On Sat, Aug 23, 2008 at 7:09 PM, Nils Bruin <[EMAIL PROTECTED]> wrote: > On Aug 23, 1:27 pm, "William Stein" <[EMAIL PROTECTED]> wrote: > >> Did you read through the article Alfredo Portes posted, which >> also explains some of the gotchas and subtleties of disallowing >> comparisons? I'm curious what you thought of it. > > At the very least, "<" should be transitive wherever it is allowed. > The one example that David Mertz gives in favour of universal ordering > is sorting, which completely hinges on transitivity of "<". As it > stands at the moment with 1 < None < int(0), this is already violated. > That means that any algorithm based on sorting can fail in > unpredictable ways.
[...] Just as another data point, since I happened to see it when reading source code, in the Ginac library (http://www.ginac.de) we find this comment: /** This method establishes a canonical order on all numbers. For complex * numbers this is not possible in a mathematically consistent way but we need * to establish some order and it ought to be fast. So we simply define it * to be compatible with our method csgn. * * @return csgn(*this-other) * @see numeric::csgn() */ I'm not making or suggesting any conclusions -- just adding another data point. William --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
