In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, NonAlternating, 26]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, NonAlternating, 26]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[5, 13, 6, 12], X[2, 8, 3, 7],
> X[14, 9, 15, 10], X[18, 12, 19, 11], X[13, 7, 14, 6], X[20, 15, 21, 16],
> X[22, 17, 1, 18], X[10, 20, 11, 19], X[16, 21, 17, 22]] |
In[4]:= | GaussCode[Knot[11, NonAlternating, 26]] |
Out[4]= | GaussCode[1, -4, 2, -1, -3, 7, 4, -2, 5, -10, 6, 3, -7, -5, 8, -11, 9, -6, 10,
> -8, 11, -9] |
In[5]:= | DTCode[Knot[11, NonAlternating, 26]] |
Out[5]= | DTCode[4, 8, -12, 2, 14, 18, -6, 20, 22, 10, 16] |
In[6]:= | alex = Alexander[Knot[11, NonAlternating, 26]][t] |
Out[6]= | -3 5 9 2 3
11 - t + -- - - - 9 t + 5 t - t
2 t
t |
In[7]:= | Conway[Knot[11, NonAlternating, 26]][z] |
Out[7]= | 2 4 6
1 + 2 z - z - z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[9, 20], Knot[10, 149], Knot[11, NonAlternating, 26]} |
In[9]:= | {KnotDet[Knot[11, NonAlternating, 26]], KnotSignature[Knot[11, NonAlternating, 26]]} |
Out[9]= | {41, 0} |
In[10]:= | J=Jones[Knot[11, NonAlternating, 26]][q] |
Out[10]= | -2 3 2 3 4 5 6 7
5 + q - - - 6 q + 7 q - 6 q + 6 q - 4 q + 2 q - q
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, NonAlternating, 26]} |
In[12]:= | A2Invariant[Knot[11, NonAlternating, 26]][q] |
Out[12]= | -6 -4 -2 2 4 6 8 10 12 14 16 20 22
q - q + q - q + q - q + 2 q + q + q + 2 q - q - q - q |
In[13]:= | HOMFLYPT[Knot[11, NonAlternating, 26]][a, z] |
Out[13]= | 2 2 2 4 4 6
2 4 2 2 z 6 z 5 z 4 2 z 4 z z
1 - -- + -- - -- + 2 z - -- + ---- - ---- + z + ---- - ---- - --
6 4 2 6 4 2 4 2 2
a a a a a a a a a |
In[14]:= | Kauffman[Knot[11, NonAlternating, 26]][a, z] |
Out[14]= | 2 2 2
2 4 2 4 z 7 z 5 z 3 z 2 6 z 11 z 7 z
1 + -- + -- + -- - --- - --- - --- - --- - a z - z - ---- - ----- - ---- +
6 4 2 7 5 3 a 6 4 2
a a a a a a a a a
3 3 3 3 4 4 4
2 2 8 z 19 z 16 z 8 z 3 4 12 z 20 z 9 z
> a z + ---- + ----- + ----- + ---- + 3 a z + z + ----- + ----- + ---- -
7 5 3 a 6 4 2
a a a a a a
5 5 5 5 6 6 6 7 7 7
5 z 13 z 16 z 8 z 6 9 z 19 z 9 z z 2 z 3 z
> ---- - ----- - ----- - ---- + z - ---- - ----- - ---- + -- + ---- + ---- +
7 5 3 a 6 4 2 7 3 a
a a a a a a a a
8 8 8 9 9
2 z 5 z 3 z z z
> ---- + ---- + ---- + -- + --
6 4 2 5 3
a a a a a |
In[15]:= | {Vassiliev[2][Knot[11, NonAlternating, 26]], Vassiliev[3][Knot[11, NonAlternating, 26]]} |
Out[15]= | {2, 4} |
In[16]:= | Kh[Knot[11, NonAlternating, 26]][q, t] |
Out[16]= | 3 1 2 1 3 3 2 5 2 5 3
- + 3 q + ----- + ---- + --- + 4 q t + 2 q t + 3 q t + 4 q t + 3 q t +
q 5 2 3 q t
q t q t
7 3 7 4 9 4 9 5 11 5 11 6 13 6 15 7
> 3 q t + 3 q t + 3 q t + q t + 3 q t + q t + q t + q t |