Factored Notation for Interval I/O
M. H. van Emden
TL;DR
The article addresses how to represent interval I/O more effectively in interval arithmetic by introducing factored notation, which exposes a shared leading prefix of interval bounds to reveal width at a glance. Grounded in information-theoretic reasoning, it argues for a practical default of two to three digits inside the brackets to balance information content with readability, while allowing more digits if warranted by computation cost. It also covers handling of scientific notation through mantissa normalization and situates the approach within a landscape of related notations, highlighting its advantages for scanning and compactness. The work has practical implications for making interval results more usable in software and human inspection without sacrificing correctness.
Abstract
This note addresses the input and output of intervals in the sense of interval arithmetic and interval constraints. The most obvious, and so far most widely used notation, for intervals has drawbacks that we remedy with a new notation that we propose to call factored notation. It is more compact and allows one to find a good trade-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 the last decimal shown.