That makes sense!. Thanks.
Den 23:09 onsdag den 5. marts 2014 skrev Pascal Jasmin <godspiral2...@yahoo.ca>: I assume the main motivation for the feature is ^:(<_) > > >----- Original Message ----- >From: Bo Jacoby <bojac...@yahoo.dk> >To: "programm...@jsoftware.com" <programm...@jsoftware.com> >Cc: >Sent: Wednesday, March 5, 2014 4:43:14 PM >Subject: Re: [Jprogramming] Simple Number Theory > >Interesting, Dan, but why define ^:(<20) meaning ^:(i.<20) ? > > (-:&(+ (2&| * >:&+:)))^:(<20)11 >11 17 26 13 20 10 5 8 4 2 1 2 1 2 1 2 1 2 1 2 > (-:&(+ (2&| * >:&+:)))^:(i.20)11 >11 17 26 13 20 10 5 8 4 2 1 2 1 2 1 2 1 2 1 2 >- Bo > > > > >Den 16:35 onsdag den 5. marts 2014 skrev Raul Miller <rauldmil...@gmail.com>: > >And with ^:(-i.|integer) where 0 >: integer >> >>Of course, if you want more control you'll need to be more explicit: >> >> >:^:(i:4) 5 6 7 >>1 2 3 >>2 3 4 >>3 4 5 >>4 5 6 >>5 6 7 >>6 7 8 >>7 8 9 >>8 9 10 >>9 10 11 >> >>Also, >:^:(n) y is n+/y with n constrained to integers. >> >>Thanks, >> >>-- >>Raul >> >> >>On Wed, Mar 5, 2014 at 10:10 AM, Dan Bron <j...@bron.us> wrote: >> >>> FYI, ^:(<integer) is a synonym for ^:(i.integer) where 0 < integer < _ . >>> >>> -Dan >>> >>> >>> >>> ----- Original Message --------------- >>> >>> Subject: Re: [Jprogramming] Simple Number Theory >>> From: "Linda Alvord" <lindaalv...@verizon.net> >>> Date: Tue, 04 Mar 2014 21:46:16 -0500 >>> To: <programm...@jsoftware.com> >>> >>> |. f ^:(i.80)2324 >>> 2 1 2 4 8 5 10 20 40 80 53 35 23 46 92 61 122 244 488 325.... >>> >>> Linda >>> >>> >>> -----Original Message----- >>> From: programming-boun...@forums.jsoftware.com >>> [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Linda >>> Alvord >>> Sent: Tuesday, March 04, 2014 8:59 PM >>> To: programm...@jsoftware.com >>> Subject: Re: [Jprogramming] Simple Number Theory >>> >>> >>> Also: >>> >>> collatz=:-:&(+2&|*>:&+:) >>> collatz ^:(i.10)17 >>> 17 26 13 20 10 5 8 4 2 1 >>> >>> f=: 13 :'-: y+(2|y)*>:+:y' >>> f ^:(i.10)17 >>> 17 26 13 20 10 5 8 4 2 1 >>> >>> collatz >>> -:&(+ (2&| * >:&+:)) >>> f >>> [: -: ] + (2 | ]) * [: >: +: >>> >>> Linda >>> >>> >>> -----Original Message----- >>> From: programming-boun...@forums.jsoftware.com >>> [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of Devon >>> McCormick >>> Sent: Tuesday, March 04, 2014 12:56 PM >>> To: J-programming forum >>> Subject: Re: [Jprogramming] Simple Number Theory >>> >>> "Power" is a very useful conjunction. Here's some simple examples of using >>> it: >>> >>> >:10 NB. Start with the increment-by-one verb ">:" >>> 11 >>> >:^:99]10 NB. Now apply it 99 times to the argument "10" by using ^: >>> 109 >>> >:^:(99) 10 NB. Another way to distinguish the "power" arg from the arg >>> to which it's applied. >>> 109 >>> >>> >:^:(i.10) 10 NB. Vector arg to power shows intermediate results. >>> 10 11 12 13 14 15 16 17 18 19 >>> >>> >:^:(25>]) 10 NB. Use verb (25>]) to control power... >>> 11 >>> >:^:(25>])^:_ ] 10 NB. Use with verb (25>]) "infinite" number of times >>> 25 >>> >>> "Infinite" power keeps applying the verb until it converges (stops >>> changing). >>> >>> So, J gives you infinite power. >>> >>> On Tue, Mar 4, 2014 at 10:25 AM, Raul Miller <rauldmil...@gmail.com> >>> wrote: >>> >>> > It might be worthwhile taking a look at the different display forms of >>> the >>> > veb collatz. For example, consider the atomicrepresentation: >>> > >>> > 5!:1<'collatz' >>> > +------------------------------------------------+ >>> > ¦+----------------------------------------------+¦ >>> > ¦¦"¦+------------------------------------------+¦¦ >>> > ¦¦ ¦¦+----------------------------------+¦+---+¦¦¦ >>> > ¦¦ ¦¦¦@.