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