On Mon, 3 Sep 2007, John Voight wrote: > Unfortunately, even after the week's optimizations, my number field > enumeration algorithm runs (on meccah) almost 20 times slower on SAGE > than on Magma (181s vs. 9s)--and with identical verbose output. I > just don't see how there can be that much of a difference! But then > again, this was even after I implemented a rather silly shortcut in > Cython to evaluate a polynomial, treated as an array to avoid coercion > overhead which runs almost 3 times as fast as commands like > numpy.poly1d(cfs)(x), and a Newton method which also in many cases > beat the root finding in numpy--but only because of overhead costs. > Note that these trial runs use very little of the number field > machinery: the bottleneck is still real arithmetic and whatever other > overhead is sneaking in... Very frustrating!
Polynomial evaluation, through the perspective of a CAS, is very interesting to me. I did a fair amount of work on the algorithmic side of it, but I haven't had time to finish the job on the implementation side. Using the coersion model, it should be possible to *vastly* reduce the overhead in evaluating most polynomials. Hopefully, I'll be able to get to this sometime in the next month. If anybody else wants to make it happen sooner, I'd love to share my ideas. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
