PD Presentation: |
X25,3,26,2 X48,4,49,3 X15,5,16,4 X38,6,39,5 X49,27,50,26 X16,28,17,27 X39,29,40,28 X6,30,7,29 X17,51,18,50 X40,52,41,51 X7,53,8,52 X30,54,31,53 X41,19,42,18 X8,20,9,19 X31,21,32,20 X54,22,55,21 X9,43,10,42 X32,44,33,43 X55,45,56,44 X22,46,23,45 X33,11,34,10 X56,12,1,11 X23,13,24,12 X46,14,47,13 X1,35,2,34 X24,36,25,35 X47,37,48,36 X14,38,15,37 |
Gauss Code: |
{-25, 1, 2, 3, 4, -8, -11, -14, -17, 21, 22, 23, 24, -28, -3, -6, -9, 13, 14, 15, 16, -20, -23, -26, -1, 5, 6, 7, 8, -12, -15, -18, -21, 25, 26, 27, 28, -4, -7, -10, -13, 17, 18, 19, 20, -24, -27, -2, -5, 9, 10, 11, 12, -16, -19, -22} |
In[1]:= |
<< KnotTheory` |
Loading KnotTheory` (version of August 30, 2005, 10:15:35)... |
In[2]:= | TubePlot[TorusKnot[7, 5]] |
|  |
Out[2]= | -Graphics- |
In[3]:= | Crossings[TorusKnot[7, 5]] |
Out[3]= | 28 |
In[4]:= | PD[TorusKnot[7, 5]] |
Out[4]= | PD[X[25, 3, 26, 2], X[48, 4, 49, 3], X[15, 5, 16, 4], X[38, 6, 39, 5],
> X[49, 27, 50, 26], X[16, 28, 17, 27], X[39, 29, 40, 28], X[6, 30, 7, 29],
> X[17, 51, 18, 50], X[40, 52, 41, 51], X[7, 53, 8, 52], X[30, 54, 31, 53],
> X[41, 19, 42, 18], X[8, 20, 9, 19], X[31, 21, 32, 20], X[54, 22, 55, 21],
> X[9, 43, 10, 42], X[32, 44, 33, 43], X[55, 45, 56, 44], X[22, 46, 23, 45],
> X[33, 11, 34, 10], X[56, 12, 1, 11], X[23, 13, 24, 12], X[46, 14, 47, 13],
> X[1, 35, 2, 34], X[24, 36, 25, 35], X[47, 37, 48, 36], X[14, 38, 15, 37]] |
In[5]:= | GaussCode[TorusKnot[7, 5]] |
Out[5]= | GaussCode[-25, 1, 2, 3, 4, -8, -11, -14, -17, 21, 22, 23, 24, -28, -3, -6, -9,
> 13, 14, 15, 16, -20, -23, -26, -1, 5, 6, 7, 8, -12, -15, -18, -21, 25, 26,
> 27, 28, -4, -7, -10, -13, 17, 18, 19, 20, -24, -27, -2, -5, 9, 10, 11, 12,
> -16, -19, -22] |
In[6]:= | BR[TorusKnot[7, 5]] |
Out[6]= | BR[5, {1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4, 1, 2, 3, 4,
> 1, 2, 3, 4}] |
In[7]:= | alex = Alexander[TorusKnot[7, 5]][t] |
Out[7]= | -12 -11 -7 -6 -5 -4 -2 1 2 4 5 6
1 + t - t + t - t + t - t + t - - - t + t - t + t - t +
t
7 11 12
> t - t + t |
In[8]:= | Conway[TorusKnot[7, 5]][z] |
Out[8]= | 2 4 6 8 10 12 14
1 + 48 z + 628 z + 3498 z + 10032 z + 16511 z + 16757 z + 10949 z +
16 18 20 22 24
> 4692 z + 1311 z + 230 z + 23 z + z |
In[9]:= | Select[AllKnots[], (alex === Alexander[#][t])&] |
Out[9]= | {} |
In[10]:= | {KnotDet[TorusKnot[7, 5]], KnotSignature[TorusKnot[7, 5]]} |
Out[10]= | {1, 16} |
In[11]:= | J=Jones[TorusKnot[7, 5]][q] |
Out[11]= | 12 14 16 20 22
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, 5]][q] |
Out[13]= | NotAvailable |
In[14]:= | Kauffman[TorusKnot[7, 5]][a, z] |
Out[14]= | NotAvailable |
In[15]:= | {Vassiliev[2][TorusKnot[7, 5]], Vassiliev[3][TorusKnot[7, 5]]} |
Out[15]= | {48, 280} |
In[16]:= | Kh[TorusKnot[7, 5]][q, t] |
Out[16]= | 23 25 27 2 31 3 29 4 31 4 33 5 35 5 31 6
q + q + q t + q t + q t + q t + q t + q t + q t +
33 6 35 7 37 7 33 8 35 8 37 9 39 9
> q t + q t + q t + q t + 2 q t + q t + 2 q t +
37 10 41 11 39 12 41 12 45 12 43 13
> 2 q t + 3 q t + q t + 2 q t + q t + 2 q t +
45 13 43 14 47 14 47 15 47 16 51 16 51 17
> 2 q t + q t + q t + 2 q t + q t + q t + q t |