¦+-----------------------------+¦¦¦0¦0¦¦¦¦ >>> > ¦¦ ¦¦¦ ¦¦+-------------+¦+-----------+¦¦¦+---+¦¦¦ >>> > ¦¦ ¦¦¦ ¦¦¦0¦+---------+¦¦¦&¦+-------+¦¦¦¦ ¦¦¦ >>> > ¦¦ ¦¦¦ ¦¦¦ ¦¦cole¦colo¦¦¦¦ ¦¦+---+¦|¦¦¦¦¦ ¦¦¦ >>> > ¦¦ ¦¦¦ ¦¦¦ ¦+---------+¦¦¦ ¦¦¦0¦2¦¦ ¦¦¦¦¦ ¦¦¦ >>> > ¦¦ ¦¦¦ ¦¦+-------------+¦¦ ¦¦+---+¦ ¦¦¦¦¦ ¦¦¦ >>> > ¦¦ ¦¦¦ ¦¦ ¦¦ ¦+-------+¦¦¦¦ ¦¦¦ >>> > ¦¦ ¦¦¦ ¦¦ ¦+-----------+¦¦¦ ¦¦¦ >>> > ¦¦ ¦¦¦ ¦+-----------------------------+¦¦ ¦¦¦ >>> > ¦¦ ¦¦+----------------------------------+¦ ¦¦¦ >>> > ¦¦ ¦+------------------------------------------+¦¦ >>> > ¦+----------------------------------------------+¦ >>> > +------------------------------------------------+ >>> > >>> > >>> > Working inwards from the outside, we see that the top level control is >>> the >>> > rank adverb. Its arguments are represented as a gerund and the noun 0 >>> (the >>> > first '0' says that this is a noun, the second is the value of the noun). >>> > >>> > The top level control in the gerund is the @. conjunction. And >>> > http://www.jsoftware.com/help/dictionary/d621.htm says that the rank of >>> @. >>> > is determined by the rank of its right verb, which leads to your >>> question. >>> > But what is that right verb? >>> > >>> > According to the diagram, above, the right verb for @. has & as its top >>> > level control. And according to >>> > http://www.jsoftware.com/help/dictionary/d630n.htm the monadic rank of >>> 2&| >>> > is infinite. >>> > >>> > (Hopefully you do not consider this approach to be too tedious - or, if >>> so, >>> > hopefully you skipped down to the end and then read the last couple >>> > paragraphs.) >>> > >>> > Thanks, >>> > >>> > -- >>> > Raul >>> > >>> > >>> > >>> > On Tue, Mar 4, 2014 at 10:07 AM, Jon Hough <jgho...@outlook.com> wrote: >>> > >>> > > Thanks for all the replies.OK, I'm starting to understand more now. I >>> did >>> > > not know about agenda (@.). Well actually, I read about it in the >>> > > jsoftware.com dictionary, but I think J is one of those things you >>> have >>> > > to see in action before it clicks. >>> > > What I've gone with: >>> > > cole =. 2&(%~) NB. even case >>> > > colo =. (1&+)@(3&*) >>> > > collatz =.cole`colo@.(2&|)"0 NB. Rank 0 lets us work on each element >>> > of >>> > > a list >>> > > >>> > > So my next question is how do I go about iterating this until we reach >>> 1? >>> > > Incidentally, it seems to me that | is rank 0 (right rank) >>> > > http://www.jsoftware.com/help/dictionary/d230.htm Therefore I am >>> puzzled >>> > > why the verb collatz does not act on each rank 0 element of the noun. >>> Why >>> > > did I have to explicitly force its right rank to be 0? >>> > > Regarding iterations,Bo Jacoby kindly mentioned: >>> > > collatz=:-:&(+2&|*>:&+:) collatz ^:(i.10)17 >>> > > 17 26 13 20 10 5 8 4 2 1 >>> > > But I'm struggling to understand this verb. Any help explaining this >>> > would >>> > > be appreciated. Or help making my own collatz verb into an iterative >>> > > function (verb). >>> > > Regards,Jon >>> > > > Date: Mon, 3 Mar 2014 18:59:04 -0800 >>> > > > From: d...@shaw.ca >>> > > > To: programm...@jsoftware.com >>> > > > Subject: Re: [Jprogramming] Simple Number Theory >>> > > > >>> > > > This might be more readable - I had some bold faced characters so got >>> > > > the extra dusting of * >>> > > > >>> > > > Don >>> > > > >>> > > > collatz=:(1 0=2|])#(3*1+]),2%~] >>> > > > >>> > > > collatz 4 >>> > > > >>> > > > 2 >>> > > > >>> > > > collatz 5 >>> > > > >>> > > > 18 >>> > > > >>> > > > collatz _4 >>> > > > >>> > > > _2 >>> > > > >>> > > > collatz _5 >>> > > > >>> > > > _12 >>> > > > >>> > > > >>> > > > Test for odd/even is 2|nreturning 1 for odd and 