maybe, maybe not

[Jon]

The attempt is made to find the roots to polynomials.

if
N=(a[1],a[2],..,a[n])
T=(t,t^2,t^3,..,t^n)
N*T+a[0]=0 is the nth degree polynomial.

dT=(1,2t,3t^2,..)dt

-a[0]=INT N*dT = INT(a[1]+2a[2]t+3a[3]t^2+...)dt

using the virtue that
a[1]t+a[2]t^2+...=-a[0],

-a[0]=INT(-a[0]/t + a[2]t+2a[3]t^2+...)dt

which results in,

-a[0]=-a[0]ln|t|+(1/2)a[2]t^2+(2/3)a[3]t^3+(3/4)a[4]t^4+...

again, using the virtue that
a[1]t+a[2]t^2+...=-a[0],

-a[0]=-a[0]ln|t|-a[0]-a[1]t-(1/2)a[2]t^2-(1/3)a[3]t^3-..

or,


n
a[0]ln|t|=-SUM(1/p)a[p]t^p eqn i.
p=1

Both sides of eqn i. are expressed as two Taylor Series

f(c)+f'(c)(t-c)+.. = g(c)+g'(c)(t-c)+...

Consequently, after n derivatives,

c=((-1)^n a[0]/a[n])^(1/n)

After n+1 derivatives, the right hand side of eqn i. becomes zero, but
the left hand side continues to produce values and is subtracted from
the result.

If
n
D=(-1/a[0])SUM[(1/p)a[p]((-1)^n a[0]/a[n])^(p/n)] and
p=1

oo
R=SUM [(a[0]/k)((-1)^n a[0]/a[n])^(-k/n) ]
k=n+1

then

t= e^D - R

Jon Giffen

[C. Bond]

Post by Jon
The attempt is made to find the roots to polynomials.
if
N=(a[1],a[2],..,a[n])
T=(t,t^2,t^3,..,t^n)
N*T+a[0]=0 is the nth degree polynomial.
dT=(1,2t,3t^2,..)dt
-a[0]=INT N*dT = INT(a[1]+2a[2]t+3a[3]t^2+...)dt
using the virtue that
a[1]t+a[2]t^2+...=-a[0],
-a[0]=INT(-a[0]/t + a[2]t+2a[3]t^2+...)dt
which results in,
-a[0]=-a[0]ln|t|+(1/2)a[2]t^2+(2/3)a[3]t^3+(3/4)a[4]t^4+...
again, using the virtue that
a[1]t+a[2]t^2+...=-a[0],
-a[0]=-a[0]ln|t|-a[0]-a[1]t-(1/2)a[2]t^2-(1/3)a[3]t^3-..
or,
n
a[0]ln|t|=-SUM(1/p)a[p]t^p eqn i.
p=1
Both sides of eqn i. are expressed as two Taylor Series
f(c)+f'(c)(t-c)+.. = g(c)+g'(c)(t-c)+...
Consequently, after n derivatives,
c=((-1)^n a[0]/a[n])^(1/n)
After n+1 derivatives, the right hand side of eqn i. becomes zero, but
the left hand side continues to produce values and is subtracted from
the result.

If the "right hand side of eqn i. becomes zero, but the left hand
sidecontinues to produce values" then it is *not* an equation.

--
There are two things you must never attempt to prove: the unprovable --
and the obvious.
--
Democracy: The triumph of popularity over principle.
--
http://www.crbond.com

[Peter Pan]

Post by Jon
The attempt is made to find the roots to polynomials.
Jon Giffen

Mr. Jon Giffen

Dear Jon,

I am normally a very friendly and patient person, and I haven't flamed
anybody since I got my first computer some 30 years ago.

But enough is enough ...

Since about 4 weeks I am reading your attempts to make yourself a name
as a super-mathematician claiming to have solved what is not solvable
in principle, and trying to tyrannize this newsgroup with your
numerous nonsense posts and useless links to your website.

You have been asked to put your money where your mouth is and to prove
to us what you are claiming - you haven't. You haven't even made the
slightest attempt.

It appears that the only 'creative' idea in your approach is to write
a polynomial as p = N*T+a_0. There's NOTHING else what's new in your
approach. So I believe that you are just one of those nerds who claim
to have doubled the cube or found the recipe to turn iron into gold.

Jon, I'm afraid I have to say that very frankly: IT'S JUST PLAIN
BULLSHIT, SO LEAVE US ALONE.

Sorry for having used strong language, but you don't seem to
understand other statements.

[Kevin O'Neill]

What he's doing reminds me of political campaigning.

Ari

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Post by Peter Pan

Post by Jon
The attempt is made to find the roots to polynomials.
Jon Giffen

Mr. Jon Giffen
Dear Jon,
I am normally a very friendly and patient person, and I haven't flamed
anybody since I got my first computer some 30 years ago.
But enough is enough ...
Since about 4 weeks I am reading your attempts to make yourself a name
as a super-mathematician claiming to have solved what is not solvable
in principle, and trying to tyrannize this newsgroup with your
numerous nonsense posts and useless links to your website.
You have been asked to put your money where your mouth is and to prove
to us what you are claiming - you haven't. You haven't even made the
slightest attempt.
It appears that the only 'creative' idea in your approach is to write
a polynomial as p = N*T+a_0. There's NOTHING else what's new in your
approach. So I believe that you are just one of those nerds who claim
to have doubled the cube or found the recipe to turn iron into gold.
Jon, I'm afraid I have to say that very frankly: IT'S JUST PLAIN
BULLSHIT, SO LEAVE US ALONE.
Sorry for having used strong language, but you don't seem to
understand other statements.

[Proginoskes]

Post by Kevin O'Neill
What he's doing reminds me of political campaigning.

"If you repeat a lie enough times, it becomes true." Except that
mathematics can't be campaigned. (Ooh! I get to use one of my favorite
Richard Feynman quotes: "For a successful technology, reality must take
precidence over public relations, for Nature cannot be fooled.")

Post by Kevin O'Neill

Post by Peter Pan

Post by Jon
The attempt is made to find the roots to polynomials.
Jon Giffen

Mr. Jon Giffen
Dear Jon,
I am normally a very friendly and patient person, and I haven't flamed
anybody since I got my first computer some 30 years ago.
But enough is enough ...
Since about 4 weeks I am reading your attempts to make yourself a name
as a super-mathematician claiming to have solved what is not solvable
in principle, and trying to tyrannize this newsgroup with your
numerous nonsense posts and useless links to your website.
You have been asked to put your money where your mouth is and to prove
to us what you are claiming - you haven't. You haven't even made the
slightest attempt.

He's tried, but his own examples have failed him. (He worked through
the procedure for the polynomial (x-2)(x-3)(x-4) multiplied out and only
got "approximations".) But that doesn't mean anything to him, evidently.

You think that's bad, though, go back through his posts and see how long
it took for him to learn the difference between an "example" and an
"application".
-- Christopher Heckman

Post by Kevin O'Neill

Post by Peter Pan
It appears that the only 'creative' idea in your approach is to write
a polynomial as p = N*T+a_0. There's NOTHING else what's new in your
approach. So I believe that you are just one of those nerds who claim
to have doubled the cube or found the recipe to turn iron into gold.
Jon, I'm afraid I have to say that very frankly: IT'S JUST PLAIN
BULLSHIT, SO LEAVE US ALONE.
Sorry for having used strong language, but you don't seem to
understand other statements.

[David Bandