[Axiom-math] Re: [Axiom-developer] APL, J, and Axiom documentation

[M. Edward (Ed) Borasky]

address@hidden wrote:
> 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
>
>
>
>
>
>
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Actually, I think the "open-source" dialect of APL is called "A-Plus",
not J. I don't think there's an open-source J implementation.

I've never used any APL -- it was always on my list of things to do but
I never had an opportunity to get paid for it, so other things got
learned. :)