[seqfan] Re: Additive combination of unique cyclotomic polynomials
jfb at brennen.net
Sat Feb 7 05:42:48 CET 2009
No, that looks good, probably just a bug in my PARI-GP script that was *supposed* to
do exhaustive search up to polcyclo(12) -- 3^12 different combinations to try
(each polynomial can have coefficient -1, 0, or +1). Apparently, it either wasn't
exhaustive or did the sums wrong. Probably it wasn't exhaustive, because all of
the sums that it did report did seem to be valid.
Thanks for finding those, but now I've got a bug to find... :)
Maximilian Hasler wrote:
>> - For x^n, what is the minimum integer A such that x^n can
>> be expressed using only some subset of the first A
>> cyclotomic polynomials?
>> The second sequence seems to begin (with n=0):
> I get
> x^5 = -polcyclo(1)+polcyclo(2)-polcyclo(3)+polcyclo(7)-polcyclo(8)-polcyclo(9)
> x^6 = polcyclo(1)-polcyclo(2)+polcyclo(3)-polcyclo(5)+polcyclo(8)+polcyclo(9)
> so 10,12 should read 9,9 - or did I get something wrong ?
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