Re: [Jprogramming] Golf - and a J crash

[Aai]

Factorized (MAXIMA)

1 0 1; 1 0 1; 1 0 _1 0 1

; +//.@(*/)&.>/1 0 1; 1 0 1; 1 0 _1 0 1
1 0 1 0 0 0 1 0 1

roots per factor

,.1&{::@p.&.> 1 0 1;1 0 1;1 0 _1 0 1
┌───────────────────────────────────────────────────────┐
│0j1 0j_1 │
├───────────────────────────────────────────────────────┤
│0j1 0j_1 │
├───────────────────────────────────────────────────────┤
│0.866025j0.5 0.866025j_0.5 _0.866025j0.5 _0.866025j_0.5│
└───────────────────────────────────────────────────────┘

and that looks like the PARI answer


On 03-06-14 19:29, I wrote:

This one causes a crash for me:
p. 1 0 1 0 0 0 1 0 1

PARI/GP shows

? polroots(x^8+x^6+x^2+1)

%2 = [0.8660254037844386467637231707 - 0.5000000000000000000000000000*I, 0.8660254037844386467637231707 + 0.5000000000000000000000000000*I, -0.8660254037844386467637231707 + 0.5000000000000000000000000000*I, -0.8660254037844386467637231707 - 0.5000000000000000000000000000*I, 0.E-28 + 1.000000000000000000000000000*I, 0.E-28 - 1.000000000000000000000000000*I, 0.E-28 + 1.000000000000000000000000000*I, 0.E-28 - 1.000000000000000000000000000*I]~

On 03-06-14 17:51, Don Guinn wrote:

Played with the golf problem some. I don't get the same answers as listed but then the text says they may not be correct. Anyway my answers match the

first few terms.

Then I tried to go one power more and J crashes!

golf 7

2 6 12 38 96 290 804


My script:


NB. golf - Extract counts for each order polynomial. ____________

golf=:3 : 0

|.#/.~,([:{.[:I.|)&>}."1 build_poly y

)


NB. build_poly - Build polynomials order from 2 to y with high order
coefficient of 1 and other coefficients 1, 0 or _1. Each order is boxed

list of coefficients. Use check_rou to find roots that are roots of unity.

Drop polynomials without any root of unity.

build_poly=:3 : 0

p=.;<"1&.>([:|."1[:<:3#.^:_1[:][:(+:+i.)3^])&.>>:i.y

c=.check_rou&.>p

(*#&>c)#c,.p

)


NB. check_rou - Select polynomial roots that are roots of unity. Each

selected is returned with the unity power. In polar coordinates a root must have a radius of 1 and the angle must be a "small" number of rotations to become a multiple of o.2 . I picked 10000 as "small". Maybe that's too big.

check_rou=:3 : 0

r=.~.;}.p.y

r=.r#~1=|r

m=.10000>s=.*./"1]2 x:(12 o. r)%o.2

m#s,.r

)

NB. ______________________________________________________

If I do "golf 8" J crashes with a Windows message that jqt.exe has stopped

working.

JVERSION

Engine: j701/2011-01-10/11:25

Library: 8.02.09

Qt IDE: 1.1.2/5.3.0

Platform: Win 64

Installer: J802 install

InstallPath: c:/j/j64-802


This is on Windows 7 with 8G of memory.
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Met vriendelijke groet,
@@i = Arie Groeneveld

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