Could you not use the binomial theorem? Where x^y =(1 +(x-1))^y
For any nonzero x and y. Also it is suspicious that | is allowed, perhaps. --- Original Message --- From: "Dan Bron" <[email protected]> Sent: August 5, 2014 2:01 PM To: [email protected] Subject: Re: [Jprogramming] Power for the powerless 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
