In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 161]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 161]] |
Out[3]= | PD[X[4, 2, 5, 1], X[10, 3, 11, 4], X[18, 5, 19, 6], X[14, 8, 15, 7],
> X[12, 10, 13, 9], X[2, 11, 3, 12], X[8, 14, 9, 13], X[20, 15, 21, 16],
> X[22, 17, 1, 18], X[6, 19, 7, 20], X[16, 21, 17, 22]] |
In[4]:= | GaussCode[Knot[11, Alternating, 161]] |
Out[4]= | GaussCode[1, -6, 2, -1, 3, -10, 4, -7, 5, -2, 6, -5, 7, -4, 8, -11, 9, -3, 10,
> -8, 11, -9] |
In[5]:= | DTCode[Knot[11, Alternating, 161]] |
Out[5]= | DTCode[4, 10, 18, 14, 12, 2, 8, 20, 22, 6, 16] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 161]][t] |
Out[6]= | 2 8 12 2 3
13 - -- + -- - -- - 12 t + 8 t - 2 t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 161]][z] |
Out[7]= | 2 4 6
1 + 2 z - 4 z - 2 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[10, 14], Knot[11, Alternating, 161], Knot[11, NonAlternating, 2]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 161]], KnotSignature[Knot[11, Alternating, 161]]} |
Out[9]= | {57, -4} |
In[10]:= | J=Jones[Knot[11, Alternating, 161]][q] |
Out[10]= | -9 2 4 6 7 9 8 7 6 2
4 - q + -- - -- + -- - -- + -- - -- + -- - - - 2 q + 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, Alternating, 161]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 161]][q] |
Out[12]= | -28 -26 -22 -20 -18 -16 3 -10 -8 2 -2
1 - q - q - q + q + q + q + --- + q - q - -- - q +
14 6
q q
2 6
> q + q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 161]][a, z] |
Out[13]= | 2 4 6 8 2 2 2 4 2 6 2 8 2 4
2 - 3 a + a + 3 a - 2 a + 3 z - 5 a z - a z + 6 a z - a z + z -
2 4 4 4 6 4 2 6 4 6
> 4 a z - 3 a z + 2 a z - a z - a z |
In[14]:= | Kauffman[Knot[11, Alternating, 161]][a, z] |
Out[14]= | 2 4 6 8 3 5 7 9 11
2 + 3 a + a - 3 a - 2 a + 3 a z + 5 a z + 2 a z + 2 a z + a z - a z -
2 2 2 4 2 6 2 8 2 10 2 3
> 9 z - 20 a z - 13 a z + 4 a z + 5 a z - a z - 12 a z -
3 3 5 3 7 3 9 3 11 3 4 2 4
> 16 a z - 2 a z - a z - 2 a z + a z + 12 z + 32 a z +
4 4 6 4 8 4 10 4 5 3 5 5 5
> 29 a z + a z - 6 a z + 2 a z + 19 a z + 31 a z + 3 a z -
7 5 9 5 6 2 6 4 6 6 6 8 6
> 6 a z + 3 a z - 6 z - 14 a z - 21 a z - 9 a z + 4 a z -
7 3 7 5 7 7 7 8 2 8 4 8 6 8
> 11 a z - 23 a z - 8 a z + 4 a z + z - a z + 2 a z + 4 a z +
9 3 9 5 9 2 10 4 10
> 2 a z + 5 a z + 3 a z + a z + a z |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 161]], Vassiliev[3][Knot[11, Alternating, 161]]} |
Out[15]= | {2, -7} |
In[16]:= | Kh[Knot[11, Alternating, 161]][q, t] |
Out[16]= | 4 4 1 1 1 3 1 3 3
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
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
2
4 3 5 4 3 5 3 t 3 t t 2
> ------ + ----- + ----- + ----- + ---- + ---- + --- + --- + -- + 3 q t +
11 3 9 3 9 2 7 2 7 5 3 q q
q t q t q t q t q t q t q
3 3 3 5 4
> q t + q t + q t |