In the following code:
pp=: 3 : 0
for_e. 2+i.>.2^.y do.
m=. e <....@%: y
if. y=m^x: e do. m,e return. end.
end.
''
)
I understand that:
if. y=m^x: e do. m,e return. end.
will exit when the input y equals the m^x: and display m,e
1. Where does the "x" come from. I do not supply it as a
left-hand-side argument.
2. what is the significance of "x:"
Thanks for the explanation.
A comment:
In reading about the "perfect power" there was a statement I
found that (I think) ...
said that the only exponents I should test were those that
were prime.
Is it cheaper time-wise to just do all the exponents from 2
to >. 2 ^. y or would
it be faster to prune the for_e list so it only contains
primes.
----- Original Message Follows -----
From: Roger Hui <[email protected]>
To: Programming forum <[email protected]>
Subject: Re: [Jprogramming] perfect power???
Date: Mon, 08 Jun 2009 16:11:41 -0700
>Somewhere in the bowels of q: it calls 1&p:
>before launching into the much more expensive
>factoring routine.
>
>It seems to me there should be a straightforward
>determination of whether a number y is a perfect power:
>just try all possible exponents from 2 to 2 >....@^. y .
>For example, for 2^607x the exponents are from 2 to 607,
>which is not many exponents to try. Thus:
>
>pp=: 3 : 0
> for_e. 2+i.>.2^.y do.
> m=. e <....@%: y
> if. y=m^x: e do. m,e return. end.
> end.
> ''
>)
>
> pp 81
>9 2
> pp 128
>2 7
> pp 125
>5 3
> pp 2^100x
>1125899906842624 2
> pp <:2^607x
>
> 6!:2 'pp <: 2^607x'
>0.159832
>
>pptest=: *...@#@pp
>
>
>
>
>----- Original Message -----
>From: Raul Miller <[email protected]>
>Date: Monday, June 8, 2009 15:32
>Subject: Re: [Jprogramming] perfect power???
>To: Programming forum <[email protected]>
>
>> On Mon, Jun 8, 2009 at 6:13 PM,
>> <[email protected]> wrote:
>> > From what I am read in this article, determing if a
>> > number is a "Perfect Power" should be
>> > a lot faster. Either that or I am totally
mis-reading
>> > the article.
>>
>> Determining if a number is a perfect power is certainly
>> faster than some algorithm for determining if a number
>> is prime.
>>
>> But do you have any reason to believe J uses that
>> algorithm, in its implementation of q?
>>
>> That said, 1 p: will determine whether or not a number
>> is prime, and might be faster than 1 = # q: in some
>> cases.
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