In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, NonAlternating, 65]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, NonAlternating, 65]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[14, 5, 15, 6], X[2, 8, 3, 7],
> X[18, 9, 19, 10], X[16, 11, 17, 12], X[13, 20, 14, 21], X[6, 15, 7, 16],
> X[10, 17, 11, 18], X[19, 1, 20, 22], X[21, 12, 22, 13]] |
In[4]:= | GaussCode[Knot[11, NonAlternating, 65]] |
Out[4]= | GaussCode[1, -4, 2, -1, 3, -8, 4, -2, 5, -9, 6, 11, -7, -3, 8, -6, 9, -5, -10,
> 7, -11, 10] |
In[5]:= | DTCode[Knot[11, NonAlternating, 65]] |
Out[5]= | DTCode[4, 8, 14, 2, 18, 16, -20, 6, 10, -22, -12] |
In[6]:= | alex = Alexander[Knot[11, NonAlternating, 65]][t] |
Out[6]= | 3 8 2
11 + -- - - - 8 t + 3 t
2 t
t |
In[7]:= | Conway[Knot[11, NonAlternating, 65]][z] |
Out[7]= | 2 4
1 + 4 z + 3 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[8, 15], Knot[11, NonAlternating, 65]} |
In[9]:= | {KnotDet[Knot[11, NonAlternating, 65]], KnotSignature[Knot[11, NonAlternating, 65]]} |
Out[9]= | {33, 0} |
In[10]:= | J=Jones[Knot[11, NonAlternating, 65]][q] |
Out[10]= | -7 2 4 5 5 6 4
4 - q + -- - -- + -- - -- + -- - - - 2 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, NonAlternating, 65]} |
In[12]:= | A2Invariant[Knot[11, NonAlternating, 65]][q] |
Out[12]= | -22 2 -12 -10 3 2 3 4
-q - --- - q + q + -- + -- + -- - 2 q
16 8 6 4
q q q q |
In[13]:= | HOMFLYPT[Knot[11, NonAlternating, 65]][a, z] |
Out[13]= | 2 4 6 2 2 2 4 2 6 2 2 4 4 4
-2 + 5 a - a - a - 2 z + 6 a z + a z - a z + 2 a z + a z |
In[14]:= | Kauffman[Knot[11, NonAlternating, 65]][a, z] |
Out[14]= | 2 4 6 2 z 3 5 7 2 2 2
-2 - 5 a - a + a + --- + 4 a z + 2 a z - 4 a z - 4 a z + 2 z + 5 a z -
a
4 2 6 2 3 3 3 5 3 7 3 4 2 4
> a z - 4 a z - 3 a z + 2 a z + 13 a z + 8 a z + z + 2 a z +
4 4 6 4 5 3 5 5 5 7 5 2 6
> 12 a z + 11 a z - a z - 5 a z - 9 a z - 5 a z - 6 a z -
4 6 6 6 7 3 7 5 7 7 7 2 8 4 8
> 15 a z - 9 a z + a z - a z - a z + a z + 2 a z + 4 a z +
6 8 3 9 5 9
> 2 a z + a z + a z |
In[15]:= | {Vassiliev[2][Knot[11, NonAlternating, 65]], Vassiliev[3][Knot[11, NonAlternating, 65]]} |
Out[15]= | {4, -5} |
In[16]:= | Kh[Knot[11, NonAlternating, 65]][q, t] |
Out[16]= | 3 1 1 1 3 1 2 3 3
- + 2 q + ------ + ------ + ------ + ------ + ----- + ----- + ----- + ----- +
q 15 7 13 6 11 6 11 5 9 5 9 4 7 4 7 3
q t q t q t q t q t q t q t q t
2 3 3 1 3 3
> ----- + ----- + ----- + ---- + --- + 2 q t
5 3 5 2 3 2 3 q t
q t q t q t q t |