JSH: Key insight, algebra

From: James Harris (jstevh_at_msn.com)
Date: 09/25/04 

Date: 25 Sep 2004 16:14:43 -0700

What I did was utilize what some might see as a neat trick as first
look at

f^2((m^3 f^4 - 3m^2 f^2 + 3m) x^3 - 3(-1+mf^2 )x u^2 + u^3 f)

then multiply through by f^2, to get

(m^3 f^4 - 3m^2 f^2 + 3m)f^2 x^3 - 3(-1+mf^2 )x u^2 f^2 + u^3 f^3

and you have this neat situation where there's a factor of f^2, but
when you multiply through with it, you can get to something quite
different, as using y=uf on the last two coefficients to get

(m^3 f^4 - 3m^2 f^2 + 3m)f^2 x^3 - 3(-1+mf^2 )x y + y^3

and if you let A = (m^3 f^4 - 3m^2 f^2 + 3m)f^2 and B = -1+mf^2 ), you
have

Ax^3 -3Bxy + y^3

and you don't have a multiple.

The mathematics handles ALL CASES as notice all I've done really is
deliberately set y in one example to uf, so that I can see how that
impacts a factorization.

That doesn't change the fact that y is an independent variable.

I simply set it to get a multiple--f^2--so that I can figure some
things out.

The math can be kind of subtle here, but it's not really that hard.

What can be hard is a will to be wrong on the part of people who fight
against the truth against all evidence.

Some of you feel a NEED to be wrong, as your biology compels you to
fight for what you were trained to believe even if mathematics says
it's false.

Your GUT INSTINCTS lead you astray, and you forget that you are a
biological machine.

You're like religious people.

Before I came along, multiples of polynomials were these trivial
things that you just divided off, but I guess maybe another lesson of
mathematics is that very little is actually trivial.

If you use a multiple as I have, you can see how factors distribute
with roots even if they're irrational, which is a powerful analysis
tool.

Now then, I point out that m and f are independent of each other so
that I can set m=0, and see what happens with a key factorization when
that f^2 multiple is divided off.

For some reason, many of you seem susceptible to the belief that
SUDDENLY a multiple of a polynomial must be a variable that varies in
how it divides off.

That's not just bizarre; it's not sane.

James Harris

Relevant Pages

  • Re: multiple.....
    ... ad is multiple of u. ... So any u in Z that divides rsmust divide rs. ... and if f,g are monic polynomials in Ksuch that fg is in Dthen ... Contents of polynomials and invertibility, ...
    (sci.math)
  • Re: JSH: Without a trace
    ... given a multiple of a polynomial it has been well ... > and it is true that you can divide 5 from that factorizaton giving ... > without leaving a trace. ... > In my case I have precedent from thousands of years of mathematics ...
    (sci.math)
  • JSH: Without a trace
    ... given a multiple of a polynomial it has been well ... and it is true that you can divide 5 from that factorizaton giving ... without leaving a trace. ... In my case I have precedent from thousands of years of mathematics ...
    (sci.math)
  • Re: What is wrong with this code?
    ... In mathematics, "bar" means b multiplied ... you would need to have multiple variables with descriptive names. ... Most multi-variable situations call for the variables to be held ...
    (comp.lang.c)
  • Re: Bring Math Arguments against this FERMAT LAST THEOREM PROOF
    ... He got to regnoise that the key ideea of the proof is original and ... > contradicting the ... > divides one of them, ... > multiple of 9. ...
    (sci.math)