In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 197]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 197]] |
Out[3]= | PD[X[4, 2, 5, 1], X[12, 4, 13, 3], X[16, 5, 17, 6], X[14, 8, 15, 7],
> X[18, 10, 19, 9], X[2, 12, 3, 11], X[8, 14, 9, 13], X[22, 15, 1, 16],
> X[20, 18, 21, 17], X[10, 20, 11, 19], X[6, 21, 7, 22]] |
In[4]:= | GaussCode[Knot[11, Alternating, 197]] |
Out[4]= | GaussCode[1, -6, 2, -1, 3, -11, 4, -7, 5, -10, 6, -2, 7, -4, 8, -3, 9, -5, 10,
> -9, 11, -8] |
In[5]:= | DTCode[Knot[11, Alternating, 197]] |
Out[5]= | DTCode[4, 12, 16, 14, 18, 2, 8, 22, 20, 10, 6] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 197]][t] |
Out[6]= | 3 14 33 2 3
-43 + -- - -- + -- + 33 t - 14 t + 3 t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 197]][z] |
Out[7]= | 2 4 6
1 + 4 z + 4 z + 3 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 197]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 197]], KnotSignature[Knot[11, Alternating, 197]]} |
Out[9]= | {143, 2} |
In[10]:= | J=Jones[Knot[11, Alternating, 197]][q] |
Out[10]= | -2 3 2 3 4 5 6 7 8 9
-7 - q + - + 14 q - 19 q + 23 q - 23 q + 21 q - 16 q + 10 q - 5 q + q
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, Alternating, 197]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 197]][q] |
Out[12]= | -6 -4 -2 2 4 6 8 10 12 14
-2 - q + q - q + 5 q - 3 q + 3 q + 3 q - 2 q + 4 q - 4 q +
16 20 22 24 26 28
> 3 q - 3 q + 3 q - 3 q - q + q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 197]][a, z] |
Out[13]= | 2 2 2 2 4 4 4
2 2 2 2 z 5 z 7 z 3 z 4 3 z 6 z 2 z
-1 - -- + -- + -- - 2 z + -- - ---- + ---- + ---- - z - ---- + ---- + ---- +
6 4 2 8 6 4 2 6 4 2
a a a a a a a a a a
6 6
2 z z
> ---- + --
4 2
a a |
In[14]:= | Kauffman[Knot[11, Alternating, 197]][a, z] |
Out[14]= | 2 2
2 2 2 z 3 z 6 z 2 z z 2 2 z 15 z
-1 + -- + -- - -- + -- - --- - --- - --- + - + a z + 3 z - ---- - ----- -
6 4 2 9 7 5 3 a 8 6
a a a a a a a a a
2 2 3 3 3 3 4 4
15 z z 4 z 14 z 16 z 8 z 3 4 z 11 z
> ----- + -- + ---- + ----- + ----- + ---- - 2 a z - 5 z - --- + ----- +
4 2 9 7 5 3 10 8
a a a a a a a a
4 4 4 5 5 5 5 5
42 z 41 z 6 z 10 z 17 z 6 z 5 z 5 z 5 6
> ----- + ----- + ---- - ----- - ----- - ---- - ---- - ---- + a z + 3 z +
6 4 2 9 7 5 3 a
a a a a a a a
6 6 6 6 6 7 7 7 7 7
z 20 z 51 z 42 z 9 z 5 z 5 z 18 z 3 z 5 z
> --- - ----- - ----- - ----- - ---- + ---- - ---- - ----- - ---- + ---- +
10 8 6 4 2 9 7 5 3 a
a a a a a a a a a
8 8 8 8 9 9 9 10 10
9 z 17 z 15 z 7 z 7 z 13 z 6 z 2 z 2 z
> ---- + ----- + ----- + ---- + ---- + ----- + ---- + ----- + -----
8 6 4 2 7 5 3 6 4
a a a a a a a a a |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 197]], Vassiliev[3][Knot[11, Alternating, 197]]} |
Out[15]= | {4, 6} |
In[16]:= | Kh[Knot[11, Alternating, 197]][q, t] |
Out[16]= | 3 1 2 1 5 2 q 3 5 5 2
9 q + 6 q + ----- + ----- + ---- + --- + --- + 11 q t + 8 q t + 12 q t +
5 3 3 2 2 q t t
q t q t q t
7 2 7 3 9 3 9 4 11 4 11 5
> 11 q t + 11 q t + 12 q t + 10 q t + 11 q t + 6 q t +
13 5 13 6 15 6 15 7 17 7 19 8
> 10 q t + 4 q t + 6 q t + q t + 4 q t + q t |