Re: JSH: The "Published" paper he dosen't what you to know about.

Sue wrote:
Paper published and withdrawn paper by crank/crackpot James Harris exposes

I did NOT withdraw it. The editors did after some sci.math'ers emailed
them claiming it was wrong.

They unfortunately chose to use "Withdrawn" at their site before the
journal later went belly-up, which gives the unfortunate impression
that I withdrew it.

Oh yeah, readers can note the endorsement by someone other than me.

Beckwith has Ph.D's in mathematics AND physics, but I'm sure plenty of
sci.math'ers will happily tell you that means nothing.

Amazing what means nothing to sci.math'ers when their views are
challenged.

Regardless, the fact of his legitimacy by what most people consider
adequate measure within the mathematical world itself is a point
against those who claim I am a lone person.

Oh yeah, Sue calls me some names!

I am not a crank or a crackpot. I am someone who discovered
mathematics that mathematicians do not want despite it being true.

What names might I call her in return?

the "Over Iinterpertations of Galois Theory" by mathematicians.
http://www.ne-plus-ultra.net/pubs/beckwith_factorization.pdf

ADVANCED POLYNOMIAL FACTORIZATION
James Harris
A. W. Beckwith
Department of Physics and
Texas Center for Superconductivity
University of Houston,
Houston, Texas 77204-5005, USA,
Fermi National Laboratory
Batavia, IL 60510-050

Abstract.
Algebraic method for determining distribution of factors within a polynomial
factorization, which breaks through what was seen as a barrier from over
interpretations of Galois Theory

Correspondence:
A. W. Beckwith: projectbeckwith2@xxxxxxxxx
PACS numbers : 02.10.-v, 02.10.De, 02.10.Ox , 02.20.Bb

A.M.S. (MOS) Subject Classification Codes. 11R04,11R09
KeyWords and Phrases. Polynomial factorization, Galois theory, Factorization
lemma, Ring of algebraic integers

Advanced Polynomial Factorization Approached.

Determining the distribution of factors within irrational algebraic integers
has long been considered impossible as it is not possible to do using Galois
Theory. However a simple technique through the introduction of more
variables makes it possible. To highlight the standard belief consider the
algebraic integer roots of x^2 + x - 5.

While you know that the algebraic integer factors are themselves factors of
5, can either not have non unit factors of 5? How do you know?

In looking to consider distribution of algebraic integer factors within a
factorization I'll be using a more complicated example than x^2 + x ? 5.

This paper will show, using basic algebraic methods, that given the
factorization, in the ring of algebraic integers,

65x^3 - 12x+ 1 = (a1x + 1)(a2x + 1)(a3x+ 1)

one of the a's is coprime to 5.

First I'll need a simple lemma to generalize beyond factors of a polynomial
that are themselves polynomials.

Factorization Lemma:.
Given a factor g of a polynomial P(x), further defined as a factor for all
x, which means that the value of g for a value 'a' of x is a factor of P(a),
within the ring of algebraic integers, there exists r and c such that


The key point in attacks on this paper is my stating at THAT point that
the ring is the ring of algebraic integers.

<deleted>

Therefore, with the factorization

65*x^3 - 12*x+ 1 = (a1*x + 1)(a2*x + 1)(a3*x+ 1)

one of the a's is coprime to 5, which shows where some of the algebraic
integer factors distribute despite the factors being irrational.

But an outside argument can prove that none of the a's is coprime to 5
in the ring of algebraic integers.

However, the argument given proves that one of the a's is coprime to 5.

The apparent contradiction is handled by noting that the ring of
algebraic integers is flawed in terms of coverage, so it lacks that
ability to have one of the a's coprime to 5.

An example to understand that point can be found by considering evens
to be a ring.

Then 6 is coprime to 2 within that ring because 3 is NOT EVEN and it is
crucial that you undrstand that example to get the point of the paper
and the controversy.

Quite simply, what I found is that the ring of algebraic integers is
incomplete.

That argument has never been refuted. Posters willing to step up to
the plate and challenge that claim need only give the mathematics.

I dare you.

The real problem here is that mathematicians wimped out, crumbled, and
chose to keep teaching things proven wrong, to this day.

The real story here is that the world let them.


James Harris

.

Relevant Pages

  • Re: JSH: The "Published" paper he dosent what you to know about.
    ... ADVANCED POLYNOMIAL FACTORIZATION ... Determining the distribution of factors within irrational algebraic integers ... that are themselves polynomials. ... Mathematicians have decided to hold on to flawed ideas that I easily ...
    (sci.math)
  • Re: JSH: The "Published" paper he dosent what you to know about.
    ... ADVANCED POLYNOMIAL FACTORIZATION ... Determining the distribution of factors within irrational algebraic integers ... that are themselves polynomials. ... Mathematicians have decided to hold on to flawed ideas that I easily ...
    (sci.math)
  • Re: Amateur takes on Wiless work
    ... >Mathematicians would check various elliptic curves and find they could ... Below is a copy of the paper "Advanced Polynomial Factorization" ... Factorization lemma, Ring of algebraic integers ... polynomial that are themselves polynomials. ...
    (sci.math)
  • Re: The actual math, advanced polynomial factorization
    ... > and, remember, x, m, f and u are all independent variables. ... > ALGEBRAIC INTEGERS they do not always have f as a factor. ... Then if w is any factor of r in the ring of algebraic ... My result holds for a family of polynomials. ...
    (sci.math)
  • Re: JSH: The "Published" paper he dosent what you to know about.
    ... the "Over Iinterpertations of Galois Theory" by mathematicians. ... ADVANCED POLYNOMIAL FACTORIZATION ... Determining the distribution of factors within irrational algebraic integers ... that are themselves polynomials. ...
    (sci.math)
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