In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 17, 2005, 14:44:34)... |
In[2]:= | Crossings[Link[8, Alternating, 14]] |
Out[2]= | 8 |
In[3]:= | PD[Link[8, Alternating, 14]] |
Out[3]= | PD[X[10, 1, 11, 2], X[2, 11, 3, 12], X[12, 3, 13, 4], X[14, 5, 15, 6],
X[16, 7, 9, 8], X[8, 9, 1, 10], X[4, 13, 5, 14], X[6, 15, 7, 16]] |
In[4]:= | GaussCode[Link[8, Alternating, 14]] |
Out[4]= | GaussCode[{1, -2, 3, -7, 4, -8, 5, -6}, {6, -1, 2, -3, 7, -4, 8, -5}] |
In[5]:= | BR[Link[8, Alternating, 14]] |
Out[5]= | BR[Link[8, Alternating, 14]] |
In[6]:= | alex = Alexander[Link[8, Alternating, 14]][t] |
Out[6]= | ComplexInfinity |
In[7]:= | Conway[Link[8, Alternating, 14]][z] |
Out[7]= | ComplexInfinity |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {} |
In[9]:= | {KnotDet[Link[8, Alternating, 14]], KnotSignature[Link[8, Alternating, 14]]} |
Out[9]= | {Infinity, -7} |
In[10]:= | J=Jones[Link[8, Alternating, 14]][q] |
Out[10]= | -(23/2) -(21/2) -(19/2) -(17/2) -(15/2) -(13/2)
-q + q - q + q - q + q -
-(11/2) -(7/2)
q - q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {} |
In[12]:= | A2Invariant[Link[8, Alternating, 14]][q] |
Out[12]= | -34 -32 -30 -20 -18 2 -14 -12
q + q + q + q + q + --- + q + q
16
q |
In[13]:= | Kauffman[Link[8, Alternating, 14]][a, z] |
Out[13]= | 7 9
8 a a 7 9 11 13 15 8 2
a - -- - -- + 10 a z + 7 a z - a z + a z - a z - 6 a z -
z z
10 2 12 2 14 2 7 3 9 3 11 3
3 a z + 2 a z - a z - 15 a z - 11 a z + 3 a z -
13 3 8 4 10 4 12 4 7 5 9 5 11 5
a z + 5 a z + 4 a z - a z + 7 a z + 6 a z - a z -
8 6 10 6 7 7 9 7
a z - a z - a z - a z |
In[14]:= | {Vassiliev[2][Link[8, Alternating, 14]], Vassiliev[3][Link[8, Alternating, 14]]} |
Out[14]= | 317
{0, -(---)}
12 |
In[15]:= | Kh[Link[8, Alternating, 14]][q, t] |
Out[15]= | -8 -6 1 1 1 1 1 1
q + q + ------ + ------ + ------ + ------ + ------ + ------ +
24 8 22 8 22 7 18 6 18 5 14 4
q t q t q t q t q t q t
1 1
------ + ------
14 3 10 2
q t q t |