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Re: Remarks on Motion 11



John Pryce wrote:
One remark: I believe that Corollary 1 is false---which should
address the question raised by Nate Hayes' mail. For example, take

A=[0,2]
B=[-1,1]
C=[1,1]

Good point. Thanks for clarifying it. It's the order in which "hull"
and "intersect" are done that makes the difference, I think.

A few comments/observations:

   -- The result [1,2] may be obtained without reverse mode by checking if
zero is an element of B and then processing each side of the branch-cut
separately.

   -- The same is true if A=[-2,2], i.e., if zero is element of B the
intervals

   [-2,-1]=(-oo,-1] \intersect [-2,2] and [1,2]=[1,+oo) \intersect [-2,2]

are obtained without reverse mode operations. In interval Newton, it is
advantageous to process intervals [-2,-1] and [1,2] separately, rather than
their union [-2,2].

Sincerely,

Nate