Re: Polroots/mod suggestion

[Bill Allombert <Bill.Allombert@math.u-bordeaux1.fr>]

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.