PD Presentation: |
X6172 X10,3,11,4 X14,7,15,8 X8,13,5,14 X11,19,12,18 X15,21,16,20 X17,9,18,22 X21,17,22,16 X19,13,20,12 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]= | 3 |
In[3]:= | Show[DrawMorseLink[Link[11, NonAlternating, 267]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 267]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 3, 11, 4], X[14, 7, 15, 8], X[8, 13, 5, 14],
> X[11, 19, 12, 18], X[15, 21, 16, 20], X[17, 9, 18, 22], X[21, 17, 22, 16],
> X[19, 13, 20, 12], X[2, 5, 3, 6], X[4, 9, 1, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, 3, -4},
> {11, -2, -5, 9, 4, -3, -6, 8, -7, 5, -9, 6, -8, 7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -5 -4 4 2 4 2 3 4 5
-1 + q - q + -- - -- + - + q - q - q + q - q
3 2 q
q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -16 3 4 7 8 9 6 4 2 4 6 8
2 + q + --- + --- + --- + -- + -- + -- + -- - 3 q - 3 q - 5 q - 3 q -
14 12 10 8 6 4 2
q q q q q q q
10 12 14 16
> 2 q - q + q - q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 267]][a, z] |
Out[8]= | 2 4 2 2
7 2 4 7 2 8 a 3 a 2 z 6 z
21 - -- - 18 a + 4 a + -- - ----- - ---- + ---- + 23 z - -- - ---- -
2 2 2 2 2 2 4 2
a z a z z z a a
4
2 2 4 2 4 z 2 4 6
> 14 a z + a z + 12 z - -- - 3 a z + 2 z
2
a |
In[9]:= | Kauffman[Link[11, NonAlternating, 267]][a, z] |
Out[9]= | 2 4
-4 7 2 4 7 2 8 a 3 a 1 1 7
22 + a + -- + 28 a + 13 a - -- - ----- - ---- - ---- - ---- - ---- + --- +
2 2 2 2 2 2 5 3 a z
a z a z z z a z a z
3 2 2
15 a 8 a 3 z 3 z 21 z 3 2 z 9 z
> ---- + ---- + --- + --- - ---- - 45 a z - 24 a z - 42 z + -- - ---- -
z z 5 3 a 4 2
a a a a
3 3 3
2 2 4 2 4 z 3 z 33 z 3 3 3 4
> 54 a z - 22 a z - ---- - ---- + ----- + 53 a z + 21 a z + 50 z -
5 3 a
a a
4 4 5 5
4 z 3 z 2 4 4 4 z 20 z 5 3 5
> ---- + ---- + 61 a z + 18 a z + -- - ----- - 21 a z - 2 a z -
4 2 5 a
a a a
6 6 7
6 z z 2 6 4 6 3 z 7 3 7 8
> 26 z + -- - -- - 31 a z - 7 a z + ---- - a z - 4 a z + 4 z +
4 2 a
a a
2 8 4 8 9 3 9
> 5 a z + a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 3 3 1 1 4 3 1 1 3 1
- + 4 q + q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + ---- +
q 11 6 7 5 7 4 5 4 5 3 3 3 3 2 2
q t q t q t q t q t q t q t q t
1 3 q 3 5 3 2 5 2 7 3 7 4 11 5
> --- + --- + q t + 2 q t + 3 q t + q t + q t + q t + q t + q t
q t t |