In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, NonAlternating, 8]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, NonAlternating, 8]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 3, 9, 4], X[10, 6, 11, 5], X[7, 14, 8, 15],
> X[2, 9, 3, 10], X[11, 18, 12, 19], X[13, 6, 14, 7], X[15, 20, 16, 21],
> X[17, 12, 18, 13], X[19, 22, 20, 1], X[21, 16, 22, 17]] |
In[4]:= | GaussCode[Knot[11, NonAlternating, 8]] |
Out[4]= | GaussCode[1, -5, 2, -1, 3, 7, -4, -2, 5, -3, -6, 9, -7, 4, -8, 11, -9, 6, -10,
> 8, -11, 10] |
In[5]:= | DTCode[Knot[11, NonAlternating, 8]] |
Out[5]= | DTCode[4, 8, 10, -14, 2, -18, -6, -20, -12, -22, -16] |
In[6]:= | alex = Alexander[Knot[11, NonAlternating, 8]][t] |
Out[6]= | -3 6 12 2 3
15 - t + -- - -- - 12 t + 6 t - t
2 t
t |
In[7]:= | Conway[Knot[11, NonAlternating, 8]][z] |
Out[7]= | 2 6
1 + 3 z - z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, NonAlternating, 8], Knot[11, NonAlternating, 59]} |
In[9]:= | {KnotDet[Knot[11, NonAlternating, 8]], KnotSignature[Knot[11, NonAlternating, 8]]} |
Out[9]= | {53, -4} |
In[10]:= | J=Jones[Knot[11, NonAlternating, 8]][q] |
Out[10]= | -9 3 6 8 9 9 7 6 3
1 - q + -- - -- + -- - -- + -- - -- + -- - -
8 7 6 5 4 3 2 q
q q q q q q q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, NonAlternating, 8]} |
In[12]:= | A2Invariant[Knot[11, NonAlternating, 8]][q] |
Out[12]= | -28 -24 2 -20 -18 2 -12 3 -8 -6 -4 -2
1 - q + q - --- + q - q + --- - q + --- - q + q + q - q
22 14 10
q q q |
In[13]:= | HOMFLYPT[Knot[11, NonAlternating, 8]][a, z] |
Out[13]= | 2 6 8 2 2 4 2 6 2 8 2 2 4 4 4
a + a - a + 2 a z - 2 a z + 4 a z - a z + a z - 3 a z +
6 4 4 6
> 2 a z - a z |
In[14]:= | Kauffman[Knot[11, NonAlternating, 8]][a, z] |
Out[14]= | 2 6 8 3 5 7 9 11 2 2 4 2
-a - a - a - a z - 4 a z - 3 a z - a z - a z + 3 a z + 4 a z +
6 2 10 2 3 3 5 3 7 3 9 3 11 3
> 3 a z - 2 a z + 6 a z + 14 a z + 10 a z + 3 a z + a z -
2 4 4 4 6 4 8 4 10 4 3 5 5 5
> 3 a z - 3 a z + 3 a z + 6 a z + 3 a z - 9 a z - 18 a z -
7 5 2 6 4 6 6 6 8 6 3 7 5 7
> 9 a z + a z - 6 a z - 11 a z - 4 a z + 3 a z + 4 a z +
7 7 9 7 4 8 6 8 8 8 5 9 7 9
> 2 a z + a z + 3 a z + 5 a z + 2 a z + a z + a z |
In[15]:= | {Vassiliev[2][Knot[11, NonAlternating, 8]], Vassiliev[3][Knot[11, NonAlternating, 8]]} |
Out[15]= | {3, -6} |
In[16]:= | Kh[Knot[11, NonAlternating, 8]][q, t] |
Out[16]= | 3 4 1 2 1 4 2 4 4
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
5 3 19 7 17 6 15 6 15 5 13 5 13 4 11 4
q q q t q t q t q t q t q t q t
5 4 4 5 3 4 t 2 t 2
> ------ + ----- + ----- + ----- + ---- + ---- + -- + --- + q t
11 3 9 3 9 2 7 2 7 5 3 q
q t q t q t q t q t q t q |