In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, NonAlternating, 29]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, NonAlternating, 29]] |
Out[3]= | PD[X[4, 2, 5, 1], X[8, 4, 9, 3], X[5, 13, 6, 12], X[2, 8, 3, 7],
> X[14, 9, 15, 10], X[18, 12, 19, 11], X[13, 7, 14, 6], X[22, 15, 1, 16],
> X[20, 17, 21, 18], X[10, 20, 11, 19], X[16, 21, 17, 22]] |
In[4]:= | GaussCode[Knot[11, NonAlternating, 29]] |
Out[4]= | GaussCode[1, -4, 2, -1, -3, 7, 4, -2, 5, -10, 6, 3, -7, -5, 8, -11, 9, -6, 10,
> -9, 11, -8] |
In[5]:= | DTCode[Knot[11, NonAlternating, 29]] |
Out[5]= | DTCode[4, 8, -12, 2, 14, 18, -6, 22, 20, 10, 16] |
In[6]:= | alex = Alexander[Knot[11, NonAlternating, 29]][t] |
Out[6]= | 3 13 2
-19 - -- + -- + 13 t - 3 t
2 t
t |
In[7]:= | Conway[Knot[11, NonAlternating, 29]][z] |
Out[7]= | 2 4
1 + z - 3 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[10, 36], Knot[11, Alternating, 230], Knot[11, NonAlternating, 29]} |
In[9]:= | {KnotDet[Knot[11, NonAlternating, 29]], KnotSignature[Knot[11, NonAlternating, 29]]} |
Out[9]= | {51, 2} |
In[10]:= | J=Jones[Knot[11, NonAlternating, 29]][q] |
Out[10]= | 2 2 3 4 5 6 7 8
-4 + - + 6 q - 8 q + 9 q - 8 q + 7 q - 4 q + 2 q - q
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, NonAlternating, 29]} |
In[12]:= | A2Invariant[Knot[11, NonAlternating, 29]][q] |
Out[12]= | 2 2 4 8 12 16 20 22 24 26
-- + 2 q - 3 q - q + 2 q + 3 q - q + q - q - q
4
q |
In[13]:= | HOMFLYPT[Knot[11, NonAlternating, 29]][a, z] |
Out[13]= | 2 2 2 4 4
-8 -6 2 3 2 2 z z 4 z z 2 z
2 - a + a + -- - -- + 2 z + ---- + -- - ---- - -- - ----
4 2 6 4 2 4 2
a a a a a a a |
In[14]:= | Kauffman[Knot[11, NonAlternating, 29]][a, z] |
Out[14]= | 2 2
-8 -6 2 3 2 z 2 z z 3 z 2 z 2 3 z 11 z
2 - a - a + -- + -- + --- + --- + -- + --- + --- - 6 z + ---- - ----- -
4 2 9 7 5 3 a 8 4
a a a a a a a a
2 3 3 3 3 4 4 4 4
14 z 3 z 3 z 5 z 5 z 4 5 z 2 z 18 z 14 z
> ----- - ---- - ---- - ---- - ---- + 3 z - ---- + ---- + ----- + ----- +
2 9 7 3 a 8 6 4 2
a a a a a a a a
5 5 5 5 6 6 6 6 7 7 7
z 2 z 4 z z 2 z 3 z 11 z 6 z 2 z z z
> -- - ---- + ---- + -- + ---- - ---- - ----- - ---- + ---- - -- + -- +
9 7 3 a 8 6 4 2 7 3 a
a a a a a a a a a
8 8 8 9 9
2 z 4 z 2 z z z
> ---- + ---- + ---- + -- + --
6 4 2 5 3
a a a a a |
In[15]:= | {Vassiliev[2][Knot[11, NonAlternating, 29]], Vassiliev[3][Knot[11, NonAlternating, 29]]} |
Out[15]= | {1, 4} |
In[16]:= | Kh[Knot[11, NonAlternating, 29]][q, t] |
Out[16]= | 3 2 2 2 q 3 5 5 2 7 2
4 q + 3 q + ----- + --- + --- + 5 q t + 3 q t + 4 q t + 5 q t +
3 2 q t t
q t
7 3 9 3 9 4 11 4 11 5 13 5 13 6
> 4 q t + 4 q t + 3 q t + 4 q t + q t + 3 q t + q t +
15 6 17 7
> q t + q t |