PD Presentation: |
X6172 X12,3,13,4 X13,22,14,19 X7,20,8,21 X19,10,20,11 X9,16,10,17 X17,14,18,15 X15,8,16,9 X21,18,22,5 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]= | 3 |
In[3]:= | Show[DrawMorseLink[Link[11, NonAlternating, 411]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 411]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[13, 22, 14, 19], X[7, 20, 8, 21],
> X[19, 10, 20, 11], X[9, 16, 10, 17], X[17, 14, 18, 15], X[15, 8, 16, 9],
> X[21, 18, 22, 5], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {-5, 4, -9, 3},
> {10, -1, -4, 8, -6, 5, 11, -2, -3, 7, -8, 6, -7, 9}] |
In[6]:= | Jones[L][q] |
Out[6]= | -13 2 2 -10 -8 2 -6 2 -4 -3
-q + --- - --- + q + q + -- - q + -- - q + q
12 11 7 5
q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -42 3 -38 -36 3 3 6 5 6 4 -20 2
-q - --- - q - q + --- + --- + --- + --- + --- + --- + q + --- +
40 32 30 28 26 24 22 18
q q q q q q q q
-16 -14 -10
> q + q + q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 411]][a, z] |
Out[8]= | 8 10 12 14
6 8 10 12 2 a 5 a 4 a a 6 2 8 2
2 a + 5 a - 12 a + 5 a + ---- - ----- + ----- - --- + 6 a z + 6 a z -
2 2 2 2
z z z z
10 2 6 4 8 4 10 4 6 6 8 6
> 8 a z + 5 a z + 5 a z - a z + a z + a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 411]][a, z] |
Out[9]= | 8 10 12 14 9
6 8 10 12 14 2 a 5 a 4 a a 5 a
-2 a + 7 a + 21 a + 16 a + 3 a - ---- - ----- - ----- - --- + ---- +
2 2 2 2 z
z z z z
11 13 15
9 a 5 a a 9 11 13 15 6 2
> ----- + ----- + --- - 22 a z - 39 a z - 21 a z - 4 a z + 6 a z -
z z z
8 2 10 2 12 2 14 2 7 3 9 3
> 10 a z - 43 a z - 35 a z - 8 a z + 2 a z + 32 a z +
11 3 13 3 15 3 6 4 8 4 10 4
> 54 a z + 30 a z + 6 a z - 5 a z + 7 a z + 44 a z +
12 4 14 4 7 5 9 5 11 5 13 5
> 47 a z + 15 a z - 4 a z - 19 a z - 20 a z - 10 a z -
15 5 6 6 8 6 10 6 12 6 14 6 7 7
> 5 a z + a z - 5 a z - 21 a z - 26 a z - 11 a z + a z +
9 7 11 7 13 7 15 7 8 8 10 8 12 8
> 3 a z - 2 a z - 3 a z + a z + a z + 3 a z + 4 a z +
14 8 11 9 13 9
> 2 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -7 -5 1 1 1 1 1 3 2
q + q + ------- + ------- + ------- + ------ + ------ + ------ + ------ +
27 11 25 10 23 10 23 9 21 9 21 8 19 8
q t q t q t q t q t q t q t
3 2 2 1 5 2 2 2
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
21 7 19 7 17 7 19 6 17 6 15 6 17 5 15 5
q t q t q t q t q t q t q t q t
2 3 5 1 2 1 1 1
> ------ + ------ + ------ + ------ + ------ + ------ + ----- + ------ +
13 5 15 4 13 4 11 4 13 3 11 3 9 3 11 2
q t q t q t q t q t q t q t q t
2 1
> ----- + ----
9 2 7
q t q t |