Hi Joel, Well done on annihilating singular on the horror example you had. I've sat down to read the code a few times, but it is slow going for me, as I don't speak python well yet. But I'll make a few comments when I do get some spare moments to finish reading your code. That'll probably be tomorrow at this point.
Over the summer I hope to have a student work on univariate factoring over Z/pZ to which multivariate factoring reduces. Hopefully by then I'll have more to say about the multivariate factoring in that case. Do you think you'll work on that in the near future? I'm still convinced that the specialisation technique works just as well there too. I'm quite sure it works for the example on the trac ticket anyway. First remove the content xz. Then specialise at y=1, z=1 and factor the univariate polynomial over GF5. Then lift that to a factorisation of (from memory) the polynomial specialised at z=1. Finally lift to a factorisation of the full polynomial. Does that sound sensible to you? In general one specialises at random points in GF5 and looks for information about the structure of any factors. In the example on the trac ticket it all works out pretty easy. There is also this paper which the Magma group says contains the algorithm they use (modulo a few improvements): BM97 Laurent Bernardin and Michael B. Monagan. Efficient Multivariate Factorization Over Finite Fields. In Proceedings of AAECC, volume 1255 of LNCS, pages 15--28. Springer-Verlag, 1997. I admit I haven't had time to actually read it. Bill. On 16 Feb, 20:52, "Joel B. Mohler" <[EMAIL PROTECTED]> wrote: > Hi, > > I've finally got around to polishing off the implementation I made over > Christmas of multi-variate factoring over ZZ. For small cases singular > (working over QQ) beats it by a large factor, but for some larger cases they > become much more comparable. My favorite horrific example (in which I > annihilate singular) is referenced in the ticket > athttp://trac.sagemath.org/sage_trac/ticket/2179 > > It's not immediately evident to me if the ideas in the patch are applicable > tohttp://trac.sagemath.org/sage_trac/ticket/2152 > However, I thought I would bring it to the attention of the mailing list if it > could be helpful there. It does seem more likely that a proper fix for 2152 > would provide a better implementation for my algorithm given the CRT. > > -- > Joel --~--~---------~--~----~------------~-------~--~----~ 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://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
