PD Presentation: |
X53,65,54,64 X42,66,43,65 X31,67,32,66 X20,68,21,67 X9,69,10,68 X43,55,44,54 X32,56,33,55 X21,57,22,56 X10,58,11,57 X69,59,70,58 X33,45,34,44 X22,46,23,45 X11,47,12,46 X70,48,1,47 X59,49,60,48 X23,35,24,34 X12,36,13,35 X1,37,2,36 X60,38,61,37 X49,39,50,38 X13,25,14,24 X2,26,3,25 X61,27,62,26 X50,28,51,27 X39,29,40,28 X3,15,4,14 X62,16,63,15 X51,17,52,16 X40,18,41,17 X29,19,30,18 X63,5,64,4 X52,6,53,5 X41,7,42,6 X30,8,31,7 X19,9,20,8 |
Gauss Code: |
{-18, -22, -26, 31, 32, 33, 34, 35, -5, -9, -13, -17, -21, 26, 27, 28, 29, 30, -35, -4, -8, -12, -16, 21, 22, 23, 24, 25, -30, -34, -3, -7, -11, 16, 17, 18, 19, 20, -25, -29, -33, -2, -6, 11, 12, 13, 14, 15, -20, -24, -28, -32, -1, 6, 7, 8, 9, 10, -15, -19, -23, -27, -31, 1, 2, 3, 4, 5, -10, -14} |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[7, 6]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[7, 6]] |
Out[3]= | 35 |
In[4]:= | PD[TorusKnot[7, 6]] |
Out[4]= | PD[X[53, 65, 54, 64], X[42, 66, 43, 65], X[31, 67, 32, 66], X[20, 68, 21, 67],
> X[9, 69, 10, 68], X[43, 55, 44, 54], X[32, 56, 33, 55], X[21, 57, 22, 56],
> X[10, 58, 11, 57], X[69, 59, 70, 58], X[33, 45, 34, 44], X[22, 46, 23, 45],
> X[11, 47, 12, 46], X[70, 48, 1, 47], X[59, 49, 60, 48], X[23, 35, 24, 34],
> X[12, 36, 13, 35], X[1, 37, 2, 36], X[60, 38, 61, 37], X[49, 39, 50, 38],
> X[13, 25, 14, 24], X[2, 26, 3, 25], X[61, 27, 62, 26], X[50, 28, 51, 27],
> X[39, 29, 40, 28], X[3, 15, 4, 14], X[62, 16, 63, 15], X[51, 17, 52, 16],
> X[40, 18, 41, 17], X[29, 19, 30, 18], X[63, 5, 64, 4], X[52, 6, 53, 5],
> X[41, 7, 42, 6], X[30, 8, 31, 7], X[19, 9, 20, 8]] |
In[5]:= | GaussCode[TorusKnot[7, 6]] |
Out[5]= | GaussCode[-18, -22, -26, 31, 32, 33, 34, 35, -5, -9, -13, -17, -21, 26, 27, 28,
> 29, 30, -35, -4, -8, -12, -16, 21, 22, 23, 24, 25, -30, -34, -3, -7, -11,
> 16, 17, 18, 19, 20, -25, -29, -33, -2, -6, 11, 12, 13, 14, 15, -20, -24,
> -28, -32, -1, 6, 7, 8, 9, 10, -15, -19, -23, -27, -31, 1, 2, 3, 4, 5, -10,
> -14] |
In[6]:= | BR[TorusKnot[7, 6]] |
Out[6]= | BR[6, {1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4,
> 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5}] |
In[7]:= | alex = Alexander[TorusKnot[7, 6]][t] |
Out[7]= | -15 -14 -9 -7 -3 3 7 9 14 15
-1 + t - t + t - t + t + t - t + t - t + t |
In[8]:= | Conway[TorusKnot[7, 6]][z] |
Out[8]= | 2 4 6 8 10 12
1 + 70 z + 1365 z + 11649 z + 52844 z + 142208 z + 244074 z +
14 16 18 20 22 24
> 281144 z + 224826 z + 127282 z + 51359 z + 14674 z + 2900 z +
26 28 30
> 377 z + 29 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[7, 6]], KnotSignature[TorusKnot[7, 6]]} |
Out[10]= | {7, 18} |
In[11]:= | J=Jones[TorusKnot[7, 6]][q] |
Out[11]= | 15 17 19 21 22 24 26
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[7, 6]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[7, 6]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[7, 6]], Vassiliev[3][TorusKnot[7, 6]]} |
Out[15]= | {70, 490} |
In[16]:= | Kh[TorusKnot[7, 6]][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 39 8 41 8 43 9 45 9
> q t + q t + q t + q t + 2 q t + q t + 2 q t +
41 10 43 10 45 11 47 11 45 12 47 12 51 12
> q t + 2 q t + q t + 3 q t + 2 q t + q t + q t +
49 13 51 13 47 14 49 14 53 14 51 15 53 15
> 3 q t + q t + q t + q t + q t + 2 q t + 2 q t +
49 16 51 16 55 16 57 16 53 17 55 17 53 18
> q t + q t + q t + q t + q t + q t + q t +
57 19
> q t |