Technical Correspondence

Transcribed from the printed issue; not yet reviewed. Read it in the PDF of the issue, page 116

Re: E.E. McDonnell’s article “At Play with J: The Magical Matrix” in Vector Volume 20, Number 2, October 2003.

In the article, Mr. McDonnell insinuated that my use of the “magical matrix” and indexing to generate permutations is due that I “wrote it all”. That statement is far from the truth! Revisionist history, even!

The “magical matrix”, computed as:

   \:"1 = i. 4
0 1 2 3
1 0 2 3
2 0 1 3
3 0 1 2

(grade-down each row of the identity matrix) first saw the light of day in the APL87 conference proceedings, in the paper “Some Uses of { and }”, section 4.3, computed as:

k ~{rank}1 0 k{is}{iota}{omega}

The paper also presented functions for generating combinations, compositions, and self-upgrading and self-downgrading permutations, using a similar technique of growing a table from a seed through indexing.

I should point out that in 1987 J was not yet even a gleam in Ken Iverson’s eyes. Therefore, I deny the allegation, and I defy the allegator!

Roger Hui (with tongue firmly in cheek)