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