D: is used in the inverse of factorial.
!^:_1 ]0.001 |NaN error | (-(!-y"_)%0.001&*!"0 D:1])^:_<.&170^:(-:+)^.y On Mon, Aug 26, 2019, 7:46 PM Mike Powell <[email protected]> wrote: > 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 Starting with Release 9.01, primitive support for calculus is withdrawn.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 > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
