Re: Factoring Polynomials

In article <Xns982EB0B9F208Dlkajehoriuasldfjknak@xxxxxxxxxxxxxx>,
John Schutkeker <jschutkeker@xxxxxxxxxxxxxxxxxxxx> wrote:
"Nathan" <ntspam2@xxxxxxxxxxxx> wrote in
news:1156807252.010769.187280@xxxxxxxxxxxxxxxxxxxxxxxxxxx:

John Schutkeker wrote:
Does anybody know what is the name of the theorem proving it
impossible to find an algorithm to factor polynomials of order >5?
TIA.

Your question as asked is incorrect, but the subject I think
you want
is Galois theory.

That would be a general algorithm that's impossible. I
expected that there
would be exceptions, depending on their specific forms.

No, this has very little to do with algorithms. The roots
in general don't have expressions in terms of radicals.
It's not a question of how to find some expression, it's that
the expression doesn't exist. On the other hand, it is
quite possible to express the roots in other ways, e.g. using
hypergeometric functions.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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