In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, NonAlternating, 36]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, NonAlternating, 36]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[5, 13, 6, 12], X[2, 8, 3, 7],
> X[9, 17, 10, 16], X[11, 18, 12, 19], X[13, 7, 14, 6], X[15, 20, 16, 21],
> X[17, 1, 18, 22], X[19, 14, 20, 15], X[21, 10, 22, 11]] |
In[4]:= | GaussCode[Knot[11, NonAlternating, 36]] |
Out[4]= | GaussCode[1, -4, 2, -1, -3, 7, 4, -2, -5, 11, -6, 3, -7, 10, -8, 5, -9, 6, -10,
> 8, -11, 9] |
In[5]:= | DTCode[Knot[11, NonAlternating, 36]] |
Out[5]= | DTCode[4, 8, -12, 2, -16, -18, -6, -20, -22, -14, -10] |
In[6]:= | alex = Alexander[Knot[11, NonAlternating, 36]][t] |
Out[6]= | -4 4 8 13 2 3 4
-15 - t + -- - -- + -- + 13 t - 8 t + 4 t - t
3 2 t
t t |
In[7]:= | Conway[Knot[11, NonAlternating, 36]][z] |
Out[7]= | 2 4 6 8
1 + z - 4 z - 4 z - z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, NonAlternating, 36], Knot[11, NonAlternating, 44]} |
In[9]:= | {KnotDet[Knot[11, NonAlternating, 36]], KnotSignature[Knot[11, NonAlternating, 36]]} |
Out[9]= | {67, 2} |
In[10]:= | J=Jones[Knot[11, NonAlternating, 36]][q] |
Out[10]= | -3 3 6 2 3 4 5 6
-9 + q - -- + - + 11 q - 11 q + 11 q - 8 q + 5 q - 2 q
2 q
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, NonAlternating, 7], Knot[11, NonAlternating, 36],
> Knot[11, NonAlternating, 44]} |
In[12]:= | A2Invariant[Knot[11, NonAlternating, 36]][q] |
Out[12]= | -8 -6 2 -2 2 4 6 8 10 12 16 18
q - q + -- - q + q - 3 q + 3 q - 2 q + 3 q + q + 2 q - 2 q -
4
q
22
> q |
In[13]:= | HOMFLYPT[Knot[11, NonAlternating, 36]][a, z] |
Out[13]= | 2 2 2 4 4 6
2 5 4 2 z 9 z 12 z 4 5 z 13 z 6 z
2 - -- + -- - -- + 5 z - -- + ---- - ----- + 4 z + ---- - ----- + z + -- -
6 4 2 6 4 2 4 2 4
a a a a a a a a a
6 8
6 z z
> ---- - --
2 2
a a |
In[14]:= | Kauffman[Knot[11, NonAlternating, 36]][a, z] |
Out[14]= | 2 2
2 5 4 3 z 6 z 6 z 5 z 2 5 z 16 z
2 + -- + -- + -- - --- - --- - --- - --- - 2 a z - 5 z - ---- - ----- -
6 4 2 7 5 3 a 6 4
a a a a a a a a
2 3 3 3 3 4
18 z 2 2 3 z 13 z 17 z 14 z 3 4 4 z
> ----- + 2 a z + ---- + ----- + ----- + ----- + 7 a z + 8 z + ---- +
2 7 5 3 a 6
a a a a a
4 4 5 5 5 6
23 z 30 z 2 4 8 z 14 z 15 z 5 6 z
> ----- + ----- - 3 a z - ---- - ----- - ----- - 9 a z - 11 z + -- -
4 2 5 3 a 6
a a a a a
6 6 7 7 7 8 8
14 z 27 z 2 6 4 z 2 z z 7 8 5 z 9 z
> ----- - ----- + a z + ---- + ---- + -- + 3 a z + 4 z + ---- + ---- +
4 2 5 3 a 4 2
a a a a a a
9 9
2 z 2 z
> ---- + ----
3 a
a |
In[15]:= | {Vassiliev[2][Knot[11, NonAlternating, 36]], Vassiliev[3][Knot[11, NonAlternating, 36]]} |
Out[15]= | {1, 3} |
In[16]:= | Kh[Knot[11, NonAlternating, 36]][q, t] |
Out[16]= | 3 1 2 1 4 2 5 4 q 3
6 q + 6 q + ----- + ----- + ----- + ----- + ---- + --- + --- + 6 q t +
7 4 5 3 3 3 3 2 2 q t t
q t q t q t q t q t
5 5 2 7 2 7 3 9 3 9 4 11 4
> 5 q t + 5 q t + 6 q t + 3 q t + 5 q t + 2 q t + 3 q t +
13 5
> 2 q t |