In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, NonAlternating, 100]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, NonAlternating, 100]] |
Out[3]= | PD[X[4, 2, 5, 1], X[10, 3, 11, 4], X[14, 6, 15, 5], X[12, 8, 13, 7],
> X[9, 19, 10, 18], X[2, 11, 3, 12], X[6, 14, 7, 13], X[15, 22, 16, 1],
> X[17, 20, 18, 21], X[19, 9, 20, 8], X[21, 16, 22, 17]] |
In[4]:= | GaussCode[Knot[11, NonAlternating, 100]] |
Out[4]= | GaussCode[1, -6, 2, -1, 3, -7, 4, 10, -5, -2, 6, -4, 7, -3, -8, 11, -9, 5, -10,
> 9, -11, 8] |
In[5]:= | DTCode[Knot[11, NonAlternating, 100]] |
Out[5]= | DTCode[4, 10, 14, 12, -18, 2, 6, -22, -20, -8, -16] |
In[6]:= | alex = Alexander[Knot[11, NonAlternating, 100]][t] |
Out[6]= | 2 11 2
19 + -- - -- - 11 t + 2 t
2 t
t |
In[7]:= | Conway[Knot[11, NonAlternating, 100]][z] |
Out[7]= | 2 4
1 - 3 z + 2 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[9, 37], Knot[11, NonAlternating, 100]} |
In[9]:= | {KnotDet[Knot[11, NonAlternating, 100]], KnotSignature[Knot[11, NonAlternating, 100]]} |
Out[9]= | {45, 0} |
In[10]:= | J=Jones[Knot[11, NonAlternating, 100]][q] |
Out[10]= | -3 4 5 2 3 4 5 6
7 - q + -- - - - 8 q + 7 q - 6 q + 4 q - 2 q + q
2 q
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, NonAlternating, 100]} |
In[12]:= | A2Invariant[Knot[11, NonAlternating, 100]][q] |
Out[12]= | -10 2 2 -4 2 6 8 10 14 16 18 20
-1 - q + -- + -- - q + -- - q + q - 2 q + q - q + q + q
8 6 2
q q q |
In[13]:= | HOMFLYPT[Knot[11, NonAlternating, 100]][a, z] |
Out[13]= | 2 4
-6 -4 2 2 z 2 2 4 z
a - a + a - ---- - a z + z + --
4 2
a a |
In[14]:= | Kauffman[Knot[11, NonAlternating, 100]][a, z] |
Out[14]= | 2 2 2
-6 -4 2 2 z 3 z 2 4 z 3 z 6 z 2 2
-a - a - a - --- + --- + a z - 8 z + ---- + ---- - ---- - 3 a z +
5 a 6 4 2
a a a a
3 3 3 4 4 5
6 z 4 z 4 z 3 3 3 4 4 z 13 z 2 4 7 z
> ---- + ---- - ---- - a z + a z + 13 z - ---- + ----- + 4 a z - ---- -
5 3 a 6 2 5
a a a a a
5 5 6 6 6 7 7
6 z 2 z 5 6 z 5 z 12 z 2 z z 7 8
> ---- + ---- + a z - 6 z + -- - ---- - ----- + ---- - -- + a z + 2 z +
3 a 6 4 2 5 a
a a a a a
8 8 9 9
2 z 4 z z z
> ---- + ---- + -- + --
4 2 3 a
a a a |
In[15]:= | {Vassiliev[2][Knot[11, NonAlternating, 100]], Vassiliev[3][Knot[11, NonAlternating, 100]]} |
Out[15]= | {-3, -3} |
In[16]:= | Kh[Knot[11, NonAlternating, 100]][q, t] |
Out[16]= | 5 1 3 1 2 3 3 3 2
- + 3 q + ----- + ----- + ----- + ---- + --- + 4 q t + 4 q t + 3 q t +
q 7 3 5 2 3 2 3 q t
q t q t q t q t
5 2 5 3 7 3 7 4 9 4 9 5 11 5 13 6
> 4 q t + 3 q t + 3 q t + q t + 3 q t + q t + q t + q t |