PD Presentation: |
X19,49,20,48 X49,21,50,20 X21,51,22,50 X51,23,52,22 X23,53,24,52 X53,25,54,24 X25,55,26,54 X55,27,56,26 X27,57,28,56 X57,29,58,28 X29,1,30,58 X1,31,2,30 X31,3,32,2 X3,33,4,32 X33,5,34,4 X5,35,6,34 X35,7,36,6 X7,37,8,36 X37,9,38,8 X9,39,10,38 X39,11,40,10 X11,41,12,40 X41,13,42,12 X13,43,14,42 X43,15,44,14 X15,45,16,44 X45,17,46,16 X17,47,18,46 X47,19,48,18 |
Gauss Code: |
{-12, 13, -14, 15, -16, 17, -18, 19, -20, 21, -22, 23, -24, 25, -26, 27, -28, 29, -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, 1, -2, 3, -4, 5, -6, 7, -8, 9, -10, 11} |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[29, 2]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[29, 2]] |
Out[3]= | 29 |
In[4]:= | PD[TorusKnot[29, 2]] |
Out[4]= | PD[X[19, 49, 20, 48], X[49, 21, 50, 20], X[21, 51, 22, 50], X[51, 23, 52, 22],
> X[23, 53, 24, 52], X[53, 25, 54, 24], X[25, 55, 26, 54], X[55, 27, 56, 26],
> X[27, 57, 28, 56], X[57, 29, 58, 28], X[29, 1, 30, 58], X[1, 31, 2, 30],
> X[31, 3, 32, 2], X[3, 33, 4, 32], X[33, 5, 34, 4], X[5, 35, 6, 34],
> X[35, 7, 36, 6], X[7, 37, 8, 36], X[37, 9, 38, 8], X[9, 39, 10, 38],
> X[39, 11, 40, 10], X[11, 41, 12, 40], X[41, 13, 42, 12], X[13, 43, 14, 42],
> X[43, 15, 44, 14], X[15, 45, 16, 44], X[45, 17, 46, 16], X[17, 47, 18, 46],
> X[47, 19, 48, 18]] |
In[5]:= | GaussCode[TorusKnot[29, 2]] |
Out[5]= | GaussCode[-12, 13, -14, 15, -16, 17, -18, 19, -20, 21, -22, 23, -24, 25, -26,
> 27, -28, 29, -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, 1, -2, 3, -4, 5,
> -6, 7, -8, 9, -10, 11] |
In[6]:= | BR[TorusKnot[29, 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}] |
In[7]:= | alex = Alexander[TorusKnot[29, 2]][t] |
Out[7]= | -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4
1 + t - t + t - t + t - t + t - t + t - t + t -
-3 -2 1 2 3 4 5 6 7 8 9 10 11
> t + t - - - t + t - t + t - t + t - t + t - t + t - t +
t
12 13 14
> t - t + t |
In[8]:= | Conway[TorusKnot[29, 2]][z] |
Out[8]= | 2 4 6 8 10 12
1 + 105 z + 1820 z + 12376 z + 43758 z + 92378 z + 125970 z +
14 16 18 20 22 24
> 116280 z + 74613 z + 33649 z + 10626 z + 2300 z + 325 z +
26 28
> 27 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[29, 2]], KnotSignature[TorusKnot[29, 2]]} |
Out[10]= | {29, 28} |
In[11]:= | J=Jones[TorusKnot[29, 2]][q] |
Out[11]= | 14 16 17 18 19 20 21 22 23 24 25 26 27
q + q - q + q - q + q - q + q - q + q - q + q - q +
28 29 30 31 32 33 34 35 36 37 38 39
> q - q + q - q + q - q + q - q + q - q + q - q +
40 41 42 43
> q - q + q - q |
In[12]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[12]= | {} |
In[13]:= | A2Invariant[TorusKnot[29, 2]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[29, 2]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[29, 2]], Vassiliev[3][TorusKnot[29, 2]]} |
Out[15]= | {105, 1015} |
In[16]:= | Kh[TorusKnot[29, 2]][q, t] |
Out[16]= | 27 29 31 2 35 3 35 4 39 5 39 6 43 7 43 8
q + q + q t + q t + q t + q t + q t + q t + q t +
47 9 47 10 51 11 51 12 55 13 55 14 59 15
> q t + q t + q t + q t + q t + q t + q t +
59 16 63 17 63 18 67 19 67 20 71 21 71 22
> q t + q t + q t + q t + q t + q t + q t +
75 23 75 24 79 25 79 26 83 27 83 28 87 29
> q t + q t + q t + q t + q t + q t + q t |