Henry, I’ve been writing a few documents that will hopefully be useful in the calculus world. There are currently three, all in various stages of completion: “The Derivative Revisited”, “The Derivative Rules” and “The Derivative in Machine Learning”. The idea behind them is to start with Ken Iverson’s 1979 classic paper from the 1979 ACM conference, bring it up to date and use that as a base for finding good matrix algorithms in Machine Learning.
I choose to write my code in APL. Occasionally I have moments when I’m not quite sure what I’m doing. That’s when I need an authoritative reference. And J is that. It’s my bible. Losing D., without a comparable replacement, would be a big loss. For my purposes, I’d settle for just the first derivative. I don’t need the higher derivatives, symbolic differentiation or the inverse. My most frequent resort to J is for a precise interpretation of the rules around rank and the derivative. For example, my current slowdown arises from the question: Given functions f and g of rank s and t, what is the rank of their composition (f g)? Perhaps it would help if you could explain more about “They worked, but they were not complete”. (I’m certainly not arguing for any further expansion of the capability.) Is there some documentation that describes what’s available in the math/calculus addon? Cheers, Mike Powell > On Aug 26, 2019, at 16:04, Henry Rich <[email protected]> wrote: > > J has supported symbolic differentiation and integration for some time. > Starting with Release 9.01, primitive support for calculus is withdrawn. > > The calculus primitives were a proof-of-concept that was an incomplete > success. They worked, but they were not complete, and the nature of > mathematics is such that they will never be complete. It has long been clear > that they should have been implemented in a J script, which would be much > easier to expand & maintain. > > The primitives for Taylor series - t. t: T. - are terminated with extreme > prejudice. > > The primitives for differentiation and integration - d. D. D: - are also > removed, but they are going to a Better Place. A new addon, math/calculus, > is now available. It provides most of the features of the calculus > primitives. Interested users are encouraged to fix & expand this addon to > give support for more methods of integration and differentiation. > > Henry Rich > > --- > This email has been checked for viruses by AVG. > https://www.avg.com > > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
