RE: dependent and independent intervals, proposal to toss out text2interval. Was re: about emp (was: Motion 42:no)
Openness to possible future developments is definitely a good idea, it was always something we strived for.
Minor word of caution: while arithmetic of rational numbers is easily decidable, once we start adding constants like pi etc. (especially with special functions like exp and sin added) we run into situations where there is no known algorithm for deciding equality, or where algorithms are known but are unrealistically long. For example, as we mention in Chapter 4 of our 1997 book on computational complexity of interval computations, even algorithmic decidability of exp-polynomials (i.e., functions obtained by compositions of exp and polynomials) is based on an unproven hypothesis, and if we add sin to the mix, we get problems which are either undecidable or require exponential time in some cases.
So, while in some cases, explicitly adding pi will enables us to get exact ranges, in general, we will still need enclosures :-(
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From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Vincent Lefevre
Moreover an arithmetic where 0.1 + pi is exactly representable might be used, e.g. something based on Q[pi] or simpler. This could be useful when trig functions are used. In such an arithmetic, sqrt(cos([0,pi/2])) could be evaluated without the drawback of some values being undefined.
Perhaps such an arithmetic hasn't been implemented yet, but the standard (that will be there for many years in the future) should encourage new arithmetics rather than forbidding them.
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Vincent Lefèvre <vincent@xxxxxxxxxx> - Web: <http://www.vinc17.net/> 100% accessible validated (X)HTML - Blog: <http://www.vinc17.net/blog/>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)