PD Presentation: |
X9,33,10,32 X33,11,34,10 X11,35,12,34 X35,13,36,12 X13,37,14,36 X37,15,38,14 X15,39,16,38 X39,17,40,16 X17,41,18,40 X41,19,42,18 X19,43,20,42 X43,21,44,20 X21,45,22,44 X45,23,46,22 X23,1,24,46 X1,25,2,24 X25,3,26,2 X3,27,4,26 X27,5,28,4 X5,29,6,28 X29,7,30,6 X7,31,8,30 X31,9,32,8 |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[23, 2]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[23, 2]] |
Out[3]= | 23 |
In[4]:= | PD[TorusKnot[23, 2]] |
Out[4]= | PD[X[9, 33, 10, 32], X[33, 11, 34, 10], X[11, 35, 12, 34], X[35, 13, 36, 12],
> X[13, 37, 14, 36], X[37, 15, 38, 14], X[15, 39, 16, 38], X[39, 17, 40, 16],
> X[17, 41, 18, 40], X[41, 19, 42, 18], X[19, 43, 20, 42], X[43, 21, 44, 20],
> X[21, 45, 22, 44], X[45, 23, 46, 22], X[23, 1, 24, 46], X[1, 25, 2, 24],
> X[25, 3, 26, 2], X[3, 27, 4, 26], X[27, 5, 28, 4], X[5, 29, 6, 28],
> X[29, 7, 30, 6], X[7, 31, 8, 30], X[31, 9, 32, 8]] |
In[5]:= | GaussCode[TorusKnot[23, 2]] |
Out[5]= | GaussCode[-16, 17, -18, 19, -20, 21, -22, 23, -1, 2, -3, 4, -5, 6, -7, 8, -9,
> 10, -11, 12, -13, 14, -15, 16, -17, 18, -19, 20, -21, 22, -23, 1, -2, 3,
> -4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15] |
In[6]:= | BR[TorusKnot[23, 2]] |
Out[6]= | BR[2, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}] |
In[7]:= | alex = Alexander[TorusKnot[23, 2]][t] |
Out[7]= | -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 1 2
-1 + t - t + t - t + t - t + t - t + t - t + - + t - t +
t
3 4 5 6 7 8 9 10 11
> t - t + t - t + t - t + t - t + t |
In[8]:= | Conway[TorusKnot[23, 2]][z] |
Out[8]= | 2 4 6 8 10 12 14
1 + 66 z + 715 z + 3003 z + 6435 z + 8008 z + 6188 z + 3060 z +
16 18 20 22
> 969 z + 190 z + 21 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[23, 2]], KnotSignature[TorusKnot[23, 2]]} |
Out[10]= | {23, 22} |
In[11]:= | J=Jones[TorusKnot[23, 2]][q] |
Out[11]= | 11 13 14 15 16 17 18 19 20 21 22 23 24
q + q - q + q - q + q - q + q - q + q - q + q - q +
25 26 27 28 29 30 31 32 33 34
> q - q + q - q + q - q + q - q + q - q |
In[12]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[12]= | {} |
In[13]:= | A2Invariant[TorusKnot[23, 2]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[23, 2]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[23, 2]], Vassiliev[3][TorusKnot[23, 2]]} |
Out[15]= | {66, 506} |
In[16]:= | Kh[TorusKnot[23, 2]][q, t] |
Out[16]= | 21 23 25 2 29 3 29 4 33 5 33 6 37 7 37 8
q + q + q t + q t + q t + q t + q t + q t + q t +
41 9 41 10 45 11 45 12 49 13 49 14 53 15
> q t + q t + q t + q t + q t + q t + q t +
53 16 57 17 57 18 61 19 61 20 65 21 65 22
> q t + q t + q t + q t + q t + q t + q t +
69 23
> q t |