PD Presentation: |
X12,1,13,2 X8493 X18,14,19,13 X22,20,11,19 X20,15,21,16 X14,21,15,22 X6,17,7,18 X16,7,17,8 X10,6,1,5 X4,10,5,9 X2,11,3,12 |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Length[Skeleton[L]] |
Out[2]= | 2 |
In[3]:= | Show[DrawMorseLink[Link[11, Alternating, 345]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, Alternating, 345]] |
Out[4]= | PD[X[12, 1, 13, 2], X[8, 4, 9, 3], X[18, 14, 19, 13], X[22, 20, 11, 19],
> X[20, 15, 21, 16], X[14, 21, 15, 22], X[6, 17, 7, 18], X[16, 7, 17, 8],
> X[10, 6, 1, 5], X[4, 10, 5, 9], X[2, 11, 3, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -11, 2, -10, 9, -7, 8, -2, 10, -9},
> {11, -1, 3, -6, 5, -8, 7, -3, 4, -5, 6, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(11/2) 2 6 10 15 18 3/2
-q + ---- - ---- + ---- - ---- + ------- - 19 Sqrt[q] + 17 q -
9/2 7/2 5/2 3/2 Sqrt[q]
q q q q
5/2 7/2 9/2 11/2
> 14 q + 9 q - 4 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -18 2 -14 3 -10 3 2 3 -2 2 4 6
3 + q + --- + q + --- + q - -- + -- - -- + q - q + 5 q - 3 q +
16 12 8 6 4
q q q q q
8 12 14 16
> 2 q - 3 q + 2 q - q |
In[8]:= | HOMFLYPT[Link[11, Alternating, 345]][a, z] |
Out[8]= | 3 5 3
1 4 6 a 5 a 2 a 2 z 9 z 3 5 2 z
---- - --- + --- - ---- + ---- + --- - --- + 12 a z - 8 a z + a z + ---- -
3 a z z z z 3 a 3
a z a a
3 5 5 7
8 z 3 3 3 z 4 z 5 z
> ---- + 10 a z - 3 a z + -- - ---- + 3 a z - --
a 3 a a
a |
In[9]:= | Kauffman[Link[11, Alternating, 345]][a, z] |
Out[9]= | 3 5
-4 3 2 4 1 4 6 a 5 a 2 a 4 z 19 z
3 + a + -- + a + a - ---- - --- - --- - ---- - ---- + --- + ---- + 29 a z +
2 3 a z z z z 3 a
a a z a
2 2 3 3
3 5 2 3 z 9 z 2 2 4 2 z 11 z
> 21 a z + 7 a z - 4 z - ---- - ---- + 3 a z + a z + -- - ----- -
4 2 5 3
a a a a
3 4 4 4
40 z 3 3 3 5 3 4 z 8 z 5 z
> ----- - 50 a z - 31 a z - 9 a z - 18 z - -- + ---- + ---- -
a 6 4 2
a a a
5 5 5
2 4 4 4 4 z 19 z 42 z 5 3 5 5 5
> 21 a z - 7 a z - ---- + ----- + ----- + 30 a z + 16 a z + 5 a z +
5 3 a
a a
6 6 7 7
6 9 z 12 z 2 6 4 6 13 z 9 z 7 3 7
> 38 z - ---- + ----- + 24 a z + 7 a z - ----- - ---- + 6 a z + a z -
4 2 3 a
a a a
8 9
5 7 8 11 z 2 8 4 8 5 z 9 3 9 10
> a z - 15 z - ----- - 6 a z - 2 a z - ---- - 7 a z - 2 a z - z -
2 a
a
2 10
> a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 1 1 1 5 2 6 4 9
10 + 10 q + ------ + ------ + ----- + ----- + ----- + ----- + ----- + ----- +
12 6 10 5 8 5 8 4 6 4 6 3 4 3 4 2
q t q t q t q t q t q t q t q t
6 9 9 2 4 4 2 6 2 6 3
> ----- + - + ---- + 8 q t + 9 q t + 6 q t + 8 q t + 3 q t +
2 2 t 2
q t q t
8 3 8 4 10 4 12 5
> 6 q t + q t + 3 q t + q t |