AbstractThis note addresses the input and output of intervals in the sense of intervalarithmetic and interval constraints. The most obvious, and so far most widely usednotation, for intervals has drawbacks that we remedy with a new notation that wepropose to call factored notation. It is more compact and allows one to ﬁnd a goodtrade-oﬀ between interval width and ease of reading. We describe how such a trade-oﬀ can be based on the information yield (in the sense of information theory) of thelast decimal shown. 1 Introduction Once upon a time, it was a matter of professional ethics among computers never to writea meaningless decimal. Since then computers have become machines and thereby lost anyform of ethics, professional or otherwise. The human computers of yore were helped intheir ethical behaviour by the fact that it took eﬀort to write spurious decimals. Now thesituation is reversed: the lazy way is to use the default precision of the I O library function.As a result it is common to see ﬁfteen decimals, all but three of which are meaningless.Of course interval arithmetic is not guilty of such negligence. After all, the very raisond’ˆetre of the subject is to be explicit about the precision of computed results. Yet, eveninterval arithmetic is plagued by phoney decimals, albeit in a more subtle way. Just as con-ventional computation often needs more care in the presentation of computational results,the most obvious interval notation with default precision needs improvement.As a bounded interval has two bounds, say, l and u, the most straightforward notationis something like [l,u]. Written like this, it may not be immediately obvious what is wrongwith writing it that way. But when confronted with a real-life consequence
Part 1 Introduction: nonlinear programming local methods global methods Numerica outline. Part 2 A tour of Numerica: getting started generic constraints constants ranges input parameters aggregation operators functions sets unconstrained optimization constrained optimization local constraint solving local unconstrained optimization soft constraints real constraints and uncertain data display accuracy. Part 3 The meaning of Numerica: interval analysis constraint solving unconstrained optimization interpretation of the results. Part 4 Modelling in Numerica: what can go wrong in Numerica improving Numerica statements. Part 5 The syntax of Numerica: overall structure expressions the constant section the input section the set section the variable section the function section the body section the display section the pragma section scoping rules. Part 6 The semantics of Numerica: interval arithmetic semantics of constraint solving semantics of unconstrained minimization semantics of constrained minimization non-canonical boxes. Part 7 An implementation of Numerica: overview of the algorithm domain-specific and monotonic interval extensions constraint solving unconstrained optimization constrained optimization advanced techniques an implementation of box consistency. Part 8 Experimental results: constraint solving unconstrained optimization constrained optimization appendices.