On Thu, 08 Feb 2007 00:23:16 -0700, didier deshommes <[EMAIL PROTECTED]> wrote:
> > On 2/8/07, William Stein <[EMAIL PROTECTED]> wrote: >> Didier, >> >> Would RealLib, which still hasn't fully made its way into SAGE, be very >> relevant >> to this question? Can it somehow decide equality of some class of real >> numbers >> defined via an algorithm (e.g., sqrt(2) + 1 - 1 is defined by an >> algorithm...)? >> Anyway, if RealLib is relevant, could you say something about that? > > Unfortunately, no. Reallib has strict comparisons, but equality tests > will loop indefinitely. From the documentation: > > "The equality test is undecidable, i.e. no function can exist that can > always give a positive > answer when two numbers are equal and not complete or give a negative > answer if they are > not. The system does not provide this test, nor the non-strict > inequalities which, without > the possibility to recognize equality, coincide with their strict > counterparts." Thanks. Incidentally, at some point in the not-to-distant future, sqrt will be replaced by a symbolic version, so sqrt(2) will be symbolic. Then sqrt(2) + 1 - 1 == sqrt(2) will be true (and the equality will be tested using either Maxima or Giac). William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to [email protected] 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://sage.math.washington.edu/sage/ and http://sage.scipy.org/sage/ -~----------~----~----~----~------~----~------~--~---
