Hei p j! Why are you mad at J at all? From mathematics we all know that rational numbers give a finite cf, irrational ones a periodical one (exactly as JR did say) and transcedental numbers an infinite cf. I myself am using cf exactly for the reverse task. Usually you have a table-like output of some calculations and you do not know how exact your results are. The easiest way is to take a handful of random elements of that table and develop them into cf. You always see very quickly what the hidden inner precision of your data table. (You just cut the cf-s at the place of the first big values in cf). After one short exercise you will see what I mean. More optimism wishes Leo Võhandu
> which matches the web reference I made > (http://www.rossi.com/sqr2.htm)... at least the first > 2 lines of the maple result does. > > If I understand the criticism of the web pasting I > made, it is that I only pasted approx 50 digits of the > solution, so I think the point was that even the right > 50 digits is an innacurate approximation :( > > --- John Randall <[EMAIL PROTECTED]> > wrote: > >> Maple gives >> >> > evalf(sqrt(2),503); >> > 1.4142135623730950488016887242096980785696718753769480731766797379907324784\ >> >> > 62107038850387534327641572735013846230912297024924836055850737212644121\ >> >> > 49709993583141322266592750559275579995050115278206057147010955997160597\ >> >> > 02745345968620147285174186408891986095523292304843087143214508397626036\ >> >> > 27995251407989687253396546331808829640620615258352395054745750287759961\ >> >> > 72983557522033753185701135437460340849884716038689997069900481503054402\ >> >> > 77903164542478230684929369186215805784631115966687130130156185689872372\ >> 353 >> >> Best, >> >> John >> >> Roger Hui wrote: >> > I wonder why you say "the number below is not >> correct either". >> > The following is a demonstration that <[EMAIL PROTECTED]: >> 2x*10x^2*n computes >> > the square root of 2 to n decimal places: >> > >> > n=: 500 >> > s=: <[EMAIL PROTECTED]: 2x*10x^2*n >> > $ ": s >> > 501 >> > _50 ,@(_5&(' '&,\))\ ": s >> > 14142 13562 37309 50488 01688 72420 96980 78569 >> 67187 53769 >> > 48073 17667 97379 90732 47846 21070 38850 38753 >> 43276 41572 >> > 73501 38462 30912 29702 49248 36055 85073 72126 >> 44121 49709 >> > 99358 31413 22266 59275 05592 75579 99505 01152 >> 78206 05714 >> > 70109 55997 16059 70274 53459 68620 14728 51741 >> 86408 89198 >> > 60955 23292 30484 30871 43214 50839 76260 36279 >> 95251 40798 >> > 96872 53396 54633 18088 29640 62061 52583 52395 >> 05474 57502 >> > 87759 96172 98355 75220 33753 18570 11354 37460 >> 34084 98847 >> > 16038 68999 70699 00481 50305 44027 79031 64542 >> 47823 06849 >> > 29369 18621 58057 84631 11596 66871 30130 15618 >> 56898 72372 >> > 3 >> > >> > ((i.20)&{"1 ,. ' ',. (495+i.20)&{"1) ": *: ,. >> s+_1 0 1 >> > 19999999999999999999 99999567575656983330 >> > 19999999999999999999 99999850418369457949 >> > 20000000000000000000 00000133261081932568 >> > >> > The last phrase demonstrate that s-1 is smaller >> than the square root, >> > but s+1 is larger. >> > >> > Perhaps those people with access to Mathematica or >> Maple can compute >> > the square root of 2 in those systems as a check. >> > >> > >> > >> > ----- Original Message ----- >> > From: "Don Guinn" <[EMAIL PROTECTED]> >> > To: "Programming forum" >> <[email protected]> >> > Sent: Friday, March 10, 2006 4:52 PM >> > Subject: Re: [Jprogramming] More precision >> nightmares >> > >> > The answer you listed from the web is not correct. >> It's correct only to >> > the number of digits listed. The number below is >> not correct either, >> > but it's a lot closer. >> > >> > 0j200":(10x^500)%~(<[EMAIL PROTECTED]:)2x*10x^1000 >> > >> > 1.4142135623730950488016887242096980785696718753769480731766797379907324784621070388503875343276415727350138462309122970249248360558 >> > >> > 5073721264412149709993583141322266592750559275579995050115278206057147 >> > ... >> > >> > >> > >> > ---------------------------------------------------------------------- >> > For information about J forums see >> http://www.jsoftware.com/forums.htm >> > >> >> >> > ---------------------------------------------------------------------- >> For information about J forums see >> http://www.jsoftware.com/forums.htm >> > > > __________________________________________________ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam protection around > http://mail.yahoo.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
