The J is a little out of my league, but for non-integers, youcould use Binomial Theorem, as I said.(http://en.wikipedia.org/wiki/Binomial_series) e.g. e^pi = (1+(e-1))^pi = 1+ pi*e + pi*(pi - 1)*e*e/2! +... There's no exponentiation and you can calculate to arbitrary precision.
> Date: Tue, 5 Aug 2014 05:33:42 -0700 > From: [email protected] > To: [email protected] > Subject: Re: [Jprogramming] Power for the powerless > > "A really simple approach would be " > > for integer powers, > > pow =: [: */ #~ > > > > > ----- Original Message ----- > From: Raul Miller <[email protected]> > To: Programming forum <[email protected]> > Cc: > Sent: Tuesday, August 5, 2014 2:36:53 AM > Subject: Re: [Jprogramming] Power for the powerless > > A really simple approach would be to use T. > > pow=: ^ T. 99 > That gives you a polynomial expression > > > Here's a shorter version: > > ^ T. 4 > > 1 1 0.5 0.16666666666666666&p. > > Here's the more accurate version: > > (^ -: pow) 10 11 12 > > 1 > > > It's not necessarily efficient, but it's really simple. > > > Thanks, > > > -- > > Raul > > > > On Tue, Aug 5, 2014 at 1:01 AM, Dan Bron <[email protected]> wrote: > > > That's a long page, but in brief: can you calculate the power series > > without using ^ explicitly or implicitly (e.g. via t. or #: etc)? Are all > > the ^s I see in those power series easily replaced by instances of > > */@:#"0 ? > > > > In other words, does that page teach me how to do the trick when literally > > the only mathematical functions in my toolbox are (dyads) + - * % and > > (monad) | ? > > > > -Dan > > > > ----- Original Message --------------- > > > > Subject: Re: [Jprogramming] Power for the powerless > > From: Roger Hui <[email protected]> > > Date: Mon, 4 Aug 2014 21:51:08 -0700 > > To: Programming forum <[email protected]> > > > > ?Can you not just use power series (for both exp and ln)? See > > http://www.jsoftware.com/jwiki/Essays/Extended%20Precision%20Functions .? > > > > > > On Mon, Aug 4, 2014 at 9:39 PM, Dan Bron <[email protected]> wrote: > > > > > There's a StackExchange puzzle which challeges us to implement power > > (i.e. > > > dyad ^) using only the simple arithmetic dyads + - * % and monad | [1]. > > In > > > other words, we may not use ^ or ^. or variants. There are still several > > > open questions on the puzzle, not least of which involves the domain of > > > the inputs (can the base be negative?) and range of the outputs (how much > > > precision is required?), but neverthless we can make some assumptions and > > > start to sketch an approach. > > > > > > ---------------------------------------------------------------------- > > 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
