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