In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 89]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 89]] |
Out[3]= | PD[X[4, 2, 5, 1], X[10, 3, 11, 4], X[12, 6, 13, 5], X[16, 8, 17, 7],
> X[18, 9, 19, 10], X[2, 11, 3, 12], X[22, 14, 1, 13], X[6, 16, 7, 15],
> X[20, 18, 21, 17], X[8, 19, 9, 20], X[14, 22, 15, 21]] |
In[4]:= | GaussCode[Knot[11, Alternating, 89]] |
Out[4]= | GaussCode[1, -6, 2, -1, 3, -8, 4, -10, 5, -2, 6, -3, 7, -11, 8, -4, 9, -5, 10,
> -9, 11, -7] |
In[5]:= | DTCode[Knot[11, Alternating, 89]] |
Out[5]= | DTCode[4, 10, 12, 16, 18, 2, 22, 6, 20, 8, 14] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 89]][t] |
Out[6]= | 2 12 28 2 3
-35 + -- - -- + -- + 28 t - 12 t + 2 t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 89]][z] |
Out[7]= | 2 6
1 - 2 z + 2 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 89]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 89]], KnotSignature[Knot[11, Alternating, 89]]} |
Out[9]= | {119, 2} |
In[10]:= | J=Jones[Knot[11, Alternating, 89]][q] |
Out[10]= | -3 3 7 2 3 4 5 6 7 8
-11 + q - -- + - + 16 q - 19 q + 19 q - 17 q + 13 q - 8 q + 4 q - q
2 q
q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, Alternating, 34], Knot[11, Alternating, 89]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 89]][q] |
Out[12]= | -10 -6 3 -2 2 4 6 8 12 14 16
q - q + -- - q + 3 q - 4 q + 2 q - 2 q + 2 q - 3 q + 4 q -
4
q
18 20 22 24
> q - q + 2 q - q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 89]][a, z] |
Out[13]= | 2 2 2 4 4 4 6 6
-4 -2 2 2 z 2 z z 2 2 4 z 2 z z z z
a - a + a - 3 z - -- + ---- - -- + a z - 2 z - -- + ---- + -- + -- + --
6 4 2 6 4 2 4 2
a a a a a a a a |
In[14]:= | Kauffman[Knot[11, Alternating, 89]][a, z] |
Out[14]= | 2 2 2
-4 -2 2 z 4 z 4 z 2 z 2 2 z 3 z 4 z
a + a - a - -- - --- - --- - --- - a z + 3 z + ---- + ---- - ---- -
7 5 3 a 8 6 4
a a a a a a
2 3 3 3 3 3 4 4
5 z 2 2 z 5 z 15 z 13 z 10 z 3 6 z 2 z
> ---- + 3 a z - -- + ---- + ----- + ----- + ----- + 6 a z - ---- - ---- +
2 9 7 5 3 a 8 6
a a a a a a a
4 4 5 5 5 5 5
15 z 14 z 2 4 z 11 z 19 z 12 z 13 z 5
> ----- + ----- - 3 a z + -- - ----- - ----- - ----- - ----- - 8 a z -
4 2 9 7 5 3 a
a a a a a a
6 6 6 6 7 7 7 7
6 4 z 7 z 24 z 21 z 2 6 7 z 5 z 4 z z
> 7 z + ---- - ---- - ----- - ----- + a z + ---- + ---- - ---- + -- +
8 6 4 2 7 5 3 a
a a a a a a a
8 8 8 9 9 9 10 10
7 8 7 z 12 z 9 z 4 z 7 z 3 z z z
> 3 a z + 4 z + ---- + ----- + ---- + ---- + ---- + ---- + --- + ---
6 4 2 5 3 a 4 2
a a a a a a a |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 89]], Vassiliev[3][Knot[11, Alternating, 89]]} |
Out[15]= | {-2, -1} |
In[16]:= | Kh[Knot[11, Alternating, 89]][q, t] |
Out[16]= | 3 1 2 1 5 2 6 5 q 3
10 q + 7 q + ----- + ----- + ----- + ----- + ---- + --- + --- + 10 q t +
7 4 5 3 3 3 3 2 2 q t t
q t q t q t q t q t
5 5 2 7 2 7 3 9 3 9 4 11 4
> 9 q t + 9 q t + 10 q t + 8 q t + 9 q t + 5 q t + 8 q t +
11 5 13 5 13 6 15 6 17 7
> 3 q t + 5 q t + q t + 3 q t + q t |