Thanks for providing the link. The property that I had missed was "fractionality:" that (1 < (|@- <.)) . This would ensure that while doing the Euclidian algorithm, the magnitudes of numbers always decrease. However, this is not a necessary condition for the Euclidian algorithm to work. Another sufficient condition is that (((a|b)|a) <&| a) for all a and b. It seems that this is true for the floor function |&.+. , although I haven't been able to prove it yet.
Also note that J's builtin GCD does not use floor: it uses the nearest integer. It seems that the complex remainder function was made the way it was to facilitate complex GCD, but we can just as easily make it use a nearest integer function derived from complex floor instead. Marshall On Thu, Jan 26, 2012 at 2:07 AM, Roger Hui <rogerhui.can...@gmail.com>wrote: > Eugene McDonnell's 1973 paper *Complex Floor* is now available at > http://www.jsoftware.com/papers/eem/complexfloor.htm . > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
