Here is a nice and very simple example of 'under' I don't recall being mentioned in the docs or in the forums.
Place two rectangles one beside the other, stretching them as needed but preserving their aspect ratios, so that the left side of the one coincides with the right side of the other. If the aspect ratios (w:h) of the given rectangles are a and b, that of the resulting rectangle is a +&.% b . The above operation being both commutative and associative, an obvious generalization suggests itself as the verb +/&.:% . (Note that &.: is needed in place of &. .) Notes. 1. It is interesting to observe that the associativity of the arithmetical operation on ratios is not immediately obvious, while for some reason its geometric equivalent seems self-evident. 2. The said operation on rectangles underlies one of the operations on pictures in the so called functional geometry, invented by P.Henderson and implemented in, e.g., the GeomLab programming system. 3. jwiki/Essays/Under has no example of &.: so far, and does not even mention it. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
