PD Presentation: |
X6172 X10,3,11,4 X14,7,15,8 X8,13,5,14 X18,11,19,12 X20,15,21,16 X22,17,9,18 X16,21,17,22 X12,19,13,20 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, Alternating, 387]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 387]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 3, 11, 4], X[14, 7, 15, 8], X[8, 13, 5, 14],
> X[18, 11, 19, 12], X[20, 15, 21, 16], X[22, 17, 9, 18], X[16, 21, 17, 22],
> X[12, 19, 13, 20], 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]= | -14 2 6 10 15 18 16 17 11 8 3 -3
-q + --- - --- + --- - --- + -- - -- + -- - -- + -- - -- + q
13 12 11 10 9 8 7 6 5 4
q q q q q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -44 3 3 4 5 -34 -32 5 8 6 12 3
-q - --- - --- - --- - --- + q - q + --- + --- + --- + --- + --- +
42 40 38 36 30 28 26 24 22
q q q q q q q q q
6 2 -16 3 2 -10
> --- + --- - q + --- - --- + q
20 18 14 12
q q q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 387]][a, z] |
Out[8]= | 8 10 12 14
8 10 12 14 3 a 8 a 7 a 2 a 6 2
13 a - 24 a + 12 a - a + ---- - ----- + ----- - ----- + 2 a z +
2 2 2 2
z z z z
8 2 10 2 12 2 6 4 8 4 10 4 6 6
> 19 a z - 22 a z + 4 a z + 3 a z + 13 a z - 6 a z + a z +
8 6
> 3 a z |
In[9]:= | Kauffman[Link[11, Alternating, 387]][a, z] |
Out[9]= | 8 10 12 14 9
8 10 12 14 16 3 a 8 a 7 a 2 a 8 a
13 a + 28 a + 22 a + 7 a + a - ---- - ----- - ----- - ----- + ---- +
2 2 2 2 z
z z z z
11 13 15 17
15 a 7 a a a 9 11 13 15
> ------ + ----- - --- - --- - 24 a z - 45 a z - 21 a z + 3 a z +
z z z z
17 6 2 8 2 10 2 12 2 14 2 7 3
> 3 a z + 2 a z - 25 a z - 56 a z - 38 a z - 9 a z + 3 a z +
9 3 11 3 13 3 15 3 17 3 6 4
> 31 a z + 54 a z + 26 a z - 3 a z - 3 a z - 3 a z +
8 4 10 4 12 4 14 4 16 4 7 5
> 26 a z + 64 a z + 45 a z + 7 a z - 3 a z - 7 a z -
9 5 11 5 13 5 15 5 17 5 6 6 8 6
> 19 a z - 23 a z - 14 a z - 2 a z + a z + a z - 19 a z -
10 6 12 6 14 6 16 6 7 7 9 7
> 44 a z - 31 a z - 5 a z + 2 a z + 3 a z - 2 a z -
11 7 13 7 15 7 8 8 10 8 12 8
> 6 a z + 2 a z + 3 a z + 6 a z + 12 a z + 10 a z +
14 8 9 9 11 9 13 9 10 10 12 10
> 4 a z + 4 a z + 7 a z + 3 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -7 -5 1 1 1 5 1 5 5
q + q + ------- + ------- + ------- + ------ + ------ + ------ + ------ +
29 11 27 10 25 10 25 9 23 9 23 8 21 8
q t q t q t q t q t q t q t
10 5 8 10 8 8 9 11
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
21 7 19 7 19 6 17 6 17 5 15 5 15 4 13 4
q t q t q t q t q t q t q t q t
5 6 3 5 3
> ------ + ------ + ------ + ----- + ----
13 3 11 3 11 2 9 2 7
q t q t q t q t q t |