PD Presentation: |
X6172 X18,7,19,8 X4,19,1,20 X9,14,10,15 X3849 X5,13,6,12 X13,5,14,20 X11,16,12,17 X15,10,16,11 X17,2,18,3 |
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, NonAlternating, 13]]] |
|  |
Out[3]= | -Graphics- |
In[4]:= | PD[L = Link[10, NonAlternating, 13]] |
Out[4]= | PD[X[6, 1, 7, 2], X[18, 7, 19, 8], X[4, 19, 1, 20], X[9, 14, 10, 15],
> X[3, 8, 4, 9], X[5, 13, 6, 12], X[13, 5, 14, 20], X[11, 16, 12, 17],
> X[15, 10, 16, 11], X[17, 2, 18, 3]] |
In[5]:= | GaussCode[L] |
Out[5]= | GaussCode[{1, 10, -5, -3}, {-6, -1, 2, 5, -4, 9, -8, 6, -7, 4, -9, 8, -10, -2,
> 3, 7}] |
In[6]:= | Jones[L][q] |
Out[6]= | -(17/2) 2 3 3 3 3 3 -(3/2) 1
-q + ----- - ----- + ----- - ---- + ---- - ---- + q - -------
15/2 13/2 11/2 9/2 7/2 5/2 Sqrt[q]
q q q q q q |
In[7]:= | A2Invariant[L][q] |
Out[7]= | -30 -26 -18 -16 -14 -12 -10 2 2 -4 -2
q + q - q + q - q + q + q + -- + -- + q + q
8 6
q q |
In[8]:= | HOMFLYPT[Link[10, NonAlternating, 13]][a, z] |
Out[8]= | 3 5 7 9
-2 a 4 a 3 a a 3 5 7 9 3 3
----- + ---- - ---- + -- - 7 a z + 11 a z - 7 a z + a z - 5 a z +
z z z z
5 3 7 3 3 5 5 5 7 5 5 7
> 12 a z - 5 a z - a z + 6 a z - a z + a z |
In[9]:= | Kauffman[Link[10, NonAlternating, 13]][a, z] |
Out[9]= | 3 5 7 9
4 6 8 10 2 a 4 a 3 a a 3 5
2 a + 3 a + 3 a + a - ---- - ---- - ---- - -- + 9 a z + 18 a z +
z z z z
7 9 11 4 2 6 2 8 2 10 2
> 11 a z + a z - a z - 4 a z - 12 a z - 10 a z - 2 a z -
3 3 5 3 7 3 9 3 4 4 6 4 8 4
> 12 a z - 30 a z - 17 a z + a z - 2 a z + 9 a z + 11 a z +
3 5 5 5 7 5 9 5 4 6 6 6 8 6 3 7
> 6 a z + 20 a z + 13 a z - a z + 4 a z + a z - 3 a z - a z -
5 7 7 7 4 8 6 8
> 4 a z - 3 a z - a z - a z |
In[10]:= | Kh[L][q, t] |
Out[10]= | -6 3 1 1 1 2 2 1 2
q + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
4 18 6 16 5 14 5 14 4 12 4 10 4 12 3
q q t q t q t q t q t q t q t
2 1 2 2 1 t 2
> ------ + ------ + ----- + ---- + ---- + -- + t
10 3 10 2 8 2 8 6 4
q t q t q t q t q t q |