In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, NonAlternating, 95]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, NonAlternating, 95]] |
Out[3]= | PD[X[4, 2, 5, 1], X[10, 4, 11, 3], X[14, 6, 15, 5], X[7, 13, 8, 12],
> X[2, 10, 3, 9], X[11, 21, 12, 20], X[18, 14, 19, 13], X[15, 22, 16, 1],
> X[6, 18, 7, 17], X[19, 9, 20, 8], X[21, 16, 22, 17]] |
In[4]:= | GaussCode[Knot[11, NonAlternating, 95]] |
Out[4]= | GaussCode[1, -5, 2, -1, 3, -9, -4, 10, 5, -2, -6, 4, 7, -3, -8, 11, 9, -7, -10,
> 6, -11, 8] |
In[5]:= | DTCode[Knot[11, NonAlternating, 95]] |
Out[5]= | DTCode[4, 10, 14, -12, 2, -20, 18, -22, 6, -8, -16] |
In[6]:= | alex = Alexander[Knot[11, NonAlternating, 95]][t] |
Out[6]= | -3 5 7 2 3
7 - t + -- - - - 7 t + 5 t - t
2 t
t |
In[7]:= | Conway[Knot[11, NonAlternating, 95]][z] |
Out[7]= | 2 4 6
1 + 4 z - z - z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[9, 11], Knot[11, NonAlternating, 95]} |
In[9]:= | {KnotDet[Knot[11, NonAlternating, 95]], KnotSignature[Knot[11, NonAlternating, 95]]} |
Out[9]= | {33, 4} |
In[10]:= | J=Jones[Knot[11, NonAlternating, 95]][q] |
Out[10]= | 2 3 4 5 6 7 8 9
2 q - 3 q + 5 q - 6 q + 6 q - 5 q + 4 q - 2 q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, NonAlternating, 95]} |
In[12]:= | A2Invariant[Knot[11, NonAlternating, 95]][q] |
Out[12]= | 6 10 16 18 20 22 24 26 28 32
2 q + 2 q + q - 2 q + q - q + q + q - q - q |
In[13]:= | HOMFLYPT[Knot[11, NonAlternating, 95]][a, z] |
Out[13]= | 2 2 2 4 4 4 6
-10 2 3 3 3 z 5 z 6 z z 4 z 2 z z
-a + -- - -- + -- + ---- - ---- + ---- + -- - ---- + ---- - --
8 6 4 8 6 4 8 6 4 6
a a a a a a a a a a |
In[14]:= | Kauffman[Knot[11, NonAlternating, 95]][a, z] |
Out[14]= | 2 2 2 2 3
-10 2 3 3 3 z 3 z z z 4 z 6 z 9 z 7 z 3 z
a + -- + -- + -- - --- - --- - -- - -- - ---- - ---- - ---- - ---- + ---- +
8 6 4 11 9 7 5 10 8 6 4 11
a a a a a a a a a a a a
3 3 4 4 4 4 5 5 5 6 6
7 z 4 z 2 z 5 z 6 z 3 z 4 z 5 z z z z
> ---- + ---- + ---- + ---- + ---- + ---- - ---- - ---- - -- + --- - -- -
9 7 10 8 6 4 9 7 5 10 8
a a a a a a a a a a a
6 7 7 7 8 8
2 z 2 z 3 z z z z
> ---- + ---- + ---- + -- + -- + --
6 9 7 5 8 6
a a a a a a |
In[15]:= | {Vassiliev[2][Knot[11, NonAlternating, 95]], Vassiliev[3][Knot[11, NonAlternating, 95]]} |
Out[15]= | {4, 9} |
In[16]:= | Kh[Knot[11, NonAlternating, 95]][q, t] |
Out[16]= | 3 5 5 7 7 2 9 2 9 3 11 3 11 4
2 q + q + 2 q t + q t + 3 q t + 2 q t + 3 q t + 3 q t + 3 q t +
13 4 13 5 15 5 15 6 17 6 19 7
> 3 q t + 2 q t + 3 q t + 2 q t + 2 q t + 2 q t |