In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 229]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 229]] |
Out[3]= | PD[X[4, 2, 5, 1], X[12, 4, 13, 3], X[20, 6, 21, 5], X[18, 8, 19, 7],
> X[14, 10, 15, 9], X[2, 12, 3, 11], X[10, 14, 11, 13], X[22, 15, 1, 16],
> X[8, 18, 9, 17], X[6, 20, 7, 19], X[16, 21, 17, 22]] |
In[4]:= | GaussCode[Knot[11, Alternating, 229]] |
Out[4]= | GaussCode[1, -6, 2, -1, 3, -10, 4, -9, 5, -7, 6, -2, 7, -5, 8, -11, 9, -4, 10,
> -3, 11, -8] |
In[5]:= | DTCode[Knot[11, Alternating, 229]] |
Out[5]= | DTCode[4, 12, 20, 18, 14, 2, 10, 22, 8, 6, 16] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 229]][t] |
Out[6]= | 4 18 2
-27 - -- + -- + 18 t - 4 t
2 t
t |
In[7]:= | Conway[Knot[11, Alternating, 229]][z] |
Out[7]= | 2 4
1 + 2 z - 4 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 226], Knot[11, Alternating, 229]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 229]], KnotSignature[Knot[11, Alternating, 229]]} |
Out[9]= | {71, 2} |
In[10]:= | J=Jones[Knot[11, Alternating, 229]][q] |
Out[10]= | 1 2 3 4 5 6 7 8 9 10
-2 + - + 5 q - 8 q + 10 q - 11 q + 11 q - 9 q + 7 q - 4 q + 2 q - q
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, Alternating, 229]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 229]][q] |
Out[12]= | -4 2 4 8 10 12 14 16 18 20 22 26
q + 3 q - 2 q + q - 2 q + q - q + q + q - q + 3 q - q +
28 30 32
> q - q - q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 229]][a, z] |
Out[13]= | 2 2 2 4 4 4
-10 -8 -6 -4 2 2 z z 2 z z 2 z z
1 - a + a + a - a + z + ---- + -- - ---- - -- - ---- - --
8 6 4 6 4 2
a a a a a a |
In[14]:= | Kauffman[Knot[11, Alternating, 229]][a, z] |
Out[14]= | 2 2
-10 -8 -6 -4 2 z 2 z 2 z 2 z 2 5 z 2 z
1 + a + a - a - a - --- + --- - --- - --- - 2 z - ---- - ---- +
11 7 5 3 10 8
a a a a a a
2 2 3 3 3 3 3 3 4 4
8 z 7 z 7 z z 12 z 5 z 7 z 2 z 4 12 z 2 z
> ---- + ---- + ---- - -- - ----- + ---- + ---- - ---- + z + ----- + ---- -
6 4 11 9 7 5 3 a 10 8
a a a a a a a a a
4 4 4 5 5 5 5 5 5 6
12 z 5 z 2 z 5 z 6 z 14 z 5 z 6 z 2 z 9 z
> ----- - ---- - ---- - ---- + ---- + ----- - ---- - ---- + ---- - ---- -
6 4 2 11 9 7 5 3 a 10
a a a a a a a a a
6 6 6 6 7 7 7 7 8 8 8
3 z 2 z z 3 z z 7 z 12 z 4 z 2 z z 3 z
> ---- + ---- - -- + ---- + --- - ---- - ----- + ---- + ---- - -- + ---- +
8 6 4 2 11 9 7 3 10 8 4
a a a a a a a a a a a
9 9 9 10 10
2 z 4 z 2 z z z
> ---- + ---- + ---- + --- + ---
9 7 5 8 6
a a a a a |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 229]], Vassiliev[3][Knot[11, Alternating, 229]]} |
Out[15]= | {2, 7} |
In[16]:= | Kh[Knot[11, Alternating, 229]][q, t] |
Out[16]= | 3 1 1 q 3 5 5 2 7 2 7 3
4 q + 2 q + ----- + --- + - + 5 q t + 3 q t + 5 q t + 5 q t + 6 q t +
3 2 q t t
q t
9 3 9 4 11 4 11 5 13 5 13 6 15 6
> 5 q t + 5 q t + 6 q t + 4 q t + 5 q t + 3 q t + 4 q t +
15 7 17 7 17 8 19 8 21 9
> q t + 3 q t + q t + q t + q t |