Thanks for the links to those postings by Roger and Marshall, Elijah. During the episode Marshall does refer to Einstein Summation Notation as a system that names the axes. https://en.wikipedia.org/wiki/Einstein_notation
The other multidimensional primitives that I can think of are Shift and Rotate, which can act on axes specified by their left argument, similar to transpose. Cheers, bob > On May 29, 2022, at 22:31, Elijah Stone <elro...@elronnd.net> wrote: > > I only skimmed the transcript. I have two things to add: > > 1. Two postings by Marshall and Roger: > http://www.jsoftware.com/pipermail/programming/2020-February/054999.html > http://www.jsoftware.com/pipermail/programming/2020-February/055012.html > > 2. Rank is not, on the whole and for the most part, really about > multidimensional data. Roger's posting betrays this. Rank is about > projecting a 2- or 3-dimensional structure onto multidimensional arrays. The > existence of multidimensional arrays enables multiple such projections; the > partitions of the shape, given only rank, or the partitions of the > permutations of the shape (minus some duplicates), given both rank and > transpose. Transpose _is_ really multidimensional; a rare property among > primitives. > > On Sun, 29 May 2022, 'robert therriault' via Programming wrote: > >> A bit late this week because I was travelling, but here is the most recent >> ArrayCast episode on Rank and Leading Axis theory. >> https://www.arraycast.com/episodes/episode28-rank-and-leading-axis >> >> Cheers, bob >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
