Actually, scratch that. I'm not testing enough of the candidate roots. I'll need to go study up on my complex arithmetic.
Thanks, -- Raul On Mon, Jun 2, 2014 at 4:54 PM, Raul Miller <[email protected]> wrote: > Here's how I think I would approach this problem (ignoring the "golf" issue): > > monicN=: (<1) >@,@{@,~ (<i:1) #~ ] > > primrootN=:3 :0 > if. 0=y do. 1 return. end. > <.&.(%&(9!:18'')) j./2 1 o. 2p1%2^y > ) > > rootsN=:3 :0 > (primrootN y)^i.2^y > ) > > polysN=:3 :0 > maybe=. monicN y > keep=. +./"#.0=maybe p."1 (primrootN y)^i.2^y > keep#maybe > ) > > #@polysN"0 i. 10 > 0 2 4 6 16 45 126 357 1016 2908 > > Note that these numbers are different from Peter Taylor's results. But > looking at the first example in his list of a polynomial which is > supposed to have a root which is a root of unity: > > (x^4) + (-x^3) + (-x^2) + (- x) + 1 > > I can't find any roots which make that one work. > > <./|1 _1 _1 _1 1 p. rootsN 4 > 0.414214 > > That's not very close to zero, so I don't think I've got any precision > errors. But I could be wrong. I'm actually pretty good at being wrong. > > Anyways, I'd like to know what the primitive root of 1 is that > satisfies that equation. I don't think I can get any farther without > that. > > Thanks, > > -- > Raul > > On Mon, Jun 2, 2014 at 4:12 PM, Dan Bron <[email protected]> wrote: >> Don wrote: >>> To the original problem. >> >> Here is the original problem: >> >> http://codegolf.stackexchange.com/questions/29901/find-number-of-polynomials-with-a-root-which-is-a-root-of-unity >> >>> Does it require only that the absolute value of the number be 1 or does it >>> require the actual definition of a primitive root of unity? >> >> How about you tell me? ;) >> >> -Dan >> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
