PD Presentation: |
X66,44,67,43 X21,45,22,44 X22,68,23,67 X45,1,46,68 X46,24,47,23 X1,25,2,24 X2,48,3,47 X25,49,26,48 X26,4,27,3 X49,5,50,4 X50,28,51,27 X5,29,6,28 X6,52,7,51 X29,53,30,52 X30,8,31,7 X53,9,54,8 X54,32,55,31 X9,33,10,32 X10,56,11,55 X33,57,34,56 X34,12,35,11 X57,13,58,12 X58,36,59,35 X13,37,14,36 X14,60,15,59 X37,61,38,60 X38,16,39,15 X61,17,62,16 X62,40,63,39 X17,41,18,40 X18,64,19,63 X41,65,42,64 X42,20,43,19 X65,21,66,20 |
Gauss Code: |
{-6, -7, 9, 10, -12, -13, 15, 16, -18, -19, 21, 22, -24, -25, 27, 28, -30, -31, 33, 34, -2, -3, 5, 6, -8, -9, 11, 12, -14, -15, 17, 18, -20, -21, 23, 24, -26, -27, 29, 30, -32, -33, 1, 2, -4, -5, 7, 8, -10, -11, 13, 14, -16, -17, 19, 20, -22, -23, 25, 26, -28, -29, 31, 32, -34, -1, 3, 4} |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[17, 3]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[17, 3]] |
Out[3]= | 34 |
In[4]:= | PD[TorusKnot[17, 3]] |
Out[4]= | PD[X[66, 44, 67, 43], X[21, 45, 22, 44], X[22, 68, 23, 67], X[45, 1, 46, 68],
> X[46, 24, 47, 23], X[1, 25, 2, 24], X[2, 48, 3, 47], X[25, 49, 26, 48],
> X[26, 4, 27, 3], X[49, 5, 50, 4], X[50, 28, 51, 27], X[5, 29, 6, 28],
> X[6, 52, 7, 51], X[29, 53, 30, 52], X[30, 8, 31, 7], X[53, 9, 54, 8],
> X[54, 32, 55, 31], X[9, 33, 10, 32], X[10, 56, 11, 55], X[33, 57, 34, 56],
> X[34, 12, 35, 11], X[57, 13, 58, 12], X[58, 36, 59, 35], X[13, 37, 14, 36],
> X[14, 60, 15, 59], X[37, 61, 38, 60], X[38, 16, 39, 15], X[61, 17, 62, 16],
> X[62, 40, 63, 39], X[17, 41, 18, 40], X[18, 64, 19, 63], X[41, 65, 42, 64],
> X[42, 20, 43, 19], X[65, 21, 66, 20]] |
In[5]:= | GaussCode[TorusKnot[17, 3]] |
Out[5]= | GaussCode[-6, -7, 9, 10, -12, -13, 15, 16, -18, -19, 21, 22, -24, -25, 27, 28,
> -30, -31, 33, 34, -2, -3, 5, 6, -8, -9, 11, 12, -14, -15, 17, 18, -20, -21,
> 23, 24, -26, -27, 29, 30, -32, -33, 1, 2, -4, -5, 7, 8, -10, -11, 13, 14,
> -16, -17, 19, 20, -22, -23, 25, 26, -28, -29, 31, 32, -34, -1, 3, 4] |
In[6]:= | BR[TorusKnot[17, 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, 1, 2}] |
In[7]:= | alex = Alexander[TorusKnot[17, 3]][t] |
Out[7]= | -16 -15 -13 -12 -10 -9 -7 -6 -4 -3 1
-1 + t - t + t - t + t - t + t - t + t - t + - + t -
t
3 4 6 7 9 10 12 13 15 16
> t + t - t + t - t + t - t + t - t + t |
In[8]:= | Conway[TorusKnot[17, 3]][z] |
Out[8]= | 2 4 6 8 10 12
1 + 96 z + 2280 z + 21204 z + 102752 z + 298870 z + 566618 z +
14 16 18 20 22 24
> 737276 z + 680390 z + 454195 z + 221355 z + 78705 z + 20175 z +
26 28 30 32
> 3628 z + 434 z + 31 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[17, 3]], KnotSignature[TorusKnot[17, 3]]} |
Out[10]= | {1, 24} |
In[11]:= | J=Jones[TorusKnot[17, 3]][q] |
Out[11]= | 16 18 34
q + q - q |
In[12]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[12]= | {} |
In[13]:= | A2Invariant[TorusKnot[17, 3]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[17, 3]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[17, 3]], Vassiliev[3][TorusKnot[17, 3]]} |
Out[15]= | {96, 816} |
In[16]:= | Kh[TorusKnot[17, 3]][q, t] |
Out[16]= | 31 33 35 2 39 3 37 4 39 4 41 5 43 5 41 6
q + q + q t + q t + q t + q t + q t + q t + q t +
45 7 43 8 45 8 47 9 49 9 47 10 51 11 49 12
> q t + q t + q t + q t + q t + q t + q t + q t +
51 12 53 13 55 13 53 14 57 15 55 16 57 16
> q t + q t + q t + q t + q t + q t + q t +
59 17 61 17 59 18 63 19 61 20 63 20 65 21
> q t + q t + q t + q t + q t + q t + q t +
67 21 65 22 69 23
> q t + q t + q t |