Re: How to do quickest

*To*: mathgroup at smc.vnet.net*Subject*: [mg123066] Re: How to do quickest*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Tue, 22 Nov 2011 05:35:38 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201111210929.EAA14830@smc.vnet.net>

On 21 Nov 2011, at 10:29, Artur wrote: > Dear Mathematica Gurus, > How to do quickest following procedure (which is very slowly): > > qq = {}; Do[y = Round[Sqrt[x^3]]; > If[(x^3 - y^2) != 0, > kk = m /. Solve[{4 m^2 + 6 m n + n^2 == > x, (19 m^2 + 9 m n + n^2) Sqrt[m^2 + n^2] == y}, {m, n}][[1]]; > ll = CoefficientList[MinimalPolynomial[kk][[1]], #1]; > lll = Length[ll]; > If[lll < 12, Print[{x/(x^3 - y^2)^2, kk, x, y, x^3 - y^2}]; > If[Length[ll] == 3, Print[{kk, x, y}]]]], {x, 2, 1000000}]; > qq > > > (*Best wishes Artur*) > I think it would be better to send not only the code but also the mathematical problem, as there may be a way to do it in a different way. Unless I am misunderstanding something, what you are trying to do is the same as this: In[31]:= Block[{y = Round[Sqrt[x^3]]}, Reap[Table[ If[(x^3 - y^2) != 0 && Not[IrreduciblePolynomialQ[poly]], Sow[{x, y}]], {x, 2, 1000000}]][[2]]] // Timing Out[31]= {721.327,{}} This ought to be a lot faster than your code, but I have not tried to run yours to the end. Also, it is possible that using the Eisenstein Test explicitly may be somewhat faster: Block[{y = Round[Sqrt[x^3]]}, Reap[Table[ If[x^3 - y^2 != 0 && Mod[x^6 - 2*x^3*y^2 + y^4, 4] == 0 && ! IrreduciblePolynomialQ[poly], Sow[{x, y}]], {x, 2, 1000000}]][[2]]] {} but I forgot to use Timing and don't want to wait again, particularly that the answer is the empty set. Andrzej Kozlowski

**References**:**How to do quickest***From:*Artur <grafix@csl.pl>