Remarks on Motion 11
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Dear Marco,
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.
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]
with \circ=\times
and compute \times_1^-(B,C,A) = hull({x\in[0,2]\mid\exists b\in[-1,1],
x\times b\in[1,1]})
You should get [1, 2]
Now, compute \times_1^-(B,C) = hull({x\in R\mid\exists b\in[-1,1],
x\times b\in[1,1]})
You should get hull([-\infty,-1]\cup[1,+\infty]), that is [-\infty,
+\infty]
If you intersect the last result with A=[0, 2], you get [0, 2], which is
different from [1, 2].
FG.
- --
Frédéric Goualard LINA - UMR CNRS 6241
Tel.: +33 2 51 12 58 38 Univ. of Nantes - Ecole des Mines de Nantes
Fax.: +33 2 51 12 58 12 2, rue de la Houssinière - BP 92208
http://goualard.frederic.free.fr/ F-44322 NANTES CEDEX 3
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