[PURRS-devel] filib-CoStLy

[Tatiana Zolo]

Dear Sirs,
we understand your problem to preserve the Brouwer Fixed Point Theorem
but we want explain to you our requirements.
Our aim is to use your libraries about real and complex intervals
also for our needs. Our applications are based on idea of sound
approximation.
Suppose we have two partially known real values a and b and
we want to approximate their ratio. If a is approximated by the
intervals I(a)
and b by the interval I(b), we want to approximate the ratio
I(a)/I(b). The semantic of ratio's operation in which we are interested
is:

         if b is not zero then a/b is approximated by I(a)/I(b)

(we specify that into our applications the condition 'if b is not zero'
it is always guaranteed by others tools).
If we have understood correctly the ratio's operation among intervals
defined
in your libraries, it throws an exception when I(b) contains zero.

Emphasizing the fact that we would not like to develop another library
for the
manipulation of real and complex intervals, we would like to know how we
can
obtain what we are interested in from the behavior given by filib and
CoStLy.

In the case of the ratio, that is one of the simpler cases, we could
split
the interval I(b) in two parts:
      [inf I(b), 0) and (0, sup I(b)],
but this would be possible only if filib and CoStLy support both closed
and
open intervals: this seems not to be possible with your libraries.

We would like your advice: how would you suggest to achieve our goal?
Do you think that we could easily obtain what we need from filib and
CoStLy,
or do you suggest to use another library? We are novices to the field of

intervals and we need your expert opinion.

Thank you very much in advance,

    Roberto Bagnara
    Alessandro Zaccagnini
    Tatiana Zolo