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Re: Motion 52: final "Expressions" text for vote



Bill Walster wrote:
> For a system of real, not extended real intervals, the domain
> of div(x,y) and recip(x) can be R^2 and R, respectively.  See
> Table 9.1 on page 21.

???  The inverse of 0 is not defined in the Reals, so the domains
indeed have the holes described in Table 9.1.

This does not in any way constrain flavours from extending those
domains in a flavour-specific manner for *non-common evaluations*.

> The ranges of asin, acos, atan, and atan2 functions are
> unnecessarily narrow.

Do you really want asin(0) to return an enclosure of 200*pi,
at the whim of the implementer?

If you want a function to keep track of the turning number in
an infinite stack of slotted complex planes, define a separate
function for that purpose.  This standard only defines intervals
based on Reals, or possibly extensions thereof that satisfy the
core properties of a flavour.  As far as I can tell this would
include a flavour that allows affine infinities as members of
(non-common) intervals, but that flavour would have to define,
for each operation, how they affect them.  I'm less sure about
systems based on complex disks with a single projective infinity.

As for defining containment sets -- that would be the business of
a containment-set flavour.  A few delicate points had to be settled
with respect to the definition of common evaluation in order not to
rule out a cset flavour -- see example 5 at the end of Clause 7.2,
near the bottom of page 17 in the Nov 15 draft.

Michel.
---Sent: 2013-11-25 01:09:30 UTC