PD Presentation: |
X6172 X10,3,11,4 X22,16,19,15 X7,20,8,21 X19,8,20,9 X18,14,5,13 X14,12,15,11 X12,18,13,17 X16,22,17,21 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, 401]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 401]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 3, 11, 4], X[22, 16, 19, 15], X[7, 20, 8, 21],
> X[19, 8, 20, 9], X[18, 14, 5, 13], X[14, 12, 15, 11], X[12, 18, 13, 17],
> X[16, 22, 17, 21], X[2, 5, 3, 6], X[4, 9, 1, 10]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {-5, 4, 9, -3},
> {10, -1, -4, 5, 11, -2, 7, -8, 6, -7, 3, -9, 8, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | 3 5 11 12 2 3 4 5
14 + -- - -- + -- - -- - 13 q + 11 q - 7 q + 3 q - q
4 3 2 q
q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | 2 5 3 9 7 3 5 2 4 6 8 10
-3 + --- + --- + --- + -- + -- + -- + -- + q - 3 q - q + 2 q - 3 q +
14 12 10 8 6 4 2
q q q q q q q
12 16
> q - q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 401]][a, z] |
Out[8]= | 2 4 2 2
-4 -2 2 4 4 1 5 a 2 a z 3 z 2 2
5 - a + a - 7 a + 2 a + -- - ----- - ---- + ---- - -- + ---- - 2 a z -
2 2 2 2 2 4 2
z a z z z a a
4
4 2 z 2 4 6
> 2 z + ---- + a z - z
2
a |
In[9]:= | Kauffman[Link[11, NonAlternating, 401]][a, z] |
Out[9]= | 2 4 3
-4 2 4 4 1 5 a 2 a 1 5 9 a 5 a
11 - a + 18 a + 9 a - -- - ----- - ---- - ---- + ---- + --- + --- + ---- +
2 2 2 2 2 3 a z z z
z a z z z a z
2 2
z 3 z 20 z 3 2 3 z 6 z 2 2
> -- - --- - ---- - 32 a z - 16 a z - 10 z + ---- + ---- - 26 a z -
5 3 a 4 2
a a a a
3 3 3 4 4
4 2 2 z 5 z 36 z 3 3 3 4 5 z 10 z
> 13 a z - ---- + ---- + ----- + 43 a z + 14 a z + 7 z - ---- - ----- +
5 3 a 4 2
a a a a
5 5 5 6
2 4 4 4 z 8 z 35 z 5 3 5 6 3 z
> 18 a z + 6 a z + -- - ---- - ----- - 32 a z - 6 a z - 11 z + ---- -
5 3 a 4
a a a
7 7 8 9
2 6 5 z 13 z 7 3 7 8 4 z 2 8 z
> 8 a z + ---- + ----- + 11 a z + 3 a z + 8 z + ---- + 4 a z + -- +
3 a 2 a
a a
9
> a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 9 3 2 4 1 7 4 5 7
- + 7 q + ----- + ----- + ----- + ----- + ----- + ----- + ---- + --- + 6 q t +
q 9 4 7 4 7 3 5 3 5 2 3 2 3 q t
q t q t q t q t q t q t q t
3 3 2 5 2 5 3 7 3 7 4 9 4 11 5
> 7 q t + 5 q t + 6 q t + 2 q t + 5 q t + q t + 2 q t + q t |