In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | Show[DrawMorseLink[Knot[11, Alternating, 213]]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | PD[Knot[11, Alternating, 213]] |
Out[3]= | PD[X[4, 2, 5, 1], X[12, 4, 13, 3], X[16, 6, 17, 5], X[22, 8, 1, 7],
> X[18, 10, 19, 9], X[2, 12, 3, 11], X[20, 13, 21, 14], X[10, 16, 11, 15],
> X[6, 18, 7, 17], X[14, 19, 15, 20], X[8, 22, 9, 21]] |
In[4]:= | GaussCode[Knot[11, Alternating, 213]] |
Out[4]= | GaussCode[1, -6, 2, -1, 3, -9, 4, -11, 5, -8, 6, -2, 7, -10, 8, -3, 9, -5, 10,
> -7, 11, -4] |
In[5]:= | DTCode[Knot[11, Alternating, 213]] |
Out[5]= | DTCode[4, 12, 16, 22, 18, 2, 20, 10, 6, 14, 8] |
In[6]:= | alex = Alexander[Knot[11, Alternating, 213]][t] |
Out[6]= | 3 16 33 2 3
41 - -- + -- - -- - 33 t + 16 t - 3 t
3 2 t
t t |
In[7]:= | Conway[Knot[11, Alternating, 213]][z] |
Out[7]= | 2 4 6
1 + 4 z - 2 z - 3 z |
In[8]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[8]= | {Knot[11, Alternating, 213]} |
In[9]:= | {KnotDet[Knot[11, Alternating, 213]], KnotSignature[Knot[11, Alternating, 213]]} |
Out[9]= | {145, 4} |
In[10]:= | J=Jones[Knot[11, Alternating, 213]][q] |
Out[10]= | 2 3 4 5 6 7 8 9
1 - 3 q + 8 q - 14 q + 20 q - 23 q + 24 q - 21 q + 16 q - 10 q +
10 11
> 4 q - q |
In[11]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[11]= | {Knot[11, Alternating, 213]} |
In[12]:= | A2Invariant[Knot[11, Alternating, 213]][q] |
Out[12]= | 2 4 6 8 10 12 14 16 18 20
1 - q + q + 3 q - 4 q + 4 q - 2 q - q + 4 q - 3 q + 5 q -
22 26 28 30 34
> 3 q + 2 q - 4 q + 2 q - q |
In[13]:= | HOMFLYPT[Knot[11, Alternating, 213]][a, z] |
Out[13]= | 2 2 2 2 2 4 4 4 4
-10 -8 -2 z 5 z 3 z z 2 z 3 z 5 z z z
-a + a + a - --- + ---- - ---- + -- + ---- + ---- - ---- - -- + -- -
10 8 6 4 2 8 6 4 2
a a a a a a a a a
6 6
2 z z
> ---- - --
6 4
a a |
In[14]:= | Kauffman[Knot[11, Alternating, 213]][a, z] |
Out[14]= | 2 2 2 2
-10 -8 -2 4 z 5 z 3 z 3 z z z 4 z 7 z 5 z
a + a - a - --- - --- - --- - --- - -- + --- - ---- - ---- - ---- +
11 9 7 5 3 12 10 8 6
a a a a a a a a a
2 3 3 3 3 3 3 4 4 4
3 z z 10 z 21 z 12 z 7 z 5 z 4 z 9 z 26 z
> ---- - --- + ----- + ----- + ----- + ---- + ---- - ---- + ---- + ----- +
2 13 11 9 7 5 3 12 10 8
a a a a a a a a a a
4 4 4 5 5 5 5 5 5 6
20 z 4 z 3 z z 14 z 25 z 9 z 6 z 7 z 4 z
> ----- + ---- - ---- + --- - ----- - ----- - ---- - ---- - ---- + ---- -
6 4 2 13 11 9 7 5 3 12
a a a a a a a a a a
6 6 6 6 6 7 7 7 7 7
16 z 39 z 29 z 9 z z 9 z 3 z 13 z 4 z 3 z
> ----- - ----- - ----- - ---- + -- + ---- + ---- - ----- - ---- + ---- +
10 8 6 4 2 11 9 7 5 3
a a a a a a a a a a
8 8 8 8 9 9 9 10 10
11 z 17 z 11 z 5 z 7 z 12 z 5 z 2 z 2 z
> ----- + ----- + ----- + ---- + ---- + ----- + ---- + ----- + -----
10 8 6 4 9 7 5 8 6
a a a a a a a a a |
In[15]:= | {Vassiliev[2][Knot[11, Alternating, 213]], Vassiliev[3][Knot[11, Alternating, 213]]} |
Out[15]= | {4, 10} |
In[16]:= | Kh[Knot[11, Alternating, 213]][q, t] |
Out[16]= | 3
3 5 1 2 q q 5 7 7 2 9 2
6 q + 3 q + ---- + --- + -- + 9 q t + 5 q t + 11 q t + 9 q t +
2 t t
q t
9 3 11 3 11 4 13 4 13 5 15 5
> 12 q t + 11 q t + 12 q t + 12 q t + 9 q t + 12 q t +
15 6 17 6 17 7 19 7 19 8 21 8 23 9
> 7 q t + 9 q t + 3 q t + 7 q t + q t + 3 q t + q t |