On Jul 22, 7:20 pm, William Stein <wst...@gmail.com> wrote: > Albrecht<m...@informatik.uni-bremen.de> wrote: > > Not, sure it is enough to add this though. Since it isn't clear what the the > > symbolic ring is exactly, i.e. is it a field, I don't know which definition > > of > > a GB applies. > > I think one should treat it like a field for this purpose. It is of > course not really > a field, since functions have poles, etc.; also, their are floating > point numbers in > SR and floating point numbers don't form a field either. But they are > supposed > to approximately model one. > If I have understood this correctly, and the suggestion is to use Buchberger's algorithm to compute Grobner bases in Sage's symbolic ring, which includes limited precision floating point numbers, then I'd like to point out that Buchberger's algorithm causes many cancellations, e.g. an S-polynomial frequently reduces to zero after a long computation involving large coefficients, which is an unfortunate thing to have happen when using limited precision numbers. I know that there has been research into the use of limited precision floating point numbers in Grobner bases calculations, and as I recall it requires some careful thinking to pull it off.
Cheers Bjarke H. Roune --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
