PD Presentation: |
X6172 X10,3,11,4 X14,7,15,8 X8,13,5,14 X18,11,19,12 X22,15,9,16 X20,17,21,18 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, 388]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 388]] |
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[22, 15, 9, 16], X[20, 17, 21, 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, -7, 8, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -13 2 6 10 13 16 15 16 10 7 3 -2
-q + --- - --- + --- - -- + -- - -- + -- - -- + -- - -- + q
12 11 10 9 8 7 6 5 4 3
q q q q q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -42 3 2 2 5 2 3 2 8 4 7 5 3
-q - --- - --- - --- - --- + --- + --- + --- + --- + --- + --- + --- + --- +
40 38 36 34 32 30 28 26 24 22 20 18
q q q q q q q q q q q q
6 2 -12 2 2 -6
> --- - --- + q + --- - -- + q
16 14 10 8
q q q q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 388]][a, z] |
Out[8]= | 6 8 10 12 14
6 8 10 12 a a 2 a 3 a a 4 2 6 2
4 a - a - 7 a + 4 a + -- - -- - ----- + ----- - --- + a z + 5 a z +
2 2 2 2 2
z z z z z
8 2 10 2 4 4 6 4 8 4
> 3 a z - 6 a z + a z + 3 a z + 3 a z |
In[9]:= | Kauffman[Link[11, Alternating, 388]][a, z] |
Out[9]= | 6 8 10 12 14 7
6 8 10 12 14 a a 2 a 3 a a 2 a
-4 a - 3 a + 4 a + 5 a + a + -- + -- - ----- - ----- - --- - ---- +
2 2 2 2 2 z
z z z z z
9 11 13 15
2 a 10 a 8 a 2 a 7 9 11 13
> ---- + ------ + ----- + ----- + 4 a z - 10 a z - 34 a z - 27 a z -
z z z z
15 4 2 6 2 8 2 10 2 12 2 14 2
> 7 a z - a z + 8 a z + 9 a z - 5 a z - 7 a z - 2 a z -
5 3 7 3 9 3 11 3 13 3 15 3 4 4
> 2 a z - a z + 23 a z + 49 a z + 36 a z + 9 a z + a z -
6 4 8 4 10 4 12 4 14 4 5 5 7 5
> 8 a z - 4 a z + 17 a z + 19 a z + 7 a z + 3 a z - 6 a z -
9 5 11 5 13 5 15 5 6 6 8 6
> 23 a z - 27 a z - 18 a z - 5 a z + 6 a z - 7 a z -
10 6 12 6 14 6 7 7 9 7 11 7 13 7
> 28 a z - 22 a z - 7 a z + 7 a z + 3 a z - 6 a z - a z +
15 7 8 8 10 8 12 8 14 8 9 9 11 9
> a z + 7 a z + 10 a z + 5 a z + 2 a z + 4 a z + 6 a z +
13 9 10 10 12 10
> 2 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -5 -3 1 1 1 5 1 5 5
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
8 5 8 8 7 8 9 10
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
19 7 17 7 17 6 15 6 15 5 13 5 13 4 11 4
q t q t q t q t q t q t q t q t
4 6 3 4 3
> ------ + ----- + ----- + ----- + ----
11 3 9 3 9 2 7 2 5
q t q t q t q t q t |