PD Presentation: |
X6172 X12,3,13,4 X7,18,8,19 X19,22,20,5 X13,20,14,21 X21,14,22,15 X9,16,10,17 X15,10,16,11 X17,8,18,9 X2536 X4,11,1,12 |
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, NonAlternating, 109]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[11, NonAlternating, 109]] |
Out[4]= | PD[X[6, 1, 7, 2], X[12, 3, 13, 4], X[7, 18, 8, 19], X[19, 22, 20, 5],
> X[13, 20, 14, 21], X[21, 14, 22, 15], X[9, 16, 10, 17], X[15, 10, 16, 11],
> X[17, 8, 18, 9], X[2, 5, 3, 6], X[4, 11, 1, 12]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, -10, 2, -11}, {10, -1, -3, 9, -7, 8, 11, -2, -5, 6, -8, 7, -9, 3,
> -4, 5, -6, 4}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(25/2) -(23/2) -(21/2) -(19/2) -(15/2) 2 -(11/2)
q - q + q - q + q - ----- + q -
13/2
q
2 -(7/2) -(5/2)
> ---- + q - q
9/2
q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -40 2 -36 -34 -32 2 -28 -26 -24 -22 -20
-q - --- - q - q + q + --- + q + q - q + q + q +
38 30
q q
2 3 -14 -12 -8
> --- + --- + q + q + q
18 16
q q |
In[8]:= | HOMFLYPT[Link[11, NonAlternating, 109]][a, z] |
Out[8]= | 5 7 9 11 13
a a a 2 a a 5 7 9 11 5 3
-(--) + -- - -- + ----- - --- - 3 a z - 2 a z + a z + 2 a z - 4 a z -
z z z z z
7 3 5 5 7 5
> 4 a z - a z - a z |
In[9]:= | Kauffman[Link[11, NonAlternating, 109]][a, z] |
Out[9]= | 5 7 9 11 13
6 10 12 14 a a a 2 a a 5 7
-a - 4 a - 7 a - 3 a + -- + -- + -- + ----- + --- - 3 a z - a z -
z z z z z
9 11 13 8 2 10 2 12 2 14 2
> 4 a z - 10 a z - 4 a z - 3 a z + 14 a z + 28 a z + 11 a z +
5 3 7 3 9 3 11 3 13 3 6 4 8 4
> 4 a z - 3 a z + 2 a z + 21 a z + 12 a z + 3 a z + 4 a z -
10 4 12 4 14 4 5 5 7 5 11 5
> 18 a z - 34 a z - 15 a z - a z + 4 a z - 20 a z -
13 5 6 6 8 6 10 6 12 6 14 6 7 7
> 15 a z - a z - a z + 8 a z + 15 a z + 7 a z - a z +
11 7 13 7 10 8 12 8 14 8 11 9 13 9
> 8 a z + 7 a z - a z - 2 a z - a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -6 -4 1 1 1 1 1 1 1
q + q + ------- + ------- + ------ + ------ + ------ + ------ + ------ +
26 11 22 10 22 9 20 8 18 8 20 7 16 7
q t q t q t q t q t q t q t
2 2 1 1 3 1 1 1
> ------ + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
16 6 16 5 12 5 14 4 12 4 10 4 12 3 10 3
q t q t q t q t q t q t q t q t
1 1 1
> ------ + ----- + ----
10 2 8 2 6
q t q t q t |