In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 156]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 156]] |
Out[3]= | PD[X[4, 2, 5, 1], X[10, 3, 11, 4], X[18, 5, 19, 6], X[12, 8, 13, 7],
> X[14, 10, 15, 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, 156]] |
Out[4]= | GaussCode[1, -6, 2, -1, 3, -10, 4, -7, 5, -2, 6, -4, 7, -5, 8, -11, 9, -3, 10,
> -8, 11, -9] |
In[5]:= | DTCode[Knot[11, Alternating, 156]] |
Out[5]= | DTCode[4, 10, 18, 12, 14, 2, 8, 20, 22, 6, 16] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 156]][t] |
Out[6]= | -4 5 11 18 2 3 4
-21 - t + -- - -- + -- + 18 t - 11 t + 5 t - t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 156]][z] |
Out[7]= | 2 4 6 8
1 + 3 z - z - 3 z - z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 156]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 156]], KnotSignature[Knot[11, Alternating, 156]]} |
Out[9]= | {91, -2} |
In[10]:= | J=Jones[Knot[11, Alternating, 156]][q] |
Out[10]= | -8 2 5 9 12 15 14 13 2 3
-10 - q + -- - -- + -- - -- + -- - -- + -- + 6 q - 3 q + q
7 6 5 4 3 2 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, 156]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 156]][q] |
Out[12]= | -24 -22 -20 2 3 3 3 -8 3 4 -2 2
-1 - q - q - q - --- + --- + --- + --- - q + -- - -- + q - q +
18 16 12 10 6 4
q q q q q q
4 6 8
> 2 q - q + q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 156]][a, z] |
Out[13]= | 2 4 6 2 2 2 4 2 6 2 4
2 - 6 a + 9 a - 4 a + 5 z - 15 a z + 17 a z - 4 a z + 4 z -
2 4 4 4 6 4 6 2 6 4 6 2 8
> 14 a z + 10 a z - a z + z - 6 a z + 2 a z - a z |
In[14]:= | Kauffman[Knot[11, Alternating, 156]][a, z] |
Out[14]= | 2 4 6 2 z 3 5 7 9 2
2 + 6 a + 9 a + 4 a - --- - 5 a z - 6 a z - 6 a z - a z + 2 a z - 4 z +
a
2 3
2 z 2 2 4 2 6 2 8 2 7 z 3 3 3
> ---- - 22 a z - 30 a z - 13 a z + a z + ---- + 10 a z + 8 a z +
2 a
a
4
5 3 7 3 9 3 4 3 z 2 4 4 4
> 10 a z + 2 a z - 3 a z + 6 z - ---- + 32 a z + 43 a z +
2
a
5
6 4 8 4 9 z 5 3 5 7 5 9 5 6
> 16 a z - 4 a z - ---- - 8 a z + 7 a z - 5 a z + a z - 10 z +
a
6 7
z 2 6 4 6 6 6 8 6 3 z 7 3 7
> -- - 24 a z - 25 a z - 10 a z + 2 a z + ---- - 3 a z - 13 a z -
2 a
a
5 7 7 7 8 2 8 4 8 6 8 9 3 9
> 4 a z + 3 a z + 4 z + 6 a z + 6 a z + 4 a z + 3 a z + 6 a z +
5 9 2 10 4 10
> 3 a z + a z + a z |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 156]], Vassiliev[3][Knot[11, Alternating, 156]]} |
Out[15]= | {3, -7} |
In[16]:= | Kh[Knot[11, Alternating, 156]][q, t] |
Out[16]= | 7 7 1 1 1 4 1 5 4 7
-- + - + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
3 q 17 7 15 6 13 6 13 5 11 5 11 4 9 4 9 3
q q t q t q t q t q t q t q t q t
5 8 7 6 8 4 t 2 3 2
> ----- + ----- + ----- + ---- + ---- + --- + 6 q t + 2 q t + 4 q t +
7 3 7 2 5 2 5 3 q
q t q t q t q t q t
3 3 5 3 7 4
> q t + 2 q t + q t |