In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 36]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 36]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[14, 6, 15, 5], X[2, 8, 3, 7],
> X[16, 9, 17, 10], X[20, 11, 21, 12], X[6, 14, 7, 13], X[12, 15, 13, 16],
> X[22, 17, 1, 18], X[10, 19, 11, 20], X[18, 21, 19, 22]] |
In[4]:= | GaussCode[Knot[11, Alternating, 36]] |
Out[4]= | GaussCode[1, -4, 2, -1, 3, -7, 4, -2, 5, -10, 6, -8, 7, -3, 8, -5, 9, -11, 10,
> -6, 11, -9] |
In[5]:= | DTCode[Knot[11, Alternating, 36]] |
Out[5]= | DTCode[4, 8, 14, 2, 16, 20, 6, 12, 22, 10, 18] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 36]][t] |
Out[6]= | 2 12 28 2 3
37 - -- + -- - -- - 28 t + 12 t - 2 t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 36]][z] |
Out[7]= | 2 6
1 + 2 z - 2 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 36], Knot[11, Alternating, 169]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 36]], KnotSignature[Knot[11, Alternating, 36]]} |
Out[9]= | {121, 0} |
In[10]:= | J=Jones[Knot[11, Alternating, 36]][q] |
Out[10]= | -6 4 8 13 17 19 2 3 4 5
20 + q - -- + -- - -- + -- - -- - 16 q + 12 q - 7 q + 3 q - q
5 4 3 2 q
q q q q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, Alternating, 35], Knot[11, Alternating, 36],
> Knot[11, Alternating, 316]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 36]][q] |
Out[12]= | -18 2 -14 -12 4 3 2 3 2 4 6 8
-1 + q - --- + q + q - --- + -- - -- + -- + 5 q - 2 q + q + 2 q -
16 10 8 6 2
q q q q q
10 12 16
> 3 q + q - q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 36]][a, z] |
Out[13]= | 2 2 4
-4 -2 2 2 z 3 z 2 2 4 2 4 2 z 2 4
2 - a + a - a + z - -- + ---- - 2 a z + a z - z + ---- - 2 a z +
4 2 2
a a a
4 4 6 2 6
> a z - z - a z |
In[14]:= | Kauffman[Knot[11, Alternating, 36]][a, z] |
Out[14]= | 2 2
-4 -2 2 z z 6 z 3 5 3 z 5 z
2 - a - a + a + -- - -- - --- - 8 a z - 5 a z - a z + ---- + ---- -
5 3 a 4 2
a a a a
3 3 3
2 2 6 2 2 z 4 z 20 z 3 3 3 5 3
> 3 a z + a z - ---- + ---- + ----- + 25 a z + 18 a z + 7 a z +
5 3 a
a a
4 4 5 5 5
4 5 z 5 z 2 4 4 4 6 4 z 7 z 23 z
> 7 z - ---- - ---- + 15 a z + 6 a z - 2 a z + -- - ---- - ----- -
4 2 5 3 a
a a a a
6 6
5 3 5 5 5 6 3 z 2 z 2 6 4 6
> 25 a z - 20 a z - 10 a z - 19 z + ---- - ---- - 28 a z - 13 a z +
4 2
a a
7 7 8
6 6 5 z 8 z 3 7 5 7 8 5 z 2 8 4 8
> a z + ---- + ---- + a z + 4 a z + 11 z + ---- + 12 a z + 6 a z +
3 a 2
a a
9
3 z 9 3 9 10 2 10
> ---- + 7 a z + 4 a z + z + a z
a |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 36]], Vassiliev[3][Knot[11, Alternating, 36]]} |
Out[15]= | {2, 1} |
In[16]:= | Kh[Knot[11, Alternating, 36]][q, t] |
Out[16]= | 10 1 3 1 5 3 8 5 9
-- + 11 q + ------ + ------ + ----- + ----- + ----- + ----- + ----- + ----- +
q 13 6 11 5 9 5 9 4 7 4 7 3 5 3 5 2
q t q t q t q t q t q t q t q t
8 10 9 3 3 2 5 2 5 3
> ----- + ---- + --- + 7 q t + 9 q t + 5 q t + 7 q t + 2 q t +
3 2 3 q t
q t q t
7 3 7 4 9 4 11 5
> 5 q t + q t + 2 q t + q t |