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Hi On 24 May 2009, at 07:17, Jean-Pierre Merlet wrote:
Vincent Lefevre wrote:The empty set is returned for a/b only when b = [0,0], in which case there are no solutions.Hum...Imagine that at some point of the solving process the user get the equation u*b(x,y)=a(x,y) that he want to solve in u. The user (or a symbolic software) may write u=a/b. It may happen that for some values of x,y we have b=0 and therefore according to the proposed rule the user will get the empty set for u, believing that there is no solution, while he should be notified that (all u, b=0, a=0) is also a solution, up to him to determine if such solution is possible (by checking that a=b=0 is possible) and has any interest...
People - or automatic systems - that reason incorrectly will get wrong answers. Nothing we can do will stop this.
It is precisely because of such cases, that Arnold Neumaier introduced the distinction between forward and reverse mode operations.
See Vienna proposal 3.9, also the excellent outline in Arnold's email to ieee-interval@xxxxxxxxxxxxxxxxxxxxx dated 3 June 2008, entitled "interval extensions of partial operations".
John Pryce