(Hopefully the reasoning is clear? Integral is basically a sum, and if you have infinities in your sum, adding 0 (or 1) to it isn't going to make a significant difference.)
Thanks, -- Raul On Mon, Oct 2, 2017 at 5:28 AM, Raul Miller <rauldmil...@gmail.com> wrote: > 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
