PD Presentation: |
X8192 X10,4,11,3 X20,10,7,9 X14,6,15,5 X18,13,19,14 X16,19,17,20 X12,17,13,18 X2738 X4,12,5,11 X6,16,1,15 |
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, 60]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 60]] |
Out[4]= | PD[X[8, 1, 9, 2], X[10, 4, 11, 3], X[20, 10, 7, 9], X[14, 6, 15, 5],
> X[18, 13, 19, 14], X[16, 19, 17, 20], X[12, 17, 13, 18], X[2, 7, 3, 8],
> X[4, 12, 5, 11], X[6, 16, 1, 15]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -8, 2, -9, 4, -10},
> {8, -1, 3, -2, 9, -7, 5, -4, 10, -6, 7, -5, 6, -3}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(9/2) 3 6 9 11 3/2 5/2
q - ---- + ---- - ---- + ------- - 13 Sqrt[q] + 11 q - 10 q +
7/2 5/2 3/2 Sqrt[q]
q q q
7/2 9/2 11/2
> 6 q - 3 q + q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -14 2 2 -4 -2 4 8 10 12 14 16
3 - q - -- + -- - q + q + 5 q + 3 q + q - 2 q + q - q
8 6
q q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 60]][a, z] |
Out[8]= | 3 3 3
-2 3 a a 3 z 8 z 3 3 z 10 z 3 3 3
--- + --- - -- + --- - --- + 8 a z - 2 a z + ---- - ----- + 7 a z - a z +
a z z z 3 a 3 a
a a
5 5 7
z 5 z 5 z
> -- - ---- + 2 a z - --
3 a a
a |
In[9]:= | Kauffman[Link[10, Alternating, 60]][a, z] |
Out[9]= | 3
2 4 2 3 a a z 3 z 14 z 3 2
3 + 3 a + a - --- - --- - -- - -- + --- + ---- + 13 a z + 3 a z - 10 z +
a z z z 5 3 a
a a
2 2 2 3 3 3
z 2 z 6 z 2 2 4 2 3 z 7 z 30 z 3
> -- - ---- - ---- - 10 a z - 3 a z + ---- - ---- - ----- - 28 a z -
6 4 2 5 3 a
a a a a a
4 4 4 5 5
3 3 4 z 5 z 8 z 2 4 4 4 3 z 8 z
> 8 a z + 6 z - -- + ---- + ---- + 7 a z + 3 a z - ---- + ---- +
6 4 2 5 3
a a a a a
5 6 7 7
31 z 5 3 5 6 5 z 2 6 4 6 6 z 11 z
> ----- + 29 a z + 9 a z + 10 z - ---- + 4 a z - a z - ---- - ----- -
a 4 3 a
a a
8 9
7 3 7 8 4 z 2 8 z 9
> 8 a z - 3 a z - 7 z - ---- - 3 a z - -- - a z
2 a
a |
In[10]:= | Kh[L][q, t] |
Out[10]= | 2 1 2 1 4 2 5 4 5 6
7 + 7 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + - + ---- +
10 5 8 4 6 4 6 3 4 3 4 2 2 2 t 2
q t q t q t q t q t q t q t q t
2 4 4 2 6 2 6 3 8 3 8 4
> 5 q t + 6 q t + 5 q t + 6 q t + 2 q t + 4 q t + q t +
10 4 12 5
> 2 q t + q t |