Hum.......
2+i.>.2^. 10000
2 3 4 5 6 7 8 9 10 11 12 13 14 15
i.&.(_1&p:) >.2^. 10000
2 3 5 7 11 13
which is OK
2+i.>.2^. 100
2 3 4 5 6 7 8
i.&.(_1&p:) >.2^. 100
2 3 5
A problem: missed 7 which is a prime.
----- Original Message Follows -----
From: Roger Hui <[email protected]>
To: Programming forum <[email protected]>
Subject: Re: [Jprogramming] question about Roger Hui -
perfect power code
Date: Tue, 09 Jun 2009 23:44:42 -0700
>> 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.
>
>If only prime powers are required you can use
>i.&.(_1&p:) >.2^.y instead of 2+i.>.2^.y .
>In that case you should probably rename the
>function to ppp (perfect prime power).
>
>
>
>----- Original Message -----
>From: [email protected]
>Date: Tuesday, June 9, 2009 16:40
>Subject: [Jprogramming] question about Roger Hui - perfect
>power code To: Programming forum
><[email protected]>
>
>> 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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