Yes, the sentence I wrote is essentially gibberish. I'll put it down to tiredness. (J only defines 0^0 as 1). My main point was that I'm not sure how the best way to handle integral of 0^x is. I guess it could be considered the integral of 0 (i.e. 0^x = 0). So
(0&^) d. _1 could either be 0 (+ some constant) or undefined. Wolfram Alpha decides to go with undefined. Seems reasonable, since if you are trying to integrate 0^x anyway, you probably have other issues with your code. -------------------------------------------- On Mon, 10/2/17, Jose Mario Quintana <jose.mario.quint...@gmail.com> wrote: Subject: Re: [Jsource] d. fix To: sou...@jsoftware.com Date: Monday, October 2, 2017, 1:38 AM Ups! I think Jon might have in mind x^0 as opposed to 0^x. On Sun, Oct 1, 2017 at 12:28 PM, Jose Mario Quintana < jose.mario.quint...@gmail.com> wrote: > Knuth's saying influencing the IEEE floating point standard pow > function[[0] might be the main reason why "most programming languague[s] > ... evaluate 0^0 as 1." > > At any rate, since J also evaluates 0^0 as 1, Jon's point 0^x =1 is > consistent with J's evaluation of 0^x for any x (although ignoring, for > example, 0^_). > > [0] > https://en.wikipedia.org/wiki/Exponentiation#Treatment_on_computers > > On Sun, Oct 1, 2017 at 11:22 AM, Roger Hui <rogerhui.can...@gmail.com> > wrote: > >> > Right, J, among several other programming languages, regards 0^0 as 1. >> > Wolfram Alpha and some programming languages regard 0^0 as undefined: >> >> > https://www.wolframalpha.com/input/?i=0%5E0 >> >> On this point (0^0 being undefined), Knuth says in *Two Notes on Notation >> <https://arxiv.org/PS_cache/math/pdf/9205/9205211v1.pdf>*, >> >> But no, no, ten thousand times no! >> >> Some authors who say that 0^0 is undefined continue to write polynomials >> blithely as sigma(i=0,n) a[i] times x ^ i. >> >> >> >> >> On Sun, Oct 1, 2017 at 8:11 AM, Jose Mario Quintana < >> jose.mario.quint...@gmail.com> wrote: >> >> > " >> > (0&^) d. _1 gives a domain error. Possibly this is unwanted, I mean, it >> > could be considered as a constant since 0^x = 1 in usual understanding, >> but >> > Wolfram Alpha also has issues with this: >> > https://www.wolframalpha.com/input/?i=integrate+0%5Ex >> > " >> > >> > Right, J, among several other programming languages, regards 0^0 as 1. >> > Wolfram Alpha and some programming languages regard 0^0 as undefined: >> > >> > https://www.wolframalpha.com/input/?i=0%5E0 >> > >> > >> > >> > On Sun, Oct 1, 2017 at 10:42 AM, 'Jon Hough' via Source < >> > sou...@jsoftware.com> wrote: >> > >> > > I have made a couple of minor edits and added some comments, and J >> > syntax: >> > > https://github.com/jonghough/jsource/blob/master/jsrc/cd.c LINES >> 281 - >> > > 301 >> > > >> > > A couple of points. >> > > >> > > (0&^) d. _1 gives a domain error. Possibly this is unwanted, I mean, >> it >> > > could be considered as a constant since 0^x = 1 in usual >> understanding, >> > but >> > > Wolfram Alpha also has issues with this: >> > > https://www.wolframalpha.com/input/?i=integrate+0%5Ex >> > > >> > > Negative bases for exponentials give complex results. This is >> > > mathematically correct, but thought I would mention it anyway. >> > > e.g. >> > > (_2&^) d. _1 >> > > %&0.693147180559945286j3.14159265358979312@(_2&^) NB. >> correct >> > > see: https://www.wolframalpha.com/input/?i=integrate+(-2)%5Ex >> > > >> > > Compare this to current J, where >> > > (_2&^) d. _1 >> > > gives a domain error. >> > > -------------------------------------------- >> > > On Fri, 9/29/17, 'Jon Hough' via Source <sou...@jsoftware.com> wrote: >> > > >> > > Subject: Re: [Jsource] d. fix >> > > To: sou...@jsoftware.com >> > > Date: Friday, September 29, 2017, 12:15 PM >> > > >> > > Sorry Henry, >> > > >> > > I somehow missed this email in my >> > > inbox. >> > > >> > > I will get the fixes you need done this >> > > weekend. >> > > >> > > Regards, >> > > Jon >> > > >> > > -------------------------------------------- >> > > On Mon, 9/25/17, Henry Rich <henryhr...@gmail.com> >> > > wrote: >> > > >> > > Subject: [Jsource] d. fix >> > > To: "'Jon Hough' via Source" <sou...@jsoftware.com> >> > > Date: Monday, September 25, 2017, 1:06 >> > > AM >> > > >> > > John, >> > > >> > > I finally have my PC back and >> > > would >> > > like to get your fix in before >> > > the next build, which is happening >> > > any >> > > day now. However, I have issues >> > > with it: >> > > >> > > 1. Needs commentary. The JE didn't >> > > have much to begin with & that >> > > needs >> > > to improve. So at least put in >> > > enough >> > > commentary that a reader can tell >> > > what you are doing without reading >> > > the >> > > C code. I put in an average of >> > > about one line of comment for each >> > > line >> > > of C. As it stands it will me >> > > more time than I care to spend to >> > > verify that what you are doing is >> > > valid. >> > > >> > > As part of the commentary, translate >> > > those long calls [amp(ds(CDIV...] to >> > > J. >> > > >> > > 2. AT(x)==INT is no good, because >> > > there >> > > may be flags set in more >> > > significant bits of the type. Use >> > > (AT(x)&INT) >> > > >> > > When you respond, send me your new >> > > testcase (gddot, I think) and point >> > > me to the fix, perhaps by simply >> > > sending me the new cd.c. >> > > >> > > hhr >> > > >> > > ------------------------------------------------------------ >> ---------- >> > > For information about J forums see http://www.jsoftware.com/forum >> s.htm >> > > ------------------------------------------------------------ >> ---------- >> > > For information about J forums see http://www.jsoftware.com/forum >> s.htm >> > > ------------------------------------------------------------ >> ---------- >> > > For information about J forums see http://www.jsoftware.com/forum >> s.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
