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.
No, but it does contribute: sage: sage: R.<x,y,z> = QQ[] sage: n=30;a = ((x+y+z)^n+1)*((x+y+z)^n+2) sage: time b=maxima(a) CPU times: user 0.02 s, sys: 0.00 s, total: 0.02 s Wall time: 1.86 s sage: time c=b.expand() CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 2.18 s sage: time d=c.factor() CPU times: user 0.00 s, Wall time: 7.33 s > > 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. I'm sure that's one of the reasons that Sage beats all the other systems by a large margin on this input. It isn't one of the official benchmark polynomials. It's one I just made up at random. I feel so illicit :-) > 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. That was in the above timing. I've broken that apart above though: 1.86 to convert a string 2.18 to expand 7.33 to factor Maxima is definitely the fastest on this benchmark. William > > I hope you can straighten this out before you present your results at > your conference. > > RJF > > > > -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
