In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, NonAlternating, 19]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, NonAlternating, 19]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 3, 9, 4], X[10, 6, 11, 5], X[7, 17, 8, 16],
> X[2, 9, 3, 10], X[11, 18, 12, 19], X[13, 20, 14, 21], X[15, 22, 16, 1],
> X[17, 7, 18, 6], X[19, 12, 20, 13], X[21, 14, 22, 15]] |
In[4]:= | GaussCode[Knot[11, NonAlternating, 19]] |
Out[4]= | GaussCode[1, -5, 2, -1, 3, 9, -4, -2, 5, -3, -6, 10, -7, 11, -8, 4, -9, 6, -10,
> 7, -11, 8] |
In[5]:= | DTCode[Knot[11, NonAlternating, 19]] |
Out[5]= | DTCode[4, 8, 10, -16, 2, -18, -20, -22, -6, -12, -14] |
In[6]:= | alex = Alexander[Knot[11, NonAlternating, 19]][t] |
Out[6]= | -3 2 2 3
-1 - t + -- + 2 t - t
2
t |
In[7]:= | Conway[Knot[11, NonAlternating, 19]][z] |
Out[7]= | 2 4 6
1 - z - 4 z - z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, NonAlternating, 19], Knot[11, NonAlternating, 135]} |
In[9]:= | {KnotDet[Knot[11, NonAlternating, 19]], KnotSignature[Knot[11, NonAlternating, 19]]} |
Out[9]= | {5, -4} |
In[10]:= | J=Jones[Knot[11, NonAlternating, 19]][q] |
Out[10]= | -2 1 2
1 + q - - - q + q
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[4, 1], Knot[11, NonAlternating, 19]} |
In[12]:= | A2Invariant[Knot[11, NonAlternating, 19]][q] |
Out[12]= | -20 -16 -14 -12 -6 -4 2 4 6
-q + q + q + q - q - q + q + q + q |
In[13]:= | HOMFLYPT[Knot[11, NonAlternating, 19]][a, z] |
Out[13]= | 2 4 6 2 2 2 4 2 4 2 4 4 4 2 6
3 - 5 a + 4 a - a + 4 z - 10 a z + 5 a z + z - 6 a z + a z - a z |
In[14]:= | Kauffman[Knot[11, NonAlternating, 19]][a, z] |
Out[14]= | 2 4 6 3 5 2 2 2 4 2
3 + 5 a + 4 a + a + 2 a z + 3 a z + a z - 11 z - 23 a z - 13 a z -
6 2 3 3 3 5 3 4 2 4 4 4
> a z - 11 a z - 12 a z - a z + 15 z + 30 a z + 15 a z +
5 3 5 6 2 6 4 6 7 3 7 8
> 15 a z + 15 a z - 7 z - 14 a z - 7 a z - 7 a z - 7 a z + z +
2 8 4 8 9 3 9
> 2 a z + a z + a z + a z |
In[15]:= | {Vassiliev[2][Knot[11, NonAlternating, 19]], Vassiliev[3][Knot[11, NonAlternating, 19]]} |
Out[15]= | {-1, 0} |
In[16]:= | Kh[Knot[11, NonAlternating, 19]][q, t] |
Out[16]= | -5 -3 1 1 1 1 1 t t 2 3 5 4
q + q + - + ----- + ----- + ----- + ---- + -- + - + q t + q t + q t
q 9 3 9 2 5 2 5 3 q
q t q t q t q t q |