In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 201]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 201]] |
Out[3]= | PD[X[4, 2, 5, 1], X[12, 3, 13, 4], X[16, 6, 17, 5], X[14, 8, 15, 7],
> X[20, 9, 21, 10], X[18, 11, 19, 12], X[2, 13, 3, 14], X[6, 16, 7, 15],
> X[22, 18, 1, 17], X[10, 19, 11, 20], X[8, 21, 9, 22]] |
In[4]:= | GaussCode[Knot[11, Alternating, 201]] |
Out[4]= | GaussCode[1, -7, 2, -1, 3, -8, 4, -11, 5, -10, 6, -2, 7, -4, 8, -3, 9, -6, 10,
> -5, 11, -9] |
In[5]:= | DTCode[Knot[11, Alternating, 201]] |
Out[5]= | DTCode[4, 12, 16, 14, 20, 18, 2, 6, 22, 10, 8] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 201]][t] |
Out[6]= | 4 20 2
33 + -- - -- - 20 t + 4 t
2 t
t |
In[7]:= | Conway[Knot[11, Alternating, 201]][z] |
Out[7]= | 2 4
1 - 4 z + 4 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 103], Knot[11, Alternating, 201]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 201]], KnotSignature[Knot[11, Alternating, 201]]} |
Out[9]= | {81, 0} |
In[10]:= | J=Jones[Knot[11, Alternating, 201]][q] |
Out[10]= | -6 2 5 8 10 13 2 3 4 5
13 + q - -- + -- - -- + -- - -- - 11 q + 9 q - 5 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, 201]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 201]][q] |
Out[12]= | -20 -18 -16 2 -12 3 -8 2 2 -2 2 4
-1 + q + q - q + --- + q - --- + q - -- - -- + q + 3 q - q +
14 10 6 4
q q q q
6 8 10 12 14 16
> q + 3 q - 2 q + q + q - q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 201]][a, z] |
Out[13]= | 2 4
-2 2 6 2 z 2 2 4 2 4 z 2 4
1 + a - 2 a + a + z - -- - 2 a z - 2 a z + 2 z + -- + a z
4 2
a a |
In[14]:= | Kauffman[Knot[11, Alternating, 201]][a, z] |
Out[14]= | 2 2
-2 2 6 4 z 3 2 3 z z 2 2
1 - a + 2 a - a + --- + 12 a z + 8 a z - 18 z + ---- - -- - 21 a z -
a 4 2
a a
3 3 3
4 2 6 2 2 z 3 z 6 z 3 3 3 5 3
> 3 a z + 4 a z - ---- + ---- - ---- - 32 a z - 18 a z + 3 a z +
5 3 a
a a
4 4 5 5 5
4 7 z 6 z 2 4 4 4 6 4 z 8 z 8 z
> 35 z - ---- + ---- + 33 a z + 7 a z - 4 a z + -- - ---- + ---- +
4 2 5 3 a
a a a a
6 6
5 3 5 5 5 6 3 z 8 z 2 6 4 6
> 39 a z + 16 a z - 6 a z - 20 z + ---- - ---- - 19 a z - 9 a z +
4 2
a a
7 7 8
6 6 4 z 6 z 7 3 7 5 7 8 4 z
> a z + ---- - ---- - 22 a z - 10 a z + 2 a z + 4 z + ---- +
3 a 2
a a
9
2 8 4 8 3 z 9 3 9 10 2 10
> 3 a z + 3 a z + ---- + 6 a z + 3 a z + z + a z
a |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 201]], Vassiliev[3][Knot[11, Alternating, 201]]} |
Out[15]= | {-4, 4} |
In[16]:= | Kh[Knot[11, Alternating, 201]][q, t] |
Out[16]= | 6 1 1 1 4 1 4 4 6
- + 8 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
4 7 6 3 3 2 5 2 5 3
> ----- + ---- + --- + 6 q t + 5 q t + 3 q t + 6 q t + 2 q t +
3 2 3 q t
q t q t
7 3 7 4 9 4 11 5
> 3 q t + q t + 2 q t + q t |