Vincent Delecroix wrote: > As I already mentioned on tickets, the semantic of equality is a bit > different for intervals and balls. This is annoying since they > basically represent the same objects (=intervals with diadic bounds). > This is my only objection for having it standard right now.
If I understand correctly, you disagree with some of the choices made in the high-level sage bindings for arb, that is, ball fields and their elements. But I'd say this is largely independent of whether arb is a dependency of sage or not. Isn't it? Regarding the technical issue, I am not convinced that intervals and balls should be interchangeable. Sure, they represent similar objects, but it seems to me that their typical use cases are different: basically, intervals represented by their endpoints are more convenient to do bisection, bound the range of a function on a “large” box, or similar things, while balls are better if you want to do arithmetic on real numbers and keep track of roundoff errors (though of course both balls and intervals *can* be used in both cases). To put it another way, I think of (real) intervals as ranges of real numbers, and of balls as specific reals known imprecisely. This makes a difference for instance in code like interval = ... f = x - y f(x=interval, y=interval) If you think of 'interval' as a range, say [0,1], you expect an interval enclosing the range of 'f' over [0,1]². While if you think of it as a single number, say pi ± 1e-10, it is acceptable (and better) to return 0. In the first case, 'interval == interval' should return False unless 'interval' is a point interval; in the second, you can have it return True when 'interval is interval' (but of course 'interval == copy(interval)' should still be False). And so on. The differences between the underlying libraries (arb and mpfi) in this respect are the main reason for the slightly different semantics of equality between Sage real balls and real intervals (as discussed in more detail on the same tickets you mention). I personally find it is useful to have separate parents supporting the “intervals-as-ranges” model and the “intervals-as-points” model. That being say, I too was skeptical about the semantics of ball equality at first, and I wouldn't be opposed to making RBF closer to RIF in this respect. -- Marc -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
