On Tue, Aug 18, 2009 at 5:48 PM, William Stein<wst...@gmail.com> wrote: > > On Tue, Aug 18, 2009 at 5:08 PM, Ondrej Certik<ond...@certik.cz> wrote: >> >> On Tue, Aug 18, 2009 at 4:56 PM, rjf<fate...@gmail.com> wrote: >>> >>> >>> At the risk of providing some information about what is probably going >>> on, >>> let me suggest the following. >>> >>> 1. The expand() command in Maxima is almost always the wrong thing to >>> do if the argument is a polynomial. >>> ratexpand() or ratsimp() or rat() will be much faster. I suspect >>> that in your timings of Maxima, the major >>> contributor may be expand. >>> >>> 2. This is not a good test of polynomial factoring, because it does >>> uses only a trivial part of the algorithm, >>> and that is the square-free factoring part, that consists of computing >>> P' a derivative of P and a gcd(P,P'). >>> >>> Mostly you are testing the gcd program, but only the case of the gcd >>> program for gcd(a,b) where, almost all >>> the time, a divides b. So you are not even testing the gcd program, >>> you are testing polynomial division with remainder. >>> >>> Now if that is what you want to test, fine. If you want to test >>> polynomial factoring, there is a substantial >>> literature on how to choose polynomials that are difficult to factor. >>> Especially large degree is not really necessary. >>> >>> While it is only a speculation on my part, I think what you may also >>> be timing is the conversion of >>> relatively large character strings, at least in some cases. >>> >>> I hope you can straighten this out before you present your results at >>> your conference. >> >> Thanks for joining the discussion. My presentation is on Thursday, so >> I'll try to send my slides to sage+sympy lists tomorrow, so that you >> can look at it and see if I say something that is unfair to Maxima, or >> any other program. >> >> Does anyone know some real life applications of factor(<some >> polynomial>)? E.g. simplifications, like canceling common factors from >> nominator/denominator, but is there anything else? >> >> I would like to use some real life application as a benchmark, I just >> don't know any. > > The following is basically a reinterpretation of factoring in one > context, but it is easy to understand. If you want to plot a plane > algebraic curve F(X,Y) = 0, then if you factor F(X,Y) first as say g * > h, then the plot of F=0 is the *union* of the plots of g=0 and h=0. > This is because the zeros of F are the union of the zeros of g and h. > This extends to arbitrarily many factors. So one application of > factoring is to plotting algebraic curves. There is a similar > statement in dimension 3.
Ah, very cool. I apologize for a really naive question --- do you have some more complex algebraic curve, that you used in some publication/book or something? Let's use that as a benchmark. Ondrej --~--~---------~--~----~------------~-------~--~----~ To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
