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
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>>>> 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
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