In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, NonAlternating, 160]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, NonAlternating, 160]] |
Out[3]= | PD[X[6, 2, 7, 1], X[3, 11, 4, 10], X[12, 6, 13, 5], X[20, 8, 21, 7],
> X[16, 10, 17, 9], X[11, 19, 12, 18], X[22, 13, 1, 14], X[8, 16, 9, 15],
> X[17, 4, 18, 5], X[2, 19, 3, 20], X[14, 21, 15, 22]] |
In[4]:= | GaussCode[Knot[11, NonAlternating, 160]] |
Out[4]= | GaussCode[1, -10, -2, 9, 3, -1, 4, -8, 5, 2, -6, -3, 7, -11, 8, -5, -9, 6, 10,
> -4, 11, -7] |
In[5]:= | DTCode[Knot[11, NonAlternating, 160]] |
Out[5]= | DTCode[6, -10, 12, 20, 16, -18, 22, 8, -4, 2, 14] |
In[6]:= | alex = Alexander[Knot[11, NonAlternating, 160]][t] |
Out[6]= | -3 6 16 2 3
-21 + t - -- + -- + 16 t - 6 t + t
2 t
t |
In[7]:= | Conway[Knot[11, NonAlternating, 160]][z] |
Out[7]= | 2 6
1 + z + z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, NonAlternating, 7], Knot[11, NonAlternating, 131],
> Knot[11, NonAlternating, 160]} |
In[9]:= | {KnotDet[Knot[11, NonAlternating, 160]], KnotSignature[Knot[11, NonAlternating, 160]]} |
Out[9]= | {67, 2} |
In[10]:= | J=Jones[Knot[11, NonAlternating, 160]][q] |
Out[10]= | 2 2 3 4 5 6 7 8
-5 + - + 8 q - 10 q + 12 q - 11 q + 9 q - 6 q + 3 q - q
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, NonAlternating, 160]} |
In[12]:= | A2Invariant[Knot[11, NonAlternating, 160]][q] |
Out[12]= | 2 2 4 6 12 14 16 18 20 22 24
-1 + -- + 2 q - 3 q + q + 3 q - q + 3 q - q - 2 q + q - q
4
q |
In[13]:= | HOMFLYPT[Knot[11, NonAlternating, 160]][a, z] |
Out[13]= | 2 2 2 4 4 4 6
2 5 4 2 2 z 8 z 7 z z 4 z 3 z z
2 - -- + -- - -- + 2 z - ---- + ---- - ---- - -- + ---- - ---- + --
6 4 2 6 4 2 6 4 2 4
a a a a a a a a a a |
In[14]:= | Kauffman[Knot[11, NonAlternating, 160]][a, z] |
Out[14]= | 2 2 2 2 3
2 5 4 3 z 4 z z 2 z 8 z 21 z 17 z 2 z
2 + -- + -- + -- - --- - --- + - - 5 z + -- - ---- - ----- - ----- - ---- +
6 4 2 7 5 a 8 6 4 2 9
a a a a a a a a a a
3 3 3 3 4 4 4 4 5
9 z 14 z 4 z 7 z 4 6 z 15 z 35 z 17 z z
> ---- + ----- - ---- - ---- + 3 z - ---- + ----- + ----- + ----- + -- -
7 5 3 a 8 6 4 2 9
a a a a a a a a
5 5 5 5 6 6 6 6 7 7
12 z 10 z 6 z 3 z 3 z 13 z 24 z 8 z 5 z z
> ----- - ----- + ---- + ---- + ---- - ----- - ----- - ---- + ---- + -- -
7 5 3 a 8 6 4 2 7 5
a a a a a a a a a
7 7 8 8 8 9 9
3 z z 5 z 8 z 3 z 2 z 2 z
> ---- + -- + ---- + ---- + ---- + ---- + ----
3 a 6 4 2 5 3
a a a a a a |
In[15]:= | {Vassiliev[2][Knot[11, NonAlternating, 160]], Vassiliev[3][Knot[11, NonAlternating, 160]]} |
Out[15]= | {1, 3} |
In[16]:= | Kh[Knot[11, NonAlternating, 160]][q, t] |
Out[16]= | 3 2 3 2 q 3 5 5 2 7 2
5 q + 4 q + ----- + --- + --- + 6 q t + 4 q t + 6 q t + 6 q t +
3 2 q t t
q t
7 3 9 3 9 4 11 4 11 5 13 5 13 6
> 5 q t + 6 q t + 4 q t + 5 q t + 2 q t + 4 q t + q t +
15 6 17 7
> 2 q t + q t |