---- + 3 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
2 2 2 4 2 6 3
> 5 q t + q t + 3 q t + q t |