On Sep 23, 1:31 pm, Jason Grout <[EMAIL PROTECTED]> wrote: > > OK, it is a feature. To quote from > >http://wiki.sagemath.org/sage-3.1.2(Release notes for 3.1.2): > > > The question marks at the end of the numbers in the previous example > > mean that Sage is printing out an approximation of an exact value that > > it uses. In particular, the question mark means that the last digit > > can vary by plus or minus 1. In other words, 32.46424919657298? means > > that the exact number is really between 32.46424919657297 and > > 32.46424919657299. Sage knows what the exact number is and uses the > > exact number in calculations. > > That last sentence is technically incorrect, I think (sorry; I wrote > it). It might be better to say, "Sage carries out the calculations > using interval arithmetic and essentially uses infinite precision in > these cases." > > Carl, is there some way to word things better?
I think the sentence from the release notes is fine. Elements of QQbar are exact algebraic numbers; the fact that QQbar uses interval arithmetic internally is an implementation detail that shouldn't matter to the user. (It would be nice if users of QQbar had no reason to even know about the interval arithmetic used internally. For the sake of efficiency, though, I don't always print the best possible approximation to a number, so the intervals are somewhat exposed to the user when they print QQbar elements.) Carl --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-support@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-support URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
