...Clarification: it's the Nim-addition table that has 0s down the main diagonal, not the Nim-multiplication table.
I've updated http://www.jsoftware.com/jwiki/Doc/Articles/Play191 to include all this new material: nimsum, label and References. Ian On Tue, Nov 17, 2009 at 10:05 AM, Ian Clark <earthspo...@googlemail.com> wrote: > Thanks, Fraser, for tracking that down. Yes, that works fine! > > Vector 19.1 is one of the few editions I don't happen to have. I'm > wondering where I got the original copy of Play191 from... > > FYI, I note: > > nimsum > ~:/&.#:@,"0/~ > NS > ~:/&.#: > NS 3 6 > 5 > nimsum 3 6 > 0 5 > 5 0 > > ...and so on, for all the args I've tried. > So they're not so very different. I guess nimsum is more efficient for > calculating the table (a symmetric matrix with 0s down the diagonal) > because it provides 2 entries at once. > > Ian > > > On Tue, Nov 17, 2009 at 9:11 AM, Fraser Jackson > <fraser.jack...@xtra.co.nz> wrote: >> In the printed copy (Vector 19.1) it gives >> >> nimsum =: ~:/&.#:@,"0/~ NB. EEmcD >> >> That gives the correct results from Mike Day's function. >> >> Fraser >> >> ----- Original Message ----- >> From: "Ian Clark" <earthspo...@googlemail.com> >> To: "Programming forum" <programming@jsoftware.com> >> Sent: Tuesday, November 17, 2009 7:27 AM >> Subject: Re: [Jprogramming] APWJ Chapter 31: missing object: nimsum >> >> >> I haven't explained the problem well enough. >> >> Let me try and do so without making suppositions which conceal where >> the error actually lies. >> >> Play191 exhibits a function NS, which calculates a statistic called >> the "nim sum" which helps you win at the game of Nim. NS maps into a >> domain of numbers which Conway & Guy call "nimbers", with their own >> idiosyncratic addition & multiplication. >> >> Having discussed the addition of nimbers, the paper discusses their >> multiplication. It offers two verbs for producing the multiplication >> table of nimbers. Both are called mt. I propose to call the one by >> Mike Day mtMD, which (quote) "accurately translates" a Maple program >> (not shown, but viewable at the OEIS site). >> >> Now mtMD won't work as it stands, because it uses an entity (verb?) >> named nimsum, which is nowhere defined. What is nimsum? >> >> I conjecture that nimsum is precisely the NS which is defined earlier. >> So accordingly I assign: nimsum=: NS >> Hey presto, mtMD now works, and it computes the following table: >> >> mtMD 4 >> 0 0 0 0 0 >> 0 1 2 3 4 >> 0 2 3 3 4 >> 0 3 3 3 3 >> 0 4 4 3 8 >> >> However, when you compare it with mt, they don't give the same result, >> which I conjecture they should: >> >> mt 5 NB. (index-origin strikes again!) >> 0 0 0 0 0 >> 0 1 2 3 4 >> 0 2 3 1 8 >> 0 3 1 2 12 >> 0 4 8 12 6 >> >> Now in view of the "correct" 15-by-15 multiplication table at the end >> of the article, mt is giving the right result but mtMD isn't. >> Accordingly I deduce that the assumption: nimsum <--> NS is an unsound >> one. So what should the missing verb nimsum really be? >> >> Ian >> >> >> On Mon, Nov 16, 2009 at 2:31 AM, Henry Rich <henryhr...@nc.rr.com> wrote: >>> To me, nimsum is what you use to solve the game of Nim. It is NS as >>> described in the article. A Nim position with nimsum=0 is a loser for >>> the player with the move. You calculate it by writing the number of >>> stones in the piles in binary, and adding them up in binary, EXCEPT that >>> you discard any carries produced during the addition. >>> >>> You win a Nim game by always making a move that leaves the nimsum=0. It >>> is easy to prove that such a move is possible iff the nimsum is not 0 >>> already. >>> >>> Henry Rich >>> >>> Ian Clark wrote: >>>> In: http://www.jsoftware.com/jwiki/Doc/Articles/Play191 (Chapter 31, J >>>> be nimble, J be quick) >>>> the version of mt attributed to Mike Day fails with value error: nimsum >>>> >>>> Can anyone see what nimsum is supposed to be? It only occurs once >>>> (outside a comment). I've tried equating it to the verb NS, the "nim >>>> sum" derived at the start of the article, but although mt then runs, >>>> it does not produce the same table as the previous definition of mt >>>> (quite apart from needing to be run as (mt 4) not (mt 5) like the >>>> previous one). >>>> >>>> Ian Clark >>>> Subeditor, APWJ Edn 2. >>>> ---------------------------------------------------------------------- >>>> 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
