PD Presentation: |
X41,63,42,62 X20,64,21,63 X21,43,22,42 X64,44,1,43 X1,23,2,22 X44,24,45,23 X45,3,46,2 X24,4,25,3 X25,47,26,46 X4,48,5,47 X5,27,6,26 X48,28,49,27 X49,7,50,6 X28,8,29,7 X29,51,30,50 X8,52,9,51 X9,31,10,30 X52,32,53,31 X53,11,54,10 X32,12,33,11 X33,55,34,54 X12,56,13,55 X13,35,14,34 X56,36,57,35 X57,15,58,14 X36,16,37,15 X37,59,38,58 X16,60,17,59 X17,39,18,38 X60,40,61,39 X61,19,62,18 X40,20,41,19 |
Gauss Code: |
{-5, 7, 8, -10, -11, 13, 14, -16, -17, 19, 20, -22, -23, 25, 26, -28, -29, 31, 32, -2, -3, 5, 6, -8, -9, 11, 12, -14, -15, 17, 18, -20, -21, 23, 24, -26, -27, 29, 30, -32, -1, 3, 4, -6, -7, 9, 10, -12, -13, 15, 16, -18, -19, 21, 22, -24, -25, 27, 28, -30, -31, 1, 2, -4} |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[16, 3]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[16, 3]] |
Out[3]= | 32 |
In[4]:= | PD[TorusKnot[16, 3]] |
Out[4]= | PD[X[41, 63, 42, 62], X[20, 64, 21, 63], X[21, 43, 22, 42], X[64, 44, 1, 43],
> X[1, 23, 2, 22], X[44, 24, 45, 23], X[45, 3, 46, 2], X[24, 4, 25, 3],
> X[25, 47, 26, 46], X[4, 48, 5, 47], X[5, 27, 6, 26], X[48, 28, 49, 27],
> X[49, 7, 50, 6], X[28, 8, 29, 7], X[29, 51, 30, 50], X[8, 52, 9, 51],
> X[9, 31, 10, 30], X[52, 32, 53, 31], X[53, 11, 54, 10], X[32, 12, 33, 11],
> X[33, 55, 34, 54], X[12, 56, 13, 55], X[13, 35, 14, 34], X[56, 36, 57, 35],
> X[57, 15, 58, 14], X[36, 16, 37, 15], X[37, 59, 38, 58], X[16, 60, 17, 59],
> X[17, 39, 18, 38], X[60, 40, 61, 39], X[61, 19, 62, 18], X[40, 20, 41, 19]] |
In[5]:= | GaussCode[TorusKnot[16, 3]] |
Out[5]= | GaussCode[-5, 7, 8, -10, -11, 13, 14, -16, -17, 19, 20, -22, -23, 25, 26, -28,
> -29, 31, 32, -2, -3, 5, 6, -8, -9, 11, 12, -14, -15, 17, 18, -20, -21, 23,
> 24, -26, -27, 29, 30, -32, -1, 3, 4, -6, -7, 9, 10, -12, -13, 15, 16, -18,
> -19, 21, 22, -24, -25, 27, 28, -30, -31, 1, 2, -4] |
In[6]:= | BR[TorusKnot[16, 3]] |
Out[6]= | BR[3, {1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2,
> 1, 2, 1, 2, 1, 2, 1, 2}] |
In[7]:= | alex = Alexander[TorusKnot[16, 3]][t] |
Out[7]= | -15 -14 -12 -11 -9 -8 -6 -5 -3 -2 2 3
1 + t - t + t - t + t - t + t - t + t - t - t + t -
5 6 8 9 11 12 14 15
> t + t - t + t - t + t - t + t |
In[8]:= | Conway[TorusKnot[16, 3]][z] |
Out[8]= | 2 4 6 8 10 12
1 + 85 z + 1785 z + 14637 z + 62305 z + 158389 z + 260729 z +
14 16 18 20 22 24
> 292077 z + 229517 z + 128593 z + 51589 z + 14697 z + 2901 z +
26 28 30
> 377 z + 29 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[16, 3]], KnotSignature[TorusKnot[16, 3]]} |
Out[10]= | {3, 22} |
In[11]:= | J=Jones[TorusKnot[16, 3]][q] |
Out[11]= | 15 17 32
q + q - q |
In[12]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[12]= | {} |
In[13]:= | A2Invariant[TorusKnot[16, 3]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[16, 3]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[16, 3]], Vassiliev[3][TorusKnot[16, 3]]} |
Out[15]= | {85, 680} |
In[16]:= | Kh[TorusKnot[16, 3]][q, t] |
Out[16]= | 29 31 33 2 37 3 35 4 37 4 39 5 41 5 39 6
q + q + q t + q t + q t + q t + q t + q t + q t +
43 7 41 8 43 8 45 9 47 9 45 10 49 11 47 12
> q t + q t + q t + q t + q t + q t + q t + q t +
49 12 51 13 53 13 51 14 55 15 53 16 55 16
> q t + q t + q t + q t + q t + q t + q t +
57 17 59 17 57 18 61 19 59 20 61 20 63 21
> q t + q t + q t + q t + q t + q t + q t +
65 21
> q t |