On Feb 10, 2007, at 8:35 PM, Carl Witty wrote: > > I have a design question about interval arithmetic comparisons.
[...] I don't quite know the answer to these questions, but I reckon one thing: for consistency, you want interval comparison to match up with comparison of reals and comparison of p-adic integers. What I mean is: a real number (i.e. an IEEE double, or an MPFR real, or whatever) is only ever given up to some finite precision, and therefore really it's just an interval. Similarly, a p-adic integer is only given up to congruence mod some power of p, and so also corresponds to an "interval" (really a ball). But p-adics are easier, since two balls overlap if and only if one is contained in the other, which is not at all true for real intervals. In particular the "overlap test" for p- adic balls gives a transitive relation, which seems to be the main ingredient missing in the real interval case. Do you have any other examples of undesirable behaviour apart from the business with the leading term of a polynomial? My feeling is that it's the code in the polynomials that needs to change, rather than anything else. David --~--~---------~--~----~------------~-------~--~----~ 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-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
