I like 3. It probably makes the most sense because its the behavior is simplest to define/remember, and (in)equality is by far the most important anyway.
On Jul 16, 2:44 am, Carl Witty <[EMAIL PROTECTED]> wrote: > On Jul 13, 1:57 pm, saucerful <[EMAIL PROTECTED]> wrote: > > > I see. Yes I agree it should be false. Consider: > > > CIF(RIF(0)) != CIF(RIF(-1, 1)) > > True > > > RIF(0, 0) != RIF(-1, 1) > > False > > > That these two comparisons should be different makes no sense, does > > it? > > Yes, there's probably a bug here, and it's all my fault :) > > But I'm not sure exactly where the bug is. > > For real intervals A and B, and comparison operators ==,!=,<,etc., we > define > A OP B iff (for all real numbers a in A, b in B, a OP b). > > This has several good properties (and several bad properties as well); > in particular, "A == 1" does what I consider the right thing, and all > of the comparison operators are useful. > > But this definition is less useful for complex intervals, since > complex numbers don't have a useful ordering. In Sage, we do define > less-than for complex numbers (it's the lexicographic ordering), but > that doesn't give a useful meaning for A<B for complex intervals. > > Since I couldn't think of a mathematically useful definition for A<B, > I decided to go for a definition that would be useful in CS terms: > """ Intervals are compared lexicographically on the 4-tuple > (x.real().lower(), x.real().upper(), x.imag().lower(), > x.imag().upper()) > """ > At least this is a total ordering, so complex intervals could be > sorted; and it does the right thing for equality. I guess I just > didn't think about the fact that it does the wrong thing for > inequality. > > So I see a few options here: > 1) do nothing > 2) change the definition of inequality on CIF to match RIF, but leave > the ordering operations as lexicographic > 3) change the definition of all comparison operators on CIF to match > RIF (giving us probably-useless ordering operations, but at least the > formal definition would be consistent with RIF) > 4) change RIF somehow > > Any votes, or suggestions for other options? > > > Also why is it that CIF(0) seems to not have an interval, while CIF(1) > > does? > > It's just a printing issue, inherited from CC. > > Carl --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
