[Axiom-math] APL, J, and Axiom documentation

[daly]

I have been looking at the question of documenting Axiom's algorithms.

Beyond the english description I've been pondering the use of J (an
ascii version of APL). J/APL, for those who don't know, is an
executable mathematical programming language. Ken Iverson created it
as a language for thought. <http://www.jsoftware.com>

A J description of an algorithm has the appeal that it can be very
precise and compact. It can also be executed to compare the results
with the algorithm. Re-notating the algorithm in J will certain
uncover some existing bugs and/or optimizations in the existing work.

On the down side, J is "its own subculture", meaning that even less
people speak J than speak lisp. In J, the BesselJ function is:

 BesselJ=: 1 : '(i.0) H. (1+m.)@(_0.25&*)@*: * ^&address@hidden: % (!m.)"_'
 
where 
 J0=: 0 BesselJ
 j1=: 1 BesselJ

Has anyone here used the language, besides myself?

Tim