PD Presentation: |
X31,65,32,64 X65,33,66,32 X33,1,34,66 X1,35,2,34 X35,3,36,2 X3,37,4,36 X37,5,38,4 X5,39,6,38 X39,7,40,6 X7,41,8,40 X41,9,42,8 X9,43,10,42 X43,11,44,10 X11,45,12,44 X45,13,46,12 X13,47,14,46 X47,15,48,14 X15,49,16,48 X49,17,50,16 X17,51,18,50 X51,19,52,18 X19,53,20,52 X53,21,54,20 X21,55,22,54 X55,23,56,22 X23,57,24,56 X57,25,58,24 X25,59,26,58 X59,27,60,26 X27,61,28,60 X61,29,62,28 X29,63,30,62 X63,31,64,30 |
Gauss Code: |
{-4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20, 21, -22, 23, -24, 25, -26, 27, -28, 29, -30, 31, -32, 33, -1, 2, -3, 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, 18, -19, 20, -21, 22, -23, 24, -25, 26, -27, 28, -29, 30, -31, 32, -33, 1, -2, 3} |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[33, 2]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[33, 2]] |
Out[3]= | 33 |
In[4]:= | PD[TorusKnot[33, 2]] |
Out[4]= | PD[X[31, 65, 32, 64], X[65, 33, 66, 32], X[33, 1, 34, 66], X[1, 35, 2, 34],
> X[35, 3, 36, 2], X[3, 37, 4, 36], X[37, 5, 38, 4], X[5, 39, 6, 38],
> X[39, 7, 40, 6], X[7, 41, 8, 40], X[41, 9, 42, 8], X[9, 43, 10, 42],
> X[43, 11, 44, 10], X[11, 45, 12, 44], X[45, 13, 46, 12], X[13, 47, 14, 46],
> X[47, 15, 48, 14], X[15, 49, 16, 48], X[49, 17, 50, 16], X[17, 51, 18, 50],
> X[51, 19, 52, 18], X[19, 53, 20, 52], X[53, 21, 54, 20], X[21, 55, 22, 54],
> X[55, 23, 56, 22], X[23, 57, 24, 56], X[57, 25, 58, 24], X[25, 59, 26, 58],
> X[59, 27, 60, 26], X[27, 61, 28, 60], X[61, 29, 62, 28], X[29, 63, 30, 62],
> X[63, 31, 64, 30]] |
In[5]:= | GaussCode[TorusKnot[33, 2]] |
Out[5]= | GaussCode[-4, 5, -6, 7, -8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19,
> -20, 21, -22, 23, -24, 25, -26, 27, -28, 29, -30, 31, -32, 33, -1, 2, -3,
> 4, -5, 6, -7, 8, -9, 10, -11, 12, -13, 14, -15, 16, -17, 18, -19, 20, -21,
> 22, -23, 24, -25, 26, -27, 28, -29, 30, -31, 32, -33, 1, -2, 3] |
In[6]:= | BR[TorusKnot[33, 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, 1,
> 1, 1, 1, 1, 1, 1, 1, 1, 1}] |
In[7]:= | alex = Alexander[TorusKnot[33, 2]][t] |
Out[7]= | -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6
1 + t - t + t - t + t - t + t - t + t - t + t -
-5 -4 -3 -2 1 2 3 4 5 6 7 8 9
> t + t - t + t - - - t + t - t + t - t + t - t + t - t +
t
10 11 12 13 14 15 16
> t - t + t - t + t - t + t |
In[8]:= | Conway[TorusKnot[33, 2]][z] |
Out[8]= | 2 4 6 8 10 12
1 + 136 z + 3060 z + 27132 z + 125970 z + 352716 z + 646646 z +
14 16 18 20 22 24
> 817190 z + 735471 z + 480700 z + 230230 z + 80730 z + 20475 z +
26 28 30 32
> 3654 z + 435 z + 31 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[33, 2]], KnotSignature[TorusKnot[33, 2]]} |
Out[10]= | {33, 32} |
In[11]:= | J=Jones[TorusKnot[33, 2]][q] |
Out[11]= | 16 18 19 20 21 22 23 24 25 26 27 28 29
q + q - q + q - q + q - q + q - q + q - q + q - q +
30 31 32 33 34 35 36 37 38 39 40 41
> q - q + q - q + q - q + q - q + q - q + q - q +
42 43 44 45 46 47 48 49
> 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[33, 2]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[33, 2]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[33, 2]], Vassiliev[3][TorusKnot[33, 2]]} |
Out[15]= | {136, 1496} |
In[16]:= | Kh[TorusKnot[33, 2]][q, t] |
Out[16]= | 31 33 35 2 39 3 39 4 43 5 43 6 47 7 47 8
q + q + q t + q t + q t + q t + q t + q t + q t +
51 9 51 10 55 11 55 12 59 13 59 14 63 15
> q t + q t + q t + q t + q t + q t + q t +
63 16 67 17 67 18 71 19 71 20 75 21 75 22
> q t + q t + q t + q t + q t + q t + q t +
79 23 79 24 83 25 83 26 87 27 87 28 91 29
> q t + q t + q t + q t + q t + q t + q t +
91 30 95 31 95 32 99 33
> q t + q t + q t + q t |