Regarding the Riemann-Siegel formula, you may be interested in a half-finished Android app of minehttps://github.com/jonghough/Riemanndroid (not released on Google Play) Which plots the t= 0.5+iy values along the critical line (for positive y) of the R-S function Z(t), whose roots are the same as zeta(t). Anyway, regarding precision. I was actually, just practicing making a dyadic tacit verb, and was less interested in precision than actually getting it to work.
> From: [email protected] > To: [email protected] > Date: Sun, 9 Mar 2014 16:48:29 -0400 > Subject: Re: [Jprogramming] Zeta Function as Tacit Verb > > Or: > > z2=: 13 :'+/x ([: % ^)~([: >: i.)y' > > 2 z2 2e5 > 1.64493 > > z2 > [: +/ [ ([: % ^)~ [: ([: >: i.) ] > > > Linda > > -----Original Message----- > From: [email protected] > [mailto:[email protected]] On Behalf Of Aai > Sent: Sunday, March 09, 2014 1:58 PM > To: [email protected] > Subject: Re: [Jprogramming] Zeta Function as Tacit Verb > > Or as J 'knows': > > 1r6p2 > 1.64493 > > > > On 09-03-14 18:54, Aai wrote: > > in fact something like: > > > > 2 +/@:(%@^~) 1+i.100000 > > 1.64492 > > > > > > On 09-03-14 18:49, Jon Hough wrote: > >> Ah, I see what's happened.z should be recipSorry. > >> It should be: zeta =. +/"_ @: recip NB. sum all> From: > >> [email protected] > >>> Date: Sun, 9 Mar 2014 13:41:18 -0400 > >>> To: [email protected] > >>> Subject: Re: [Jprogramming] Zeta Function as Tacit Verb > >>> > >>> But what is z? > >>> > >>> Thanks, > >>> > >>> -- > >>> Raul > >>> > >>> > >>> On Sun, Mar 9, 2014 at 1:38 PM, Jon Hough <[email protected]> wrote: > >>> > >>>> 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: [email protected] > >>>>> Date: Sun, 9 Mar 2014 13:32:54 -0400 > >>>>> To: [email protected] > >>>>> 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 <[email protected]> > >>>>> 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 > >>>> > >>> ---------------------------------------------------------------------- > >>> For information about J forums see http://www.jsoftware.com/forums.htm > >> > >> ---------------------------------------------------------------------- > >> For information about J forums see http://www.jsoftware.com/forums.htm > > > > -- > Met vriendelijke groet, > @@i = Arie Groeneveld > > ---------------------------------------------------------------------- > 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
