PD Presentation: |
X23,49,24,48 X49,25,50,24 X25,1,26,50 X1,27,2,26 X27,3,28,2 X3,29,4,28 X29,5,30,4 X5,31,6,30 X31,7,32,6 X7,33,8,32 X33,9,34,8 X9,35,10,34 X35,11,36,10 X11,37,12,36 X37,13,38,12 X13,39,14,38 X39,15,40,14 X15,41,16,40 X41,17,42,16 X17,43,18,42 X43,19,44,18 X19,45,20,44 X45,21,46,20 X21,47,22,46 X47,23,48,22 |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[25, 2]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[25, 2]] |
Out[3]= | 25 |
In[4]:= | PD[TorusKnot[25, 2]] |
Out[4]= | PD[X[23, 49, 24, 48], X[49, 25, 50, 24], X[25, 1, 26, 50], X[1, 27, 2, 26],
> X[27, 3, 28, 2], X[3, 29, 4, 28], X[29, 5, 30, 4], X[5, 31, 6, 30],
> X[31, 7, 32, 6], X[7, 33, 8, 32], X[33, 9, 34, 8], X[9, 35, 10, 34],
> X[35, 11, 36, 10], X[11, 37, 12, 36], X[37, 13, 38, 12], X[13, 39, 14, 38],
> X[39, 15, 40, 14], X[15, 41, 16, 40], X[41, 17, 42, 16], X[17, 43, 18, 42],
> X[43, 19, 44, 18], X[19, 45, 20, 44], X[45, 21, 46, 20], X[21, 47, 22, 46],
> X[47, 23, 48, 22]] |
In[5]:= | GaussCode[TorusKnot[25, 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, -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, 1, -2, 3] |
In[6]:= | BR[TorusKnot[25, 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}] |
In[7]:= | alex = Alexander[TorusKnot[25, 2]][t] |
Out[7]= | -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 1
1 + t - t + t - t + t - t + t - t + t - t + t - - -
t
2 3 4 5 6 7 8 9 10 11 12
> t + t - t + t - t + t - t + t - t + t - t + t |
In[8]:= | Conway[TorusKnot[25, 2]][z] |
Out[8]= | 2 4 6 8 10 12 14
1 + 78 z + 1001 z + 5005 z + 12870 z + 19448 z + 18564 z + 11628 z +
16 18 20 22 24
> 4845 z + 1330 z + 231 z + 23 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[25, 2]], KnotSignature[TorusKnot[25, 2]]} |
Out[10]= | {25, 24} |
In[11]:= | J=Jones[TorusKnot[25, 2]][q] |
Out[11]= | 12 14 15 16 17 18 19 20 21 22 23 24 25
q + q - q + q - q + q - q + q - q + q - q + q - q +
26 27 28 29 30 31 32 33 34 35 36 37
> q - 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[25, 2]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[25, 2]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[25, 2]], Vassiliev[3][TorusKnot[25, 2]]} |
Out[15]= | {78, 650} |
In[16]:= | Kh[TorusKnot[25, 2]][q, t] |
Out[16]= | 23 25 27 2 31 3 31 4 35 5 35 6 39 7 39 8
q + q + q t + q t + q t + q t + q t + q t + q t +
43 9 43 10 47 11 47 12 51 13 51 14 55 15
> q t + q t + q t + q t + q t + q t + q t +
55 16 59 17 59 18 63 19 63 20 67 21 67 22
> q t + q t + q t + q t + q t + q t + q t +
71 23 71 24 75 25
> q t + q t + q t |