As you begin to build definitions you will begin to realize that the rightmost parentheses can be omitted. Note that is you omit them, a ] appears in both tacit definitions:
f=: 13 :'y ,.(3*(y-1)%4)' f ] ,. 3 * 4 %~ 1 -~ ] g=: 13 :'y ,.3*(y-1)%4' g ] ,. 3 * 4 %~ 1 -~ ] Linda -----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Linda Alvord Sent: Thursday, December 20, 2012 12:59 PM To: programm...@jsoftware.com Subject: Re: [Jprogramming] arithmetic sequence Starting for an explicit version you get: f=: 13 :'y ,.(3*(y-1)%4)' f ] ,. 3 * 4 %~ 1 -~ ] f 5^i.9 1 0 5 3 25 18 125 93 625 468 3125 2343 15625 11718 78125 58593 390625 292968 This is just slightly different from Bo's version. Linda -----Original Message----- From: programming-boun...@forums.jsoftware.com [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Bo Jacoby Sent: Thursday, December 20, 2012 11:17 AM To: programm...@jsoftware.com Subject: Re: [Jprogramming] arithmetic sequence next=:0 3+*&5 (next^:(i.9)) 1 0 NB. brute force solution 1 0 5 3 25 18 125 93 625 468 3125 2343 15625 11718 78125 58593 390625 292968 (,.3*4%~1-~])5^i.9 NB. closed form solution 1 0 5 3 25 18 125 93 625 468 3125 2343 15625 11718 78125 58593 390625 292968 >________________________________ > Fra: Roger Hui <rogerhui.can...@gmail.com> >Til: Programming forum <programm...@jsoftware.com> >Sendt: 16:07 torsdag den 20. december 2012 >Emne: Re: [Jprogramming] arithmetic sequence > >In both versions of the code, if you give a single "exponent" n, the code >would produce a single answer for S(n). Internally, it would keep a single >intermediate result. If what it's doing is what you suspect (accuse! :-) >it of doing, you can verify it by using space=:7!:2 > space '10 next 1 0' > space '20 next 1 0' >and look at the grow of the space consumption. > >BTW, since the function is extremely fast growing, > > 5^.2^1023 >440.582 > 441 next 1 0 >1.76105e308 1.32079e308 > 442 next 1 0 >_ _ > >If you are not interested in rational numbers, the function has only a few >possible answers. If you are worried about time/space, one approach may be >to recompute a vector S of length 442 of all possible results, and then >define next=: {&S . > > > >On Thu, Dec 20, 2012 at 5:28 AM, alessandro codenotti <cod...@live.it>wrote: > >> >> I think I badly explained myself, or maybe i completely misunderstood the >> code: >> >> > next=.5&(0 3 + *) >> >> the verb next simply applies the "multiply by five and add 3" to is right >> argument a number of times given by is left argument, right? >> >> > (i. 20) next 1 0 >> >> this instruction, first applies 0 times "next" to 1 0, then applies once >> "next" to 1 0, then applies twice "next" to 1 0, ... , then applies 20 >> times "next" to 1 0, right? >> >> this mean that S(0) has been calculated 20 times, S(1) has been calculated >> 19 times, S(n) has been calculated 20-n times since every time the function >> next restarts from >> the first term (which is 1 0), right? >> >> What i mean is that with something like the following pseudo-code S(n) is >> calculated once avoiding a huge waste of time and memory: >> >> S(1)=1 0 >> for i=2 to 20 do >> S(i)=.3+5*S(i-1) >> end >> >> My question then was if the code: >> >> > next=.0 3+*&5 >> > 20 next@]^:(i.@[) 1 0 >> >> has the same problem or not and, in case of a positive answer, how can i >> translate my pseudo-code in J avoiding an explicit loop. >> >> It may be that I completely misunderstood your code and the problem that >> is worring me doesn't exist at all but I'm really a beginner in J... >> >> Alessandro >> >> >> >> >> >> ---------------------------------------------------------------------- >> 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 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
