In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 57]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 57]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[16, 6, 17, 5], X[2, 8, 3, 7],
> X[20, 9, 21, 10], X[22, 11, 1, 12], X[18, 13, 19, 14], X[6, 16, 7, 15],
> X[12, 17, 13, 18], X[14, 19, 15, 20], X[10, 21, 11, 22]] |
In[4]:= | GaussCode[Knot[11, Alternating, 57]] |
Out[4]= | GaussCode[1, -4, 2, -1, 3, -8, 4, -2, 5, -11, 6, -9, 7, -10, 8, -3, 9, -7, 10,
> -5, 11, -6] |
In[5]:= | DTCode[Knot[11, Alternating, 57]] |
Out[5]= | DTCode[4, 8, 16, 2, 20, 22, 18, 6, 12, 14, 10] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 57]][t] |
Out[6]= | -4 5 12 20 2 3 4
-23 - t + -- - -- + -- + 20 t - 12 t + 5 t - t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 57]][z] |
Out[7]= | 2 4 6 8
1 + z - 2 z - 3 z - z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 57], Knot[11, Alternating, 108],
> Knot[11, Alternating, 139], Knot[11, Alternating, 231]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 57]], KnotSignature[Knot[11, Alternating, 57]]} |
Out[9]= | {99, -2} |
In[10]:= | J=Jones[Knot[11, Alternating, 57]][q] |
Out[10]= | -7 3 7 12 14 16 16 2 3 4
-12 + q - -- + -- - -- + -- - -- + -- + 10 q - 5 q + 2 q - q
6 5 4 3 2 q
q q q q q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, Alternating, 57], Knot[11, Alternating, 231]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 57]][q] |
Out[12]= | -20 -18 3 -14 -12 6 -6 3 4 2 4 6
5 + q - q + --- - q - q - -- + q - -- + -- + 2 q + 4 q - 2 q -
16 8 4 2
q q q q
8 10 12
> q - q - q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 57]][a, z] |
Out[13]= | 2 4
4 2 4 2 4 z 2 2 4 2 4 z
12 - -- - 10 a + 3 a + 18 z - ---- - 19 a z + 6 a z + 10 z - -- -
2 2 2
a a a
2 4 4 4 6 2 6 4 6 2 8
> 15 a z + 4 a z + 2 z - 6 a z + a z - a z |
In[14]:= | Kauffman[Knot[11, Alternating, 57]][a, z] |
Out[14]= | 4 2 4 4 z 11 z 3 5 2
12 + -- + 10 a + 3 a - --- - ---- - 17 a z - 16 a z - 6 a z - 24 z -
2 3 a
a a
2 3 3
8 z 2 2 4 2 6 2 8 2 8 z 20 z 3
> ---- - 22 a z - 2 a z + 3 a z - a z + ---- + ----- + 29 a z +
2 3 a
a a
4
3 3 5 3 7 3 4 11 z 2 4 4 4
> 35 a z + 16 a z - 2 a z + 28 z + ----- + 30 a z + 6 a z -
2
a
5 5
6 4 8 4 5 z 9 z 5 3 5 5 5 7 5
> 6 a z + a z - ---- - ---- - 14 a z - 29 a z - 16 a z + 3 a z -
3 a
a
6 7 7
6 8 z 2 6 4 6 6 6 z 3 z 7
> 21 z - ---- - 31 a z - 12 a z + 6 a z + -- - ---- - 9 a z +
2 3 a
a a
8 9
3 7 5 7 8 2 z 2 8 4 8 2 z 9
> 4 a z + 9 a z + 4 z + ---- + 10 a z + 8 a z + ---- + 6 a z +
2 a
a
3 9 10 2 10
> 4 a z + z + a z |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 57]], Vassiliev[3][Knot[11, Alternating, 57]]} |
Out[15]= | {1, 3} |
In[16]:= | Kh[Knot[11, Alternating, 57]][q, t] |
Out[16]= | 7 10 1 2 1 5 2 7 5 7
-- + -- + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ----- +
3 q 15 6 13 5 11 5 11 4 9 4 9 3 7 3 7 2
q q t q t q t q t q t q t q t q t
7 9 7 6 t 2 3 2 3 3 5 3
> ----- + ---- + ---- + --- + 6 q t + 4 q t + 6 q t + q t + 4 q t +
5 2 5 3 q
q t q t q t
5 4 7 4 9 5
> q t + q t + q t |