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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