PD Presentation: |
X6172 X14,7,15,8 X4,15,1,16 X5,10,6,11 X8493 X17,22,18,19 X11,20,12,21 X19,12,20,13 X21,18,22,5 X9,16,10,17 X2,14,3,13 |
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, 380]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 380]] |
Out[4]= | PD[X[6, 1, 7, 2], X[14, 7, 15, 8], X[4, 15, 1, 16], X[5, 10, 6, 11],
> X[8, 4, 9, 3], X[17, 22, 18, 19], X[11, 20, 12, 21], X[19, 12, 20, 13],
> X[21, 18, 22, 5], X[9, 16, 10, 17], X[2, 14, 3, 13]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -11, 5, -3}, {-8, 7, -9, 6},
> {-4, -1, 2, -5, -10, 4, -7, 8, 11, -2, 3, 10, -6, 9}] |
In[6]:= | Jones[L][q] |
Out[6]= | -10 2 4 5 4 6 4 4 -2 1
-q + -- - -- + -- - -- + -- - -- + -- - q + -
9 8 7 6 5 4 3 q
q q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -32 2 -28 3 -24 2 3 7 6 6 4 2
-q - --- - q - --- - q + --- + --- + --- + --- + --- + --- + --- +
30 26 22 20 18 16 14 12 10
q q q q q q q q q
3 -6 -2
> -- + q + q
8
q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 380]][a, z] |
Out[8]= | 4 6 8 10
2 4 6 8 10 2 a 5 a 4 a a 2 2 4 2
a + 4 a - 10 a + 6 a - a + ---- - ---- + ---- - --- + a z + 3 a z -
2 2 2 2
z z z z
6 2 8 2 6 4
> 7 a z + 3 a z - 2 a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 380]][a, z] |
Out[9]= | 4 6 8 10 5 7
2 4 6 8 10 2 a 5 a 4 a a 5 a 9 a
-a + 6 a + 16 a + 13 a + 3 a - ---- - ---- - ---- - --- + ---- + ---- +
2 2 2 2 z z
z z z z
9 11
5 a a 5 7 9 11 2 2 4 2
> ---- + --- - 15 a z - 30 a z - 20 a z - 5 a z + a z - 7 a z -
z z
6 2 8 2 10 2 3 3 5 3 7 3 9 3
> 23 a z - 21 a z - 6 a z + a z + 17 a z + 39 a z + 31 a z +
11 3 4 4 6 4 8 4 10 4 5 5 7 5
> 8 a z + 3 a z + 23 a z + 31 a z + 11 a z - 9 a z - 21 a z -
9 5 11 5 6 6 8 6 10 6 5 7 7 7
> 17 a z - 5 a z - 14 a z - 23 a z - 9 a z + 2 a z + a z +
11 7 6 8 8 8 10 8 7 9 9 9
> a z + 3 a z + 5 a z + 2 a z + a z + a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -5 2 1 1 1 1 3 1 2 3
q + -- + - + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
3 q 21 9 19 8 17 8 17 7 15 7 15 6 13 6
q q t q t q t q t q t q t q t
3 2 1 5 4 1 2 3
> ------ + ------ + ------ + ------ + ----- + ------ + ----- + ----- +
13 5 11 5 13 4 11 4 9 4 11 3 9 3 7 3
q t q t q t q t q t q t q t q t
3 2 2
> ----- + ----- + ----
7 2 5 2 3
q t q t q t |