the roots of any polynomial equation?

This is making news...

http://www.dse.nl/~geertjan/Publikatie/The-roots-of-any-polynomial-
equation.pdf

or

http://tinyurl.com/5r4c4

-C.

--- In metatuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> This is making news...
>
> http://www.dse.nl/~geertjan/Publikatie/The-roots-of-any-polynomial-
> equation.pdf
>
> or
>
> http://tinyurl.com/5r4c4

It's a nice paper, but this sort of thing in essence has been known
for centuries. I didn't find any news reports, but one thing I did
find was this:

http://www.physicsforums.com/showthread.php?t=42402

What's being said there is complete crap.

A polynomial equation with indeterminate coefficients

x^n + a[1]x^(n-1)... + a[n] = 0

defines an algebraic variety, and an n-fold covering of C[a[1], ...,
a[n]). We can expand this covering locally, giving n power series
which define algebraic functions of n variables. Tchirnhausen in the
17th century sort of got the ball rolling for this approach. There are
also a number of ways of using various transcendental (meaning not
algebraic) functions in connection with solving the general
polynomial. The real trick is to do your solving in a slick, nice way,
and that is where this paper comes in. Uytdewilligen is a sci.math
poster, by the way, and has mentioned his paper there, but discussion
has been confined to complaints (that the download doesn't work, and
that he fails to compare how well his method works with other
methods.) It looks nice to me, but I haven't tried it.

Where did it appear in the news?

> Where did it appear in the news?

In the Netherlands, apparently.

-Carl

--- In metatuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> > Where did it appear in the news?
>
> In the Netherlands, apparently.

A followup article appeared in the newspaper yesterday.
It says the school admits its mistake in touting it as a
breakthrough and making much publicity for it.
Langrange and Poincaré have discovered similar approximations,
so it's nothing new. Uytdewilligen himself said his work is
a means of classifying the roots of a polynomial equation.
He should go to university really, so he can be given better
support.

Manuel
PS my photo of Lagrange's statue in Turin:
http://home.hccnet.nl/coul/pics/DSCN0625.JPG
and Guido in Arezzo:
http://home.hccnet.nl/coul/pics/DSCN0751.JPG

> > > Where did it appear in the news?
> >
> > In the Netherlands, apparently.
>
> A followup article appeared in the newspaper yesterday.
> It says the school admits its mistake in touting it as a
> breakthrough and making much publicity for it.
> Langrange and Poincaré have discovered similar approximations,
> so it's nothing new. Uytdewilligen himself said his work is
> a means of classifying the roots of a polynomial equation.
> He should go to university really, so he can be given better
> support.

Thanks for the update, Manuel.

> PS my photo of Lagrange's statue in Turin:
> http://home.hccnet.nl/coul/pics/DSCN0625.JPG
> and Guido in Arezzo:
> http://home.hccnet.nl/coul/pics/DSCN0751.JPG

Egad, I'm such a Europhile. If I had a graduate degree
I'd move there.

-Carl

--- In metatuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:

> Egad, I'm such a Europhile. If I had a graduate degree
> I'd move there.

Get a PhD and try for a postdoc there. It worked for me.