0 for even 1 0=2|n >>> > will >>> > > > return 1 0 for odd and 0 1 for even >>> > > > The (3*1+n) and n%2 terms are a two element result vector >>> > > > >>> > > > if odd, 1 0 # returns the odd result and if even 0 1 #returns the >>> even >>> > > > result. >>> > > > >>> > > > In this case I started with the basic (3*n+1),n%2vector and then >>> used >>> > > > 1 0= 2|n times this(residue is 1 for odd and 0 for even numbers) >>> > > > the result is(1 0=2|y) # (3*1+y),y%2which works >>> > > > I wrote this as an explicit verb s=: 13 : '(1 0=2|y)#(3*1+y),y%2' >>> > > > and typed sto get a tacit form (1 0 = 2 | ]) # (3 * 1 + ]) , 2 %~ ] >>> > > > generated by J >>> > > > >>> > > > attached collatz=:to the front and that was it. >>> > > > >>> > > > note that the y is replaced by ] and the y%2 is expressed using 2%~] >>> J >>> > > > wants the ] on the right of this operation and ~does this >>> > > > There are other variations on this but this is the simplest I came up >>> > > with. >>> > > > >>> > > > I classify myself as a beginner but I have an APL background and long >>> > > > ago found C and relatives awkward I do think it is harder to come >>> from >>> > > > C/C++/Java to J than from APL to J - the thinking is different To me >>> > > > C++ is oriented towards detailed instructions for the compiler (much >>> of >>> > > > this is done by the interpreter in J or APL) The problem comes >>> first >>> > > > in J and more times than not - use of arrays can eliminate a lot of >>> > if's >>> > > > and loops. >>> > > > >>> > > > >>> > > > Don Kelly >>> > > > >>> > > > >>> > > > On 03/03/2014 8:30 AM, Jon Hough wrote: >>> > > > > Beginner question again.I quick task I set myself was to write ONE >>> > > ITERATION of the Collatz function for a given positive integer. >>> > > http://en.wikipedia.org/wiki/Collatz_conjecture >>> > > > > >>> > > > > So my verb is supposed to do 3*n+1 if n is odd and n/2 if n is >>> > even.In >>> > > a more imperative/OOE based language (C/C++/Java) I could write this in >>> > > less than a minute. Unfortunately, I fell at the very first hurdle in >>> J. >>> > > > > I originally wrote my tacit verb for even ints:collatz_even >>> =.2&(%~) >>> > > > > collatz_even 4 >>> > > > > 2 >>> > > > > This works, but I had a terrible time trying to put the brackets in >>> > > the right place. I am not sure why %~ needs to be bracketed. Won't J >>> > parse >>> > > %~ as dyadic and "know" that the left operand is 2? >>> > > > > Next I tried to do the case for odd n: >>> > > > > collatz_odd =. 1&+@(3&*) collatz_odd 3 >>> > > > > 10 >>> > > > > That seems to work ok.Now I am not sure how to do an if statement >>> in >>> > > J. In plain English I want "If n is even do collatz_even else do >>> > > collatz_odd".The verb I wrote to test for even-ness is >>> > > > > ones =. {:@#: NB. Finds the ones column values. 1 => odd, 0=> even >>> > > > > 1 = ones 2 >>> > > > > 0 >>> > > > > So I have a test but I am not sure how to utilize this test. How >>> > > should I go about doing:"If n is even do collatz_even else do >>> > collatz_odd"? >>> > > > > Thanks and regards,Jon >>> > > > > >>> > > > > >>> > ---------------------------------------------------------------------- >>> > > > > For information about J forums seehttp:// >>> > 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 >>> > >>> >>> >>> >>> -- >>> Devon McCormick, CFA > > >> >>> ---------------------------------------------------------------------- >>> 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 >> >> >---------------------------------------------------------------------- >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
