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From: Guillaume Melquiond (gmelquio_at_[hidden])
Date: 2002-09-03 07:02:53

On Tue, 3 Sep 2002, David Bergman wrote:

> And do not be too strict on the strictness property ;-) Of course the
> relation <m, where a <m b iff |a| < |b| is an ordering on the complex
> numbers; it is obviously antisymmetric.
> Whether the "every day use" of the word "comparing" is intended to
> denote the strict order or the preorder is up to debate. Do not get
> hooked up on that; I can use exact terminology if you want, but would
> then assume the same stringence from you, which would clutter the dialog
> with unecessary formal adornments. So, please let us keep this dialog on
> a higher level than that.

I just wanted to make it clear since these definitions don't seem to ring
the same bells depending on the country. For example, my definition of
antisymmetric is: xRy and yRx => x=y (where R is a binary relation, x and
y are elements). But let's forget these details.

> IMEHO, there are potential arithmetic interval applications dealing with
> dates; even if dates are (usually) represented as numbers does not mean
> they are numbers, i.e., one does not want all the "numerical" operations
> on them. But, we still might want to do (some) arithmetics (thus falling
> in the "Arithmetic Interval") on them. There would probably not be a
> definition of sinus on david::date (or guillaume::date)...

My point was: the only arithmetic operations that I can imagine on dates
are the operation of an additive group, and it is probably not necessary
to use rounding mode properties to guarantee the inclusion property of
interval arithmetic. It's why I said this library (designed for scientific
computations) was way too complex for that.

> One question, is your arithmetic interval library intended to be used
> for anything else but "float" or "double"? If not, I think it could be
> made into such an abstraction, without changing the "arithmetic"
> property too much.

No, it is not only intended to be used with float and double. I personnaly
use it with fixed-point integers and I know people interested by using it
with multi-precision floating-point numbers and rational numbers.

> I hope you did not get offended by me seeing more applications of this
> library than pure double or float. I got a bit excited by a real (pun
> intended) interval library, and my mind flied away on applications where
> intervals, and certain arithmetic operations on them, could be useful.

I understand what you mean. And I sometimes need to use a library able to
manipulate ordered pairs of numbers. But it was not the original purpose
of this library. I worked on this library because I needed it to prove
some inequations systems had no solution, and I couldn't afford the loss
of precision on the primitive floating-point types.



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