Well, I’ve just copied/pasted your/their calc... into J807 on this iPad, and “crc”, for short, produces the same rationals, I think. I might be able to try on my Windows laptop in a short while,
Mike Sent from my iPad > On 19 Jul 2019, at 15:41, Devon McCormick <[email protected]> wrote: > > Fellow Jedi - > > There's a New Scientist article about some people who open-sourced some > code to attempt to accomplish Ramanujan-like discoveries in the area of > continued fractions: > https://www.newscientist.com/article/2209213-computer-attempts-to-replicate-the-dream-like-maths-of-ramanujan/ > . > > Unfortunately it is paywalled, so I will fair-use a little here: > > *The theorems Ramanujan produced often involved continued fractions, which > express a number as the sum of infinitely nested fractions.* > > *To mimic this approach, Gal Raayoni at the Israel Institute of Technology > and his colleagues created the Ramanujan Machine > <http://arxiv.org/abs/1907.00205>. It has already come up with tens > of conjectures that use continued fractions to approximate π and e.* > > *One method the program uses to search for new conjectures is a “meet in > the middle” approach. This involves generating many mathematical > expressions, computing their value for a limited number of iterations and > eliminating the expressions that give inaccurate results.* > Anyway, the formula for *e* they show in the article renders into J this > way: > > calcRamalikeE=: 13 : '(+`%)/,x:(3+i.y),.->:i.y'"0 > calcRamalikeE > ([: +`%`:3 [: , [: x: (3 + i.) ,. [: - [: >: i.)"0 > calcRamalikeE 10 20 > 9864101r3628800 6613313319248080001r2432902008176640000 >> 50j48":&.>calcRamalikeE 10 20 > 2.718281801146384479717813051146384479717813051146 > 2.718281828459045235339784490666415886146403434540 > > All fine and good but when I tried to replicate this from memory at home > tonight, I kept getting a "spelling error" on the "(+`%)" part. Eventually > I figured out that what I'm typing in is rendering in Unicode and is > failing a spelling test. I'm running J64 8.07, Library 8.07.26, and, as > always, under Emacs on Windows. > > I'm afraid it may just be an Emacs thing as I had saved the problematic > session as "raw-text" earlier but I'd be pleased to hear from anyone who > could replicate or explain this or, even better, make sure it never happens > to anyone else ever again. > > Thanks, > > Devon > > -- > > Devon McCormick, CFA > > Quantitative Consultant > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
