--- Dan Bron <[EMAIL PROTECTED]> wrote: > I wrote: > > >In the Dictionary, at least, axis is defined early on, if not used much. > > I'm wrong; it is used not-infrequently, and AFAICT at a quick glance, > consistently. "Dimension" > appears to mean the magnitude of an axis. > > In short. Given a the shape of an arbitrary J noun (a rank-1 array of > non-negative integers): > the rank is the length of that shape, an axis is an index into that shape (a > member of i.rank > ), and a dimension is the value at that index.
Dimension is not just value of one axis. It is, informally, a measure in coordinate (sub-)space, and belong to the same domain as shape. It can be defined as (vector of) extents of each axis. Dimension is used where shape is not applicable, i.e. for concepts which are not array objects, such as array segments like tiles (tesselations) in Cut conjunciton--they have dimension. (Whereas "size" and "lengths" are used in the same sense there, dimension has the most precise meaning.) It seems appropriate to say that k-cell has rank k and its dimension is the k trailing axes of the shape. ____________________________________________________________________________________ Now that's room service! Choose from over 150,000 hotels in 45,000 destinations on Yahoo! Travel to find your fit. http://farechase.yahoo.com/promo-generic-14795097 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
