In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 52]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 52]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 3, 9, 4], X[14, 5, 15, 6], X[12, 8, 13, 7],
> X[2, 9, 3, 10], X[18, 12, 19, 11], X[22, 13, 1, 14], X[20, 16, 21, 15],
> X[10, 18, 11, 17], X[16, 20, 17, 19], X[6, 21, 7, 22]] |
In[4]:= | GaussCode[Knot[11, Alternating, 52]] |
Out[4]= | GaussCode[1, -5, 2, -1, 3, -11, 4, -2, 5, -9, 6, -4, 7, -3, 8, -10, 9, -6, 10,
> -8, 11, -7] |
In[5]:= | DTCode[Knot[11, Alternating, 52]] |
Out[5]= | DTCode[4, 8, 14, 12, 2, 18, 22, 20, 10, 16, 6] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 52]][t] |
Out[6]= | 2 13 32 2 3
43 - -- + -- - -- - 32 t + 13 t - 2 t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 52]][z] |
Out[7]= | 2 4 6
1 + 2 z + z - 2 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 52]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 52]], KnotSignature[Knot[11, Alternating, 52]]} |
Out[9]= | {137, 0} |
In[10]:= | J=Jones[Knot[11, Alternating, 52]][q] |
Out[10]= | -5 3 7 13 18 2 3 4 5 6
22 - q + -- - -- + -- - -- - 22 q + 20 q - 15 q + 10 q - 5 q + q
4 3 2 q
q q q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, Alternating, 52]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 52]][q] |
Out[12]= | -16 -12 3 3 2 3 4 2 4 6 8 10
-3 - q + q - --- + -- + -- - -- + -- + 2 q + q - q + 5 q - 4 q +
10 8 6 4 2
q q q q q
12 14 16 18
> q + q - 3 q + q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 52]][a, z] |
Out[13]= | 2 4 4
-4 2 2 4 2 z 2 2 4 2 4 z z
-1 - a + -- + 2 a - a - z + -- + 3 a z - a z - z + -- - -- +
2 2 4 2
a a a a
6
2 4 6 z
> 2 a z - z - --
2
a |
In[14]:= | Kauffman[Knot[11, Alternating, 52]][a, z] |
Out[14]= | 2
-4 2 2 4 z 3 z 5 2 2 z 2 2
-1 - a - -- - 2 a - a + -- - --- - 3 a z + a z - z - ---- + 4 a z +
2 5 a 2
a a a
3 3 3 4
4 2 3 z 7 z 10 z 3 3 3 5 3 4 z
> 3 a z + ---- + ---- + ----- + 10 a z + 2 a z - 2 a z + 19 z - -- +
5 3 a 6
a a a
4 4 5 5 5
11 z 27 z 2 4 4 4 10 z 9 z z 5 3 5
> ----- + ----- - a z - 5 a z - ----- - ---- - -- - 9 a z - 6 a z +
4 2 5 3 a
a a a a
6 6 6 7 7
5 5 6 z 21 z 41 z 2 6 4 6 5 z 8 z
> a z - 27 z + -- - ----- - ----- - 5 a z + 3 a z + ---- - ---- -
6 4 2 5 3
a a a a a
7 8 8 9 9
18 z 3 7 8 9 z 14 z 2 8 7 z 12 z 9
> ----- + 5 a z + 11 z + ---- + ----- + 6 a z + ---- + ----- + 5 a z +
a 4 2 3 a
a a a
10
10 2 z
> 2 z + -----
2
a |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 52]], Vassiliev[3][Knot[11, Alternating, 52]]} |
Out[15]= | {2, 0} |
In[16]:= | Kh[Knot[11, Alternating, 52]][q, t] |
Out[16]= | 12 1 2 1 5 2 8 5 10
-- + 11 q + ------ + ----- + ----- + ----- + ----- + ----- + ----- + ---- +
q 11 5 9 4 7 4 7 3 5 3 5 2 3 2 3
q t q t q t q t q t q t q t q t
8 3 3 2 5 2 5 3 7 3 7 4
> --- + 11 q t + 11 q t + 9 q t + 11 q t + 6 q t + 9 q t + 4 q t +
q t
9 4 9 5 11 5 13 6
> 6 q t + q t + 4 q t + q t |