Re: Arxiv paper supposedly gives roots of any polynomial?

From: Christopher J. Henrich (chenrich_at_monmouth.com)
Date: 09/09/04 

Date: Thu, 09 Sep 2004 20:39:45 GMT

In article <pan.2004.09.09.18.06.22.271009@hotmail.com>, Ivo
<munaught@hotmail.com> wrote:

> I have a question about the following
> arxiv paper: http://arxiv.org/pdf/math.CA/0408264. Word has it that it
> shows a method that results in all the roots of a given polynomial. But
> doesn't that contradict Abel's impossibility theorem? If so, what /does/
> the paper say? (I don't have access to the first paper that is referenced
> and the whole does not make any sense to me.)

The expression of a root is as the sum of a power series. All the
coefficients of the polynomial are held fixed except for the one
belonging to the zero-th power of the unknown. Then the unknown will
be an algebraic function of that coefficient. The paper sketches a
technique for expressing this algebraic function as a power series.

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