Bill Allombert on Sun, 13 Mar 2011 15:52:48 +0100 |
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Re: Polroots/mod suggestion |
On Sun, Mar 13, 2011 at 12:53:15PM +0000, James Wanless wrote: > (Right, hopefully I really do mean to post to _this_ list this time :) > I wonder if the devs would be interested in the following suggestion > for finding roots of a general nth order polynomial, or same mod p: > The idea is basically recursive completion of the square ie, solve > for roots using the standard quadratic solution formula, but > iterated. > Each level of iteration would allow equations of up to 2^nth order > to be solved, as n++ How this is supposed to work ? > This would necessitate the introduction/evaluation of "Wanlessians", > defined recursively s.t. W[n] = sqrt(-W[n-1]). > So for instance, W[0]=1, W[1]=i, W[2]=(-1+i)/(sqrt(2)), ... > [in the mod p case, W[n] = sqrt(-W[n-1]) mod p] > If this works, and you can successfully implement it in code, I I would be quite surprised if it worked. Cheers, Bill.