In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, NonAlternating, 75]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, NonAlternating, 75]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[5, 14, 6, 15], X[2, 8, 3, 7],
> X[9, 20, 10, 21], X[11, 16, 12, 17], X[13, 6, 14, 7], X[15, 18, 16, 19],
> X[17, 12, 18, 13], X[19, 22, 20, 1], X[21, 10, 22, 11]] |
In[4]:= | GaussCode[Knot[11, NonAlternating, 75]] |
Out[4]= | GaussCode[1, -4, 2, -1, -3, 7, 4, -2, -5, 11, -6, 9, -7, 3, -8, 6, -9, 8, -10,
> 5, -11, 10] |
In[5]:= | DTCode[Knot[11, NonAlternating, 75]] |
Out[5]= | DTCode[4, 8, -14, 2, -20, -16, -6, -18, -12, -22, -10] |
In[6]:= | alex = Alexander[Knot[11, NonAlternating, 75]][t] |
Out[6]= | 2 7 14 2 3
-17 + -- - -- + -- + 14 t - 7 t + 2 t
3 2 t
t t |
In[7]:= | Conway[Knot[11, NonAlternating, 75]][z] |
Out[7]= | 2 4 6
1 + 4 z + 5 z + 2 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[10, 65], Knot[10, 77], Knot[11, NonAlternating, 71],
> Knot[11, NonAlternating, 75]} |
In[9]:= | {KnotDet[Knot[11, NonAlternating, 75]], KnotSignature[Knot[11, NonAlternating, 75]]} |
Out[9]= | {63, -2} |
In[10]:= | J=Jones[Knot[11, NonAlternating, 75]][q] |
Out[10]= | -9 3 5 9 10 10 11 7 5
-2 + 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, NonAlternating, 71], Knot[11, NonAlternating, 75]} |
In[12]:= | A2Invariant[Knot[11, NonAlternating, 75]][q] |
Out[12]= | -28 -26 -24 5 3 6 2 4 -6 2 -2
-2 + q + q - q - --- - --- + --- + --- + -- + q - -- + q
20 18 12 10 8 4
q q q q q q |
In[13]:= | HOMFLYPT[Knot[11, NonAlternating, 75]][a, z] |
Out[13]= | 2 4 6 8 2 2 4 2 6 2 8 2 2 4
-3 a + 11 a - 9 a + 2 a - 5 a z + 18 a z - 10 a z + a z - 2 a z +
4 4 6 4 4 6
> 10 a z - 3 a z + 2 a z |
In[14]:= | Kauffman[Knot[11, NonAlternating, 75]][a, z] |
Out[14]= | 2 4 6 8 3 5 7 9
3 a + 11 a + 9 a + 2 a - 3 a z - 11 a z - 21 a z - 17 a z - 4 a z -
2 2 4 2 6 2 8 2 10 2 3 3 3
> 6 a z - 20 a z - 15 a z + a z + 2 a z + 3 a z + 19 a z +
5 3 7 3 9 3 2 4 4 4 6 4 8 4
> 42 a z + 36 a z + 10 a z + 4 a z + 19 a z + 17 a z - a z -
10 4 3 5 5 5 7 5 9 5 2 6 4 6
> 3 a z - 10 a z - 31 a z - 31 a z - 10 a z + a z - 10 a z -
6 6 8 6 10 6 3 7 5 7 7 7 9 7
> 18 a z - 6 a z + a z + 4 a z + 8 a z + 7 a z + 3 a z +
4 8 6 8 8 8 5 9 7 9
> 4 a z + 7 a z + 3 a z + a z + a z |
In[15]:= | {Vassiliev[2][Knot[11, NonAlternating, 75]], Vassiliev[3][Knot[11, NonAlternating, 75]]} |
Out[15]= | {4, -5} |
In[16]:= | Kh[Knot[11, NonAlternating, 75]][q, t] |
Out[16]= | 3 3 1 2 1 3 2 6 3
-- + - + ------ + ------ + ------ + ------ + ------ + ------ + ------ +
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
4 6 6 4 5 6 2 5
> ------ + ----- + ----- + ----- + ----- + ----- + ---- + ---- + 2 q t
11 4 9 4 9 3 7 3 7 2 5 2 5 3
q t q t q t q t q t q t q t q t |