Comments on Motion 27-A "Decorated Intervals"
My comments on Motion 27-A "Decorated Intervals":
Remark 1 "The empty set may get all decorations." is not clear at this
moment. I suppose that the cause is the tracking of the worst possible
decoration (Definition 8).
Concerning Remark 4 "Applying an arithmetic function to an empty
argument produces an empty set: f(∅) = ∅", you can add "even if
f is a constant function".
Definitions 7 and 8: the notation for d_f may not be well chosen,
as d_f does not depend only on f, but also on t_1, ..., t_k.
Definition 8: do we really want to always track the worst possible
decoration? Here, if One is the constant function One(x) = 1, then
One(floor([1,3])) would have decoration def, not saf.
Section 1.3.2, "1/[ε²,1] = ([1,∞], saf)" is incorrect at Level 1.
How is the inclusion defined for the elements of DIR?
According to the examples, the decoration part is ignored (contrary
to Motion 26, which was defining decorations as sets).
About Remark 5 (and the whole motion), what do the decorations really
mean in practice? For instance, consider f(x) = tan(floor(x)*pi+pi/2),
implemented as the composition of the various basic functions, and its
interval extension. At Level 1, it is ndf for X = [1,1.5], but not at
Level 2, where it is con (because of rounding). With X = [1,3], it is
con at both Level 1 and Level 2, though f(x) is nowhere defined. So,
what confidence con brings here?
--
Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/>
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Work: CR INRIA - computer arithmetic / Arénaire project (LIP, ENS-Lyon)