On Sep 25, 11:24 am, Bill Hart <[EMAIL PROTECTED]> wrote: > Actually, to make it work, it might have to switch between polar > coordinates and rectangular coordinates, always ensuring the point you > are talking about is inside the region, regardless of whether it is a > polar rectangle or a right rectangle. > > Clearly I don't know anything about complex interval arithmetic if > such a thing exists. Is there a reference I can read. Shame you aren't > going to be at SAGE days 5 Carl. Are you going to number 6. > > Bill.
I know very little about complex interval arithmetic myself...just what I learned from Googling for "complex interval arithmetic" and spending a couple of hours skimming papers I found on the Web. Some implementations use "intervals" represented as circles in the complex plane; others use right rectangles. I don't remember any that use polar rectangles, but they might exist. In any case, if you want the tightest possible bounds, there's some fairly tricky math. Fortunately, for implementing Qbar, I'm pretty sure we wouldn't need an implementation of complex interval arithmetic that was carefully optimized to get the tightest possible bounds. I believe (although I haven't gone through the math to check) that the "extra looseness" of the simple algorithms is mostly a problem if the original bounds were loose relative to the number. However, if Qbar were implemented similarly to my algebraic reals package, we start with very tight bounds, and the result of a precision error is to make the bounds much much tighter. So I think the simplest possible implementation (a complex interval is a pair of real intervals, and arithmetic operations are implemented textbook fashion using these real intervals) would probably suffice. No, I'm not planning to go to SD6. (After all, computer algebra is only a hobby for me!) 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://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~----------~----~----~----~------~----~------~--~---
