PD Presentation: |
X29,65,30,64 X65,31,66,30 X31,67,32,66 X67,33,68,32 X33,69,34,68 X69,35,70,34 X35,1,36,70 X1,37,2,36 X37,3,38,2 X3,39,4,38 X39,5,40,4 X5,41,6,40 X41,7,42,6 X7,43,8,42 X43,9,44,8 X9,45,10,44 X45,11,46,10 X11,47,12,46 X47,13,48,12 X13,49,14,48 X49,15,50,14 X15,51,16,50 X51,17,52,16 X17,53,18,52 X53,19,54,18 X19,55,20,54 X55,21,56,20 X21,57,22,56 X57,23,58,22 X23,59,24,58 X59,25,60,24 X25,61,26,60 X61,27,62,26 X27,63,28,62 X63,29,64,28 |
Gauss Code: |
{-8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20, 21, -22, 23, -24, 25, -26, 27, -28, 29, -30, 31, -32, 33, -34, 35, -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, 30, -31, 32, -33, 34, -35, 1, -2, 3, -4, 5, -6, 7} |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[35, 2]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[35, 2]] |
Out[3]= | 35 |
In[4]:= | PD[TorusKnot[35, 2]] |
Out[4]= | PD[X[29, 65, 30, 64], X[65, 31, 66, 30], X[31, 67, 32, 66], X[67, 33, 68, 32],
> X[33, 69, 34, 68], X[69, 35, 70, 34], X[35, 1, 36, 70], X[1, 37, 2, 36],
> X[37, 3, 38, 2], X[3, 39, 4, 38], X[39, 5, 40, 4], X[5, 41, 6, 40],
> X[41, 7, 42, 6], X[7, 43, 8, 42], X[43, 9, 44, 8], X[9, 45, 10, 44],
> X[45, 11, 46, 10], X[11, 47, 12, 46], X[47, 13, 48, 12], X[13, 49, 14, 48],
> X[49, 15, 50, 14], X[15, 51, 16, 50], X[51, 17, 52, 16], X[17, 53, 18, 52],
> X[53, 19, 54, 18], X[19, 55, 20, 54], X[55, 21, 56, 20], X[21, 57, 22, 56],
> X[57, 23, 58, 22], X[23, 59, 24, 58], X[59, 25, 60, 24], X[25, 61, 26, 60],
> X[61, 27, 62, 26], X[27, 63, 28, 62], X[63, 29, 64, 28]] |
In[5]:= | GaussCode[TorusKnot[35, 2]] |
Out[5]= | GaussCode[-8, 9, -10, 11, -12, 13, -14, 15, -16, 17, -18, 19, -20, 21, -22, 23,
> -24, 25, -26, 27, -28, 29, -30, 31, -32, 33, -34, 35, -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, 30, -31, 32, -33, 34, -35, 1, -2, 3, -4, 5, -6,
> 7] |
In[6]:= | BR[TorusKnot[35, 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, 1, 1, 1, 1, 1, 1}] |
In[7]:= | alex = Alexander[TorusKnot[35, 2]][t] |
Out[7]= | -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7
-1 + t - t + t - t + t - t + t - t + t - t + t -
-6 -5 -4 -3 -2 1 2 3 4 5 6 7 8
> t + t - t + t - t + - + t - t + t - t + t - t + t - t +
t
9 10 11 12 13 14 15 16 17
> t - t + t - t + t - t + t - t + t |
In[8]:= | Conway[TorusKnot[35, 2]][z] |
Out[8]= | 2 4 6 8 10 12
1 + 153 z + 3876 z + 38760 z + 203490 z + 646646 z + 1352078 z +
14 16 18 20 22
> 1961256 z + 2042975 z + 1562275 z + 888030 z + 376740 z +
24 26 28 30 32 34
> 118755 z + 27405 z + 4495 z + 496 z + 33 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[35, 2]], KnotSignature[TorusKnot[35, 2]]} |
Out[10]= | {35, 34} |
In[11]:= | J=Jones[TorusKnot[35, 2]][q] |
Out[11]= | 17 19 20 21 22 23 24 25 26 27 28 29 30
q + q - q + q - q + q - q + q - q + q - q + q - q +
31 32 33 34 35 36 37 38 39 40 41 42
> q - q + q - q + q - q + q - q + q - q + q - q +
43 44 45 46 47 48 49 50 51 52
> 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[35, 2]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[35, 2]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[35, 2]], Vassiliev[3][TorusKnot[35, 2]]} |
Out[15]= | {153, 1785} |
In[16]:= | Kh[TorusKnot[35, 2]][q, t] |
Out[16]= | 33 35 37 2 41 3 41 4 45 5 45 6 49 7 49 8
q + q + q t + q t + q t + q t + q t + q t + q t +
53 9 53 10 57 11 57 12 61 13 61 14 65 15
> q t + q t + q t + q t + q t + q t + q t +
65 16 69 17 69 18 73 19 73 20 77 21 77 22
> q t + q t + q t + q t + q t + q t + q t +
81 23 81 24 85 25 85 26 89 27 89 28 93 29
> q t + q t + q t + q t + q t + q t + q t +
93 30 97 31 97 32 101 33 101 34 105 35
> q t + q t + q t + q t + q t + q t |