PD Presentation: |
X6172 X10,4,11,3 X14,8,15,7 X20,16,5,15 X16,9,17,10 X8,19,9,20 X18,13,19,14 X12,17,13,18 X2536 X4,12,1,11 |
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[10, Alternating, 14]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 14]] |
Out[4]= | PD[X[6, 1, 7, 2], X[10, 4, 11, 3], X[14, 8, 15, 7], X[20, 16, 5, 15],
> X[16, 9, 17, 10], X[8, 19, 9, 20], X[18, 13, 19, 14], X[12, 17, 13, 18],
> X[2, 5, 3, 6], X[4, 12, 1, 11]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -9, 2, -10}, {9, -1, 3, -6, 5, -2, 10, -8, 7, -3, 4, -5, 8, -7,
> 6, -4}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(13/2) 3 7 12 15 16 16 3/2
-q + ----- - ---- + ---- - ---- + ---- - ------- + 12 Sqrt[q] - 9 q +
11/2 9/2 7/2 5/2 3/2 Sqrt[q]
q q q q q
5/2 7/2
> 4 q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -20 3 3 -10 -8 3 3 2 2 4 6 8 10
6 + q + --- - --- + q - q - -- + -- - -- + q + q + 3 q - 2 q + q
14 12 6 4 2
q q q q q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 14]][a, z] |
Out[8]= | 3 5 3
-2 4 a 3 a a 2 z 3 5 2 z 3
--- + --- - ---- + -- - --- + 7 a z - 7 a z + 2 a z - ---- + 7 a z -
a z z z z a a
5
3 3 5 3 z 5 3 5 7
> 6 a z + a z - -- + 4 a z - 2 a z + a z
a |
In[9]:= | Kauffman[Link[10, Alternating, 14]][a, z] |
Out[9]= | 3 5
2 4 6 2 4 a 3 a a 5 z 3
2 + 3 a + 3 a + a - --- - --- - ---- - -- + --- + 15 a z + 13 a z +
a z z z z a
2 3 3
5 7 2 z 2 2 4 2 6 2 z 10 z
> 2 a z - a z - 2 z - -- - 5 a z - 7 a z - 3 a z + -- - ----- -
2 3 a
a a
4
3 3 3 5 3 7 3 4 5 z 2 4 4 4
> 33 a z - 28 a z - 4 a z + 2 a z + z + ---- - 4 a z + 5 a z +
2
a
5 5 6
6 4 z 15 z 5 3 5 5 5 7 5 6 4 z
> 5 a z - -- + ----- + 38 a z + 30 a z + 7 a z - a z + 8 z - ---- +
3 a 2
a a
7
2 6 4 6 6 6 8 z 7 3 7 5 7 8
> 18 a z + 3 a z - 3 a z - ---- - 14 a z - 11 a z - 5 a z - 7 z -
a
2 8 4 8 9 3 9
> 12 a z - 5 a z - 2 a z - 2 a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | 8 1 2 1 5 2 7 5 8
10 + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ----- +
2 14 6 12 5 10 5 10 4 8 4 8 3 6 3 6 2
q q t q t q t q t q t q t q t q t
7 8 8 2 2 2 4 2 4 3 6 3
> ----- + ---- + ---- + 6 t + 6 q t + 3 q t + 6 q t + q t + 3 q t +
4 2 4 2
q t q t q t
8 4
> q t |