Sorry, The verb zeta is dyadic.for example 2 zeta i.100 gives an estimation of the functionzeta(x), for x =2,where zeta(x) is the Riemann zeta function defined for positive integers > 1.
> From: rauldmil...@gmail.com > Date: Sun, 9 Mar 2014 13:32:54 -0400 > To: programm...@jsoftware.com > Subject: Re: [Jprogramming] Zeta Function as Tacit Verb > > Hypothetically speaking, you can get J to tell you how to build tacit verb. > > Practically speaking... here's the definitions you gave: > > pwr =. ^~ NB. this is y to the power x (dyadic tacit verb) > recip =. %@ pwr NB. take the reciprocal > zeta =. +/"_ @: z NB. sum all > > And here's how I would examine them: > > First, enable linear represenation of verbs: > > 9!:3]5 > > Second, resolve the names in your definition: > > zeta f. > |value error: z > > (oops) > > It looks like you left out a part of your definition. I've not worked with > zeta before, and I don't actually know which zeta function you were trying > to compute. At a guess, though, you were using one that happens to work > nicely with this kind of implementation. > > If you could supply the rest of the definition, though, I think one of us > could go into how it works. > > Thanks, > > -- > Raul > > > > On Sun, Mar 9, 2014 at 1:22 PM, Jon Hough <jgho...@outlook.com> wrote: > > > I have created a tacit verb to calculate the Zeta function for any integer > > greater than 1. > > http://mathworld.wolfram.com/ZetaFunction.html > > My verb was built up step by step as follows: > > pwr =. ^~ NB. this is y to the power x (dyadic tacit verb) > > recip =. %@ pwr NB. take the reciprocal > > zeta =. +/"_ @: z NB. sum all > > > > I tested it > > 2 zeta >: i.100 > > 1.63498 > > This seems about right (should be about pi*pi/6) > > My first question is: I would like to make my verb in only one line, not > > using my step-by-step approach. But every time I tried this I got all kinds > > of errors or the calculation results were hopelessly wrong. How can I write > > this verb in a single line? > > Secondly, I'm still not entirely sure how this works. > > If I do 2 pwr 3 then that is 3*3, which is fine, but then doing "recip" > > afterwards, I'm not sure how J parses the recip verb as monadic (it takes > > the reciprocal instead of "2 over". How does J do this? > > Lastly, I am not sure why I needed to make +/ to be rank _. That was just > > a guess. Why is this? I understand it is the way @: and @ interact with the > > verbs but I'm struggling to see the cause. > > Thanks. > > Jon > > ---------------------------------------------------------------------- > > 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
