PD Presentation: |
X3,53,4,52 X20,54,21,53 X37,55,38,54 X21,5,22,4 X38,6,39,5 X55,7,56,6 X39,23,40,22 X56,24,57,23 X7,25,8,24 X57,41,58,40 X8,42,9,41 X25,43,26,42 X9,59,10,58 X26,60,27,59 X43,61,44,60 X27,11,28,10 X44,12,45,11 X61,13,62,12 X45,29,46,28 X62,30,63,29 X13,31,14,30 X63,47,64,46 X14,48,15,47 X31,49,32,48 X15,65,16,64 X32,66,33,65 X49,1,50,66 X33,17,34,16 X50,18,51,17 X1,19,2,18 X51,35,52,34 X2,36,3,35 X19,37,20,36 |
Gauss Code: |
{-30, -32, -1, 4, 5, 6, -9, -11, -13, 16, 17, 18, -21, -23, -25, 28, 29, 30, -33, -2, -4, 7, 8, 9, -12, -14, -16, 19, 20, 21, -24, -26, -28, 31, 32, 33, -3, -5, -7, 10, 11, 12, -15, -17, -19, 22, 23, 24, -27, -29, -31, 1, 2, 3, -6, -8, -10, 13, 14, 15, -18, -20, -22, 25, 26, 27} |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[11, 4]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[11, 4]] |
Out[3]= | 33 |
In[4]:= | PD[TorusKnot[11, 4]] |
Out[4]= | PD[X[3, 53, 4, 52], X[20, 54, 21, 53], X[37, 55, 38, 54], X[21, 5, 22, 4],
> X[38, 6, 39, 5], X[55, 7, 56, 6], X[39, 23, 40, 22], X[56, 24, 57, 23],
> X[7, 25, 8, 24], X[57, 41, 58, 40], X[8, 42, 9, 41], X[25, 43, 26, 42],
> X[9, 59, 10, 58], X[26, 60, 27, 59], X[43, 61, 44, 60], X[27, 11, 28, 10],
> X[44, 12, 45, 11], X[61, 13, 62, 12], X[45, 29, 46, 28], X[62, 30, 63, 29],
> X[13, 31, 14, 30], X[63, 47, 64, 46], X[14, 48, 15, 47], X[31, 49, 32, 48],
> X[15, 65, 16, 64], X[32, 66, 33, 65], X[49, 1, 50, 66], X[33, 17, 34, 16],
> X[50, 18, 51, 17], X[1, 19, 2, 18], X[51, 35, 52, 34], X[2, 36, 3, 35],
> X[19, 37, 20, 36]] |
In[5]:= | GaussCode[TorusKnot[11, 4]] |
Out[5]= | GaussCode[-30, -32, -1, 4, 5, 6, -9, -11, -13, 16, 17, 18, -21, -23, -25, 28,
> 29, 30, -33, -2, -4, 7, 8, 9, -12, -14, -16, 19, 20, 21, -24, -26, -28, 31,
> 32, 33, -3, -5, -7, 10, 11, 12, -15, -17, -19, 22, 23, 24, -27, -29, -31,
> 1, 2, 3, -6, -8, -10, 13, 14, 15, -18, -20, -22, 25, 26, 27] |
In[6]:= | BR[TorusKnot[11, 4]] |
Out[6]= | BR[4, {1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3,
> 1, 2, 3, 1, 2, 3, 1, 2, 3}] |
In[7]:= | alex = Alexander[TorusKnot[11, 4]][t] |
Out[7]= | -15 -14 -11 -10 -7 -6 -4 -2 2 4 6 7
1 + t - t + t - t + t - t + t - t - t + t - t + t -
10 11 14 15
> t + t - t + t |
In[8]:= | Conway[TorusKnot[11, 4]][z] |
Out[8]= | 2 4 6 8 10 12
1 + 75 z + 1510 z + 12825 z + 56577 z + 148070 z + 249288 z +
14 16 18 20 22 24
> 283951 z + 225760 z + 127470 z + 51380 z + 14675 z + 2900 z +
26 28 30
> 377 z + 29 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[11, 4]], KnotSignature[TorusKnot[11, 4]]} |
Out[10]= | {11, 22} |
In[11]:= | J=Jones[TorusKnot[11, 4]][q] |
Out[11]= | 15 17 19 20 21 22 23 24 25 26 28
q + 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[11, 4]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[11, 4]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[11, 4]], Vassiliev[3][TorusKnot[11, 4]]} |
Out[15]= | {75, 550} |
In[16]:= | Kh[TorusKnot[11, 4]][q, t] |
Out[16]= | 29 31 33 2 37 3 35 4 37 4 39 5 41 5 37 6
q + q + q t + q t + q t + q t + q t + q t + q t +
39 6 41 7 43 7 41 8 45 9 43 10 45 10
> q t + q t + q t + 2 q t + 2 q t + q t + q t +
47 11 49 11 45 12 47 12 51 12 49 13 51 13
> 2 q t + q t + q t + 2 q t + q t + q t + 2 q t +
49 14 53 15 51 16 53 16 57 16 55 17
> 2 q t + 3 q t + q t + 2 q t + q t + 2 q t +
57 17 55 18 59 18 59 19 59 20 63 20 63 21
> 2 q t + q t + q t + 2 q t + q t + q t + q t |