William Stein wrote:
> I wonder why they switched from that faster algorithm to a slower one? > Maybe it produced incorrect results (possibly due to rounding errors)? I doubt they did. On their website there is no mention in their changelogs of any change in the algorithm for multiplication of polynomials over Z. They do however mention that they now incorporate the MPFR library. I suspect this was done between v12 and v13. To change from one to the other, it is only necessary to add a couple of #includes to the files. They probably realised that GMP doesn't necessarily give accurate results, and changing to MPRF probably guaranteed that for them, at the expense of a factor of 2. This is good evidence that my theory about them using FFT over the reals is correct. I'll dig up the relevant paper where this method is described and see if it looks tenable. I looked through the internet archive to see if MAGMA had any mention of the algorithm used or something like that on their site in the past, but haven't been able to find anything. Bill. --~--~---------~--~----~------------~-------~--~----~ 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/ -~----------~----~----~----~------~----~------~--~---
