http://www.ramanujanmachine.com
R.E. Boss > -----Oorspronkelijk bericht----- > Van: Programming <[email protected]> > Namens Devon McCormick > Verzonden: vrijdag 19 juli 2019 16:41 > Aan: J-programming forum <[email protected]> > Onderwerp: [Jprogramming] Program to replicate Ramanujan's methods > > 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
