PD Presentation: |
X3,41,4,40 X22,42,23,41 X23,5,24,4 X42,6,43,5 X43,25,44,24 X6,26,7,25 X7,45,8,44 X26,46,27,45 X27,9,28,8 X46,10,47,9 X47,29,48,28 X10,30,11,29 X11,49,12,48 X30,50,31,49 X31,13,32,12 X50,14,51,13 X51,33,52,32 X14,34,15,33 X15,53,16,52 X34,54,35,53 X35,17,36,16 X54,18,55,17 X55,37,56,36 X18,38,19,37 X19,1,20,56 X38,2,39,1 X39,21,40,20 X2,22,3,21 |
Gauss Code: |
{26, -28, -1, 3, 4, -6, -7, 9, 10, -12, -13, 15, 16, -18, -19, 21, 22, -24, -25, 27, 28, -2, -3, 5, 6, -8, -9, 11, 12, -14, -15, 17, 18, -20, -21, 23, 24, -26, -27, 1, 2, -4, -5, 7, 8, -10, -11, 13, 14, -16, -17, 19, 20, -22, -23, 25} |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[14, 3]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[14, 3]] |
Out[3]= | 28 |
In[4]:= | PD[TorusKnot[14, 3]] |
Out[4]= | PD[X[3, 41, 4, 40], X[22, 42, 23, 41], X[23, 5, 24, 4], X[42, 6, 43, 5],
> X[43, 25, 44, 24], X[6, 26, 7, 25], X[7, 45, 8, 44], X[26, 46, 27, 45],
> X[27, 9, 28, 8], X[46, 10, 47, 9], X[47, 29, 48, 28], X[10, 30, 11, 29],
> X[11, 49, 12, 48], X[30, 50, 31, 49], X[31, 13, 32, 12], X[50, 14, 51, 13],
> X[51, 33, 52, 32], X[14, 34, 15, 33], X[15, 53, 16, 52], X[34, 54, 35, 53],
> X[35, 17, 36, 16], X[54, 18, 55, 17], X[55, 37, 56, 36], X[18, 38, 19, 37],
> X[19, 1, 20, 56], X[38, 2, 39, 1], X[39, 21, 40, 20], X[2, 22, 3, 21]] |
In[5]:= | GaussCode[TorusKnot[14, 3]] |
Out[5]= | GaussCode[26, -28, -1, 3, 4, -6, -7, 9, 10, -12, -13, 15, 16, -18, -19, 21, 22,
> -24, -25, 27, 28, -2, -3, 5, 6, -8, -9, 11, 12, -14, -15, 17, 18, -20, -21,
> 23, 24, -26, -27, 1, 2, -4, -5, 7, 8, -10, -11, 13, 14, -16, -17, 19, 20,
> -22, -23, 25] |
In[6]:= | BR[TorusKnot[14, 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}] |
In[7]:= | alex = Alexander[TorusKnot[14, 3]][t] |
Out[7]= | -13 -12 -10 -9 -7 -6 -4 -3 1 3 4 6
-1 + t - t + t - t + t - t + t - t + - + t - t + t - t +
t
7 9 10 12 13
> t - t + t - t + t |
In[8]:= | Conway[TorusKnot[14, 3]][z] |
Out[8]= | 2 4 6 8 10 12 14
1 + 65 z + 1040 z + 6448 z + 20540 z + 38532 z + 45942 z + 36366 z +
16 18 20 22 24 26
> 19532 z + 7144 z + 1751 z + 275 z + 25 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[14, 3]], KnotSignature[TorusKnot[14, 3]]} |
Out[10]= | {3, 18} |
In[11]:= | J=Jones[TorusKnot[14, 3]][q] |
Out[11]= | 13 15 28
q + q - q |
In[12]:= | Select[AllKnots[], (J === Jones[#][q] || (J /. q-> 1/q) === Jones[#][q])&] |
Out[12]= | {} |
In[13]:= | A2Invariant[TorusKnot[14, 3]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[14, 3]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[14, 3]], Vassiliev[3][TorusKnot[14, 3]]} |
Out[15]= | {65, 455} |
In[16]:= | Kh[TorusKnot[14, 3]][q, t] |
Out[16]= | 25 27 29 2 33 3 31 4 33 4 35 5 37 5 35 6
q + q + q t + q t + q t + q t + q t + q t + q t +
39 7 37 8 39 8 41 9 43 9 41 10 45 11 43 12
> q t + q t + q t + q t + q t + q t + q t + q t +
45 12 47 13 49 13 47 14 51 15 49 16 51 16
> q t + q t + q t + q t + q t + q t + q t +
53 17 55 17 53 18 57 19
> q t + q t + q t + q t |