PD Presentation: |
X10,1,11,2 X2,11,3,12 X12,3,13,4 X14,5,15,6 X18,7,19,8 X20,15,9,16 X16,19,17,20 X8,9,1,10 X4,13,5,14 X6,17,7,18 |
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, 98]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, Alternating, 98]] |
Out[4]= | PD[X[10, 1, 11, 2], X[2, 11, 3, 12], X[12, 3, 13, 4], X[14, 5, 15, 6],
> X[18, 7, 19, 8], X[20, 15, 9, 16], X[16, 19, 17, 20], X[8, 9, 1, 10],
> X[4, 13, 5, 14], X[6, 17, 7, 18]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -2, 3, -9, 4, -10, 5, -8},
> {8, -1, 2, -3, 9, -4, 6, -7, 10, -5, 7, -6}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(27/2) 2 3 4 5 5 4 3 3
-q + ----- - ----- + ----- - ----- + ----- - ----- + ----- - ----- +
25/2 23/2 21/2 19/2 17/2 15/2 13/2 11/2
q q q q q q q q
-(9/2) -(7/2)
> q - q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -40 -30 -28 -26 -22 2 -18 2 -12
q + q - q + q + q + --- + q + --- + q
20 16
q q |
In[8]:= | HOMFLYPT[Link[10, Alternating, 98]][a, z] |
Out[8]= | 7 9
a a 7 11 7 3 9 3 11 3 7 5
-(--) + -- - 7 a z + 3 a z - 11 a z - 6 a z + 4 a z - 6 a z -
z z
9 5 11 5 7 7 9 7
> 5 a z + a z - a z - a z |
In[9]:= | Kauffman[Link[10, Alternating, 98]][a, z] |
Out[9]= | 7 9
8 a a 7 9 11 13 17 8 2 10 2
a - -- - -- + 7 a z + 2 a z - 3 a z + a z + a z - 3 a z + 5 a z +
z z
12 2 14 2 16 2 7 3 9 3 11 3 13 3
> 5 a z - a z + 2 a z - 11 a z - a z + 5 a z - 3 a z +
15 3 17 3 8 4 10 4 12 4 14 4 16 4
> a z - a z - 2 a z - 15 a z - 9 a z + 2 a z - 2 a z +
7 5 9 5 11 5 13 5 15 5 8 6 10 6
> 6 a z - 3 a z - 3 a z + 4 a z - 2 a z + 4 a z + 13 a z +
12 6 14 6 7 7 9 7 11 7 13 7 8 8
> 7 a z - 2 a z - a z + 4 a z + 3 a z - 2 a z - a z -
10 8 12 8 9 9 11 9
> 3 a z - 2 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -8 -6 1 1 1 2 2 3 1
q + q + ------- + ------ + ------ + ------ + ------ + ------ + ------ +
28 10 26 9 24 9 24 8 22 8 22 7 20 7
q t q t q t q t q t q t q t
2 3 3 2 1 3 2 1
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
20 6 18 6 18 5 16 5 16 4 14 4 14 3 12 3
q t q t q t q t q t q t q t q t
1 2 1
> ------ + ------ + ----
12 2 10 2 8
q t q t q t |