In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 17, 2005, 14:44:34)... |
In[2]:= | Crossings[Link[9, Alternating, 50]] |
Out[2]= | 9 |
In[3]:= | PD[Link[9, Alternating, 50]] |
Out[3]= | PD[X[6, 1, 7, 2], X[12, 4, 13, 3], X[18, 16, 11, 15], X[14, 8, 15, 7],
X[10, 12, 5, 11], X[8, 17, 9, 18], X[16, 9, 17, 10], X[2, 5, 3, 6],
X[4, 14, 1, 13]] |
In[4]:= | GaussCode[Link[9, Alternating, 50]] |
Out[4]= | GaussCode[{1, -8, 2, -9}, {8, -1, 4, -6, 7, -5},
{5, -2, 9, -4, 3, -7, 6, -3}] |
In[5]:= | BR[Link[9, Alternating, 50]] |
Out[5]= | BR[Link[9, Alternating, 50]] |
In[6]:= | alex = Alexander[Link[9, Alternating, 50]][t] |
Out[6]= | ComplexInfinity |
In[7]:= | Conway[Link[9, Alternating, 50]][z] |
Out[7]= | ComplexInfinity |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {} |
In[9]:= | {KnotDet[Link[9, Alternating, 50]], KnotSignature[Link[9, Alternating, 50]]} |
Out[9]= | {Infinity, 2} |
In[10]:= | J=Jones[Link[9, Alternating, 50]][q] |
Out[10]= | -3 2 5 2 3 4 5 6
-5 + q - -- + - + 8 q - 7 q + 7 q - 5 q + 3 q - q
2 q
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {} |
In[12]:= | A2Invariant[Link[9, Alternating, 50]][q] |
Out[12]= | -10 -8 -6 4 3 2 4 6 10 14
5 + q + q + q + -- + -- + 5 q + 2 q + 4 q + 2 q - q +
4 2
q q
16 18
q - q |
In[13]:= | Kauffman[Link[9, Alternating, 50]][a, z] |
Out[13]= | 2
2 8 2 2 1 a 2 2 a z 3 z 5 z
-9 - -- - -- - 4 a + -- + ----- + -- - --- - --- + -- + --- + --- +
4 2 2 2 2 2 a z z 5 3 a
a a z a z z a a
2 2 2 3 3 3
2 z 6 z 23 z 2 2 z 4 z 5 z
3 a z + 22 z - -- + ---- + ----- + 6 a z + -- - ---- - ---- +
6 4 2 7 5 3
a a a a a a
3 4 4 4 5 5
3 z 3 4 3 z 9 z 27 z 2 4 5 z 3 z
---- + 3 a z - 19 z + ---- - ---- - ----- - 4 a z + ---- - ---- -
a 6 4 2 5 3
a a a a a
5 6 6 7 7
14 z 5 6 6 z 8 z 2 6 4 z 6 z 7
----- - 6 a z + 3 z + ---- + ---- + a z + ---- + ---- + 2 a z +
a 4 2 3 a
a a a
8
8 z
z + --
2
a |
In[14]:= | {Vassiliev[2][Link[9, Alternating, 50]], Vassiliev[3][Link[9, Alternating, 50]]} |
Out[14]= | {0, 1} |
In[15]:= | Kh[Link[9, Alternating, 50]][q, t] |
Out[15]= | 3 1 1 1 4 2 2 3 q
6 q + 4 q + ----- + ----- + ----- + ----- + ---- + --- + --- +
7 4 5 3 3 3 3 2 2 q t t
q t q t q t q t q t
3 5 5 2 7 2 7 3 9 3 9 4
3 q t + 4 q t + 4 q t + 4 q t + 2 q t + 3 q t + q t +
11 4 13 5
2 q t + q t |