In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 138]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 138]] |
Out[3]= | PD[X[4, 2, 5, 1], X[10, 3, 11, 4], X[16, 5, 17, 6], X[14, 8, 15, 7],
> X[18, 10, 19, 9], X[2, 11, 3, 12], X[20, 14, 21, 13], X[22, 15, 1, 16],
> X[12, 18, 13, 17], X[8, 20, 9, 19], X[6, 21, 7, 22]] |
In[4]:= | GaussCode[Knot[11, Alternating, 138]] |
Out[4]= | GaussCode[1, -6, 2, -1, 3, -11, 4, -10, 5, -2, 6, -9, 7, -4, 8, -3, 9, -5, 10,
> -7, 11, -8] |
In[5]:= | DTCode[Knot[11, Alternating, 138]] |
Out[5]= | DTCode[4, 10, 16, 14, 18, 2, 20, 22, 12, 8, 6] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 138]][t] |
Out[6]= | 2 14 38 2 3
53 - -- + -- - -- - 38 t + 14 t - 2 t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 138]][z] |
Out[7]= | 4 6
1 + 2 z - 2 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 138], Knot[11, Alternating, 285]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 138]], KnotSignature[Knot[11, Alternating, 138]]} |
Out[9]= | {161, 0} |
In[10]:= | J=Jones[Knot[11, Alternating, 138]][q] |
Out[10]= | -5 4 9 16 22 2 3 4 5 6
26 - q + -- - -- + -- - -- - 26 q + 23 q - 17 q + 11 q - 5 q + q
4 3 2 q
q q q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, Alternating, 138], Knot[11, Alternating, 285]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 138]][q] |
Out[12]= | -16 -14 2 4 3 -6 4 5 2 6 8
-3 - q + q + --- - --- + -- + q - -- + -- + 3 q - 2 q + 5 q -
12 10 8 4 2
q q q q q
10 12 14 16 18
> 5 q + 2 q + 2 q - 3 q + q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 138]][a, z] |
Out[13]= | 2 4 4 6
2 z 2 2 4 2 z z 2 4 6 z
1 + z - -- + a z - a z + -- - -- + 2 a z - z - --
2 4 2 2
a a a a |
In[14]:= | Kauffman[Knot[11, Alternating, 138]][a, z] |
Out[14]= | 2 2 3
z 3 z 3 2 z 7 z 2 2 4 2 3 z
1 - -- - --- - 3 a z - a z - 9 z - -- - ---- - a z + 2 a z + ---- +
3 a 4 2 5
a a a a
3 3 4 4 4
8 z 10 z 3 3 3 5 3 4 z 12 z 35 z
> ---- + ----- + 12 a z + 6 a z - a z + 32 z - -- + ----- + ----- +
3 a 6 4 2
a a a a
5 5 5
2 4 4 4 9 z 6 z 2 z 5 3 5 5 5
> 5 a z - 5 a z - ---- - ---- + ---- - 13 a z - 11 a z + a z -
5 3 a
a a
6 6 6 7 7 7
6 z 22 z 49 z 2 6 4 6 5 z 12 z 27 z
> 42 z + -- - ----- - ----- - 12 a z + 4 a z + ---- - ----- - ----- -
6 4 2 5 3 a
a a a a a
8 8 9 9
7 3 7 8 10 z 16 z 2 8 9 z 17 z
> 2 a z + 8 a z + 16 z + ----- + ----- + 10 a z + ---- + ----- +
4 2 3 a
a a a
10
9 10 3 z
> 8 a z + 3 z + -----
2
a |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 138]], Vassiliev[3][Knot[11, Alternating, 138]]} |
Out[15]= | {0, 0} |
In[16]:= | Kh[Knot[11, Alternating, 138]][q, t] |
Out[16]= | 14 1 3 1 6 3 10 6 12
-- + 13 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + ---- +
q 11 5 9 4 7 4 7 3 5 3 5 2 3 2 3
q t q t q t q t q t q t q t q t
10 3 3 2 5 2 5 3 7 3
> --- + 13 q t + 13 q t + 10 q t + 13 q t + 7 q t + 10 q t +
q t
7 4 9 4 9 5 11 5 13 6
> 4 q t + 7 q t + q t + 4 q t + q t |