Re: Remarks on Motion 11
I agree: For reverse-mode operations to be fully useful, they should include
a comprehensive list of functions encountered commonly in practice, as in
the Vienna proposal.
Also, my view has been that reverse mode operations are different from forward
operations with intersection. In particular, in the case, say, of atan, the actual
inverse is a disconnected set of intervals, but the formal definition gives a
connected subset of [-\pi/2,\pi/2]. In the reverse-mode operation, we take
account of the actual inverse, and make the result finite through the intersection.
Baker
On 1/25/2010 8:48 AM, John Pryce wrote:
Frédéric Goualard, Marco Nehmeier& P1788
On 24 Jan 2010, at 21:00, Frédéric Goualard wrote:
Thank you very much for taking the time to write Motion 11 and submit it
to P1788. I believe that what you call "Reverse Interval Operations" are
very important and should find their place in the upcoming interval
standard.
I have, however, one regret and one remark:
The regret is that your motion only concerns itself with basic
operations, which is not reflected by its title. Why not consider
reverse cosine, reverse sine, ... ? Constraint programming, for example,
cannot make do with reverse multiplication and reverse division only.
Marco, I also am glad you have submitted this motion, but I agree with Frédéric.
Arnold Neumaier in the Vienna document proposes -= if I count correctly - 14 functions/operations
>to be provided in reverse mode. Anyone who agrees with the general concept of "reverse operation"
is probably happy to vote for the whole of Arnold's list (give or take one or two, to be argued case by case).
As a friendly amendment I suggest: include all 14 (or whatever) in your motion, and phrase it on the
lines of Juergen's motion 10.
I feel your document could be clearer on what the motion *is*, i.e. what are we voting for? At present this is hidden within the two Definitions, which say "… should …". State the motion separately, and say "shall", not "should".
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.
Best wishes
John Pryce
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