Oh, oops, I should have looked at that - definitely not dirac delta. Integral of 0^x should be _
Thanks, -- Raul On Mon, Oct 2, 2017 at 1:43 AM, Jose Mario Quintana <jose.mario.quint...@gmail.com> wrote: > " > 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 ... > " > It seems that J evaluates 0^x as follows: > > _ if x < 0 > 1 if x = 0 > 0 if x > 0 > > So, which is the function, apart from adding a constant, whose derivative > is 0&^? If x > 0 I would say it is 0"0; otherwise, it might be wise to > regard it as undefined. > Consider the derivative of 0^x, according to J, > > (0&^)d.1 > __&*@(0&^) > > If x > 0 the evaluation makes sense to me; however, for instance, > > ((0&^)d.1) _1 > __ > > is beyond my comprehension. Can anybody explain this result? > > NB. Wolfram Alpha > NB. https://www.wolframalpha.com/input/?i=d%2Fdx(+0%5Ex) > NB. d/dx(0^x) > NB. 0 if x >0 > NB. indeterminate otherwise > > Incidentally, although Wolfram Alpha regards 0^0 as undefined, it is fine > with integral x^0 dx and agrees with J... > > NB. Wolfram Alpha > NB. https://www.wolframalpha.com/input/?i=integral+x%5E0+dx > NB. integral x^0 dx > NB. x + constant > > (^&0)d._1 > [ > > NB. Wolfram Alpha > NB. https://www.wolframalpha.com/input/?i=d%2Fdx(+integral+x%5E0+dx) > NB. d/dx( integral x^0 dx) > NB. 1 > > (^&0)d._1 d.1 > 1 > > > On Sun, Oct 1, 2017 at 9:18 PM, 'Jon Hough' via Source <sou...@jsoftware.com >> wrote: > >> 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 >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
