In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 155]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 155]] |
Out[3]= | PD[X[4, 2, 5, 1], X[10, 4, 11, 3], X[18, 5, 19, 6], X[12, 7, 13, 8],
> X[2, 10, 3, 9], X[16, 11, 17, 12], X[20, 13, 21, 14], X[8, 15, 9, 16],
> X[22, 17, 1, 18], X[14, 19, 15, 20], X[6, 21, 7, 22]] |
In[4]:= | GaussCode[Knot[11, Alternating, 155]] |
Out[4]= | GaussCode[1, -5, 2, -1, 3, -11, 4, -8, 5, -2, 6, -4, 7, -10, 8, -6, 9, -3, 10,
> -7, 11, -9] |
In[5]:= | DTCode[Knot[11, Alternating, 155]] |
Out[5]= | DTCode[4, 10, 18, 12, 2, 16, 20, 8, 22, 14, 6] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 155]][t] |
Out[6]= | 3 16 40 2 3
-53 + -- - -- + -- + 40 t - 16 t + 3 t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 155]][z] |
Out[7]= | 2 4 6
1 + 3 z + 2 z + 3 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 155]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 155]], KnotSignature[Knot[11, Alternating, 155]]} |
Out[9]= | {171, -2} |
In[10]:= | J=Jones[Knot[11, Alternating, 155]][q] |
Out[10]= | -9 4 9 17 23 27 29 24 19 2
-12 + q - -- + -- - -- + -- - -- + -- - -- + -- + 5 q - q
8 7 6 5 4 3 2 q
q q q q q q q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, Alternating, 155]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 155]][q] |
Out[12]= | -28 2 3 5 3 4 4 6 2 4 5 5
-3 + q - --- + --- - --- - --- + --- - --- + --- + -- + -- - -- + -- -
24 22 20 18 16 14 12 8 6 4 2
q q q q q q q q q q q
2 4 6
> 2 q + 3 q - q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 155]][a, z] |
Out[13]= | 2 4 6 8 2 2 4 2 6 2 8 2 4 4 4
-a + 6 a - 5 a + a - 2 a z + 10 a z - 6 a z + a z - z + 6 a z -
6 4 2 6 4 6
> 3 a z + a z + 2 a z |
In[14]:= | Kauffman[Knot[11, Alternating, 155]][a, z] |
Out[14]= | 2 4 6 8 3 5 7 9 2 2
a + 6 a + 5 a + a - a z - 4 a z - 10 a z - 9 a z - 2 a z - 4 a z -
4 2 6 2 8 2 10 2 3 3 3 5 3
> 16 a z - 15 a z - 2 a z + a z + 4 a z + 13 a z + 22 a z +
7 3 9 3 4 2 4 4 4 6 4 8 4
> 20 a z + 7 a z - 3 z + 13 a z + 45 a z + 38 a z + 7 a z -
5
10 4 z 5 3 5 5 5 7 5 9 5 6
> 2 a z + -- - 15 a z - 18 a z - 7 a z - 14 a z - 9 a z + 5 z -
a
2 6 4 6 6 6 8 6 10 6 7 3 7
> 25 a z - 61 a z - 45 a z - 13 a z + a z + 12 a z - 4 a z -
5 7 7 7 9 7 2 8 4 8 6 8 8 8
> 25 a z - 5 a z + 4 a z + 16 a z + 24 a z + 15 a z + 7 a z +
3 9 5 9 7 9 4 10 6 10
> 11 a z + 18 a z + 7 a z + 3 a z + 3 a z |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 155]], Vassiliev[3][Knot[11, Alternating, 155]]} |
Out[15]= | {3, -4} |
In[16]:= | Kh[Knot[11, Alternating, 155]][q, t] |
Out[16]= | 9 11 1 3 1 6 3 11 6
-- + -- + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
3 q 19 8 17 7 15 7 15 6 13 6 13 5 11 5
q q t q t q t q t q t q t q t
12 11 15 12 14 15 10 14 4 t
> ------ + ----- + ----- + ----- + ----- + ----- + ---- + ---- + --- +
11 4 9 4 9 3 7 3 7 2 5 2 5 3 q
q t q t q t q t q t q t q t q t
2 3 2 5 3
> 8 q t + q t + 4 q t + q t |