In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 17, 2005, 14:44:34)... |
In[2]:= | Crossings[Link[7, Alternating, 6]] |
Out[2]= | 7 |
In[3]:= | PD[Link[7, Alternating, 6]] |
Out[3]= | PD[X[8, 1, 9, 2], X[10, 4, 11, 3], X[14, 10, 7, 9], X[12, 6, 13, 5],
X[2, 7, 3, 8], X[4, 12, 5, 11], X[6, 14, 1, 13]] |
In[4]:= | GaussCode[Link[7, Alternating, 6]] |
Out[4]= | GaussCode[{1, -5, 2, -6, 4, -7}, {5, -1, 3, -2, 6, -4, 7, -3}] |
In[5]:= | BR[Link[7, Alternating, 6]] |
Out[5]= | BR[Link[7, Alternating, 6]] |
In[6]:= | alex = Alexander[Link[7, Alternating, 6]][t] |
Out[6]= | ComplexInfinity |
In[7]:= | Conway[Link[7, Alternating, 6]][z] |
Out[7]= | ComplexInfinity |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {} |
In[9]:= | {KnotDet[Link[7, Alternating, 6]], KnotSignature[Link[7, Alternating, 6]]} |
Out[9]= | {Infinity, 3} |
In[10]:= | J=Jones[Link[7, Alternating, 6]][q] |
Out[10]= | 1 3/2 5/2 7/2 9/2 11/2
-(-------) + Sqrt[q] - 2 q + 2 q - 3 q + 2 q - 2 q +
Sqrt[q]
13/2
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {} |
In[12]:= | A2Invariant[Link[7, Alternating, 6]][q] |
Out[12]= | -2 2 4 8 10 12 14 20
1 + q + q + q + 2 q + q + 2 q + q - q |
In[13]:= | Kauffman[Link[7, Alternating, 6]][a, z] |
Out[13]= | 2 2 2 2 3
-2 1 1 z z 6 z 4 z z z z z 2 z
-a + ---- + --- + -- - -- - --- - --- - -- + -- + -- - -- - ---- +
3 a z 7 5 3 a 8 6 4 2 7
a z a a a a a a a a
3 3 3 4 4 4 5 5 5 6 6
3 z 9 z 4 z 2 z z 3 z 2 z 3 z z z z
---- + ---- + ---- - ---- + -- + ---- - ---- - ---- - -- - -- - --
5 3 a 6 4 2 5 3 a 4 2
a a a a a a a a a |
In[14]:= | {Vassiliev[2][Link[7, Alternating, 6]], Vassiliev[3][Link[7, Alternating, 6]]} |
Out[14]= | 31
{0, -(--)}
48 |
In[15]:= | Kh[Link[7, Alternating, 6]][q, t] |
Out[15]= | 2
2 4 1 q 4 6 6 2 8 2 8 3
2 q + q + ----- + -- + q t + q t + 2 q t + 2 q t + q t +
2 2 t
q t
10 3 10 4 12 4 14 5
q t + q t + q t + q t |