In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 66]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 66]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 3, 9, 4], X[16, 5, 17, 6], X[12, 8, 13, 7],
> X[2, 9, 3, 10], X[18, 12, 19, 11], X[20, 13, 21, 14], X[22, 15, 1, 16],
> X[10, 18, 11, 17], X[6, 19, 7, 20], X[14, 21, 15, 22]] |
In[4]:= | GaussCode[Knot[11, Alternating, 66]] |
Out[4]= | GaussCode[1, -5, 2, -1, 3, -10, 4, -2, 5, -9, 6, -4, 7, -11, 8, -3, 9, -6, 10,
> -7, 11, -8] |
In[5]:= | DTCode[Knot[11, Alternating, 66]] |
Out[5]= | DTCode[4, 8, 16, 12, 2, 18, 20, 22, 10, 6, 14] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 66]][t] |
Out[6]= | -4 6 15 24 2 3 4
-27 - t + -- - -- + -- + 24 t - 15 t + 6 t - t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 66]][z] |
Out[7]= | 2 4 6 8
1 + 2 z + z - 2 z - z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 66], Knot[11, Alternating, 163]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 66]], KnotSignature[Knot[11, Alternating, 66]]} |
Out[9]= | {119, -2} |
In[10]:= | J=Jones[Knot[11, Alternating, 66]][q] |
Out[10]= | -8 3 7 12 16 19 19 17 2 3
-12 - q + -- - -- + -- - -- + -- - -- + -- + 8 q - 4 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, 66], Knot[11, Alternating, 121]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 66]][q] |
Out[12]= | -24 2 3 2 2 2 2 4 4 3 2 4 6 8
-q - --- + --- - --- + --- + --- - -- + -- - -- + -- - q + 2 q - 2 q + q
18 16 14 12 10 8 6 4 2
q q q q q q q q q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 66]][a, z] |
Out[13]= | 2 4 6 2 2 2 4 2 6 2 4 2 4
1 - 2 a + 4 a - 2 a + 2 z - 7 a z + 10 a z - 3 a z + 3 z - 9 a z +
4 4 6 4 6 2 6 4 6 2 8
> 8 a z - a z + z - 5 a z + 2 a z - a z |
In[14]:= | Kauffman[Knot[11, Alternating, 66]][a, z] |
Out[14]= | 2 4 6 3 9 2 2 2 4 2
1 + 2 a + 4 a + 2 a + a z + 2 a z + a z - 5 z - 17 a z - 21 a z -
3
6 2 8 2 4 z 3 3 3 5 3 7 3 9 3
> 7 a z + 2 a z + ---- - a z - 12 a z - 3 a z + 2 a z - 2 a z +
a
4 5
4 2 z 2 4 4 4 6 4 8 4 10 z 5
> 16 z - ---- + 41 a z + 36 a z + 8 a z - 5 a z - ----- + 6 a z +
2 a
a
6
3 5 5 5 7 5 9 5 6 z 2 6 4 6
> 29 a z + 5 a z - 7 a z + a z - 20 z + -- - 35 a z - 26 a z -
2
a
7
6 6 8 6 4 z 7 3 7 5 7 7 7 8
> 9 a z + 3 a z + ---- - 13 a z - 28 a z - 6 a z + 5 a z + 7 z +
a
2 8 4 8 6 8 9 3 9 5 9 2 10
> 8 a z + 7 a z + 6 a z + 6 a z + 11 a z + 5 a z + 2 a z +
4 10
> 2 a z |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 66]], Vassiliev[3][Knot[11, Alternating, 66]]} |
Out[15]= | {2, -4} |
In[16]:= | Kh[Knot[11, Alternating, 66]][q, t] |
Out[16]= | 8 10 1 2 1 5 2 7 5 9
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ----- + ----- +
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
7 10 9 9 10 5 t 2 3 2
> ----- + ----- + ----- + ---- + ---- + --- + 7 q t + 3 q t + 5 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 + 3 q t + q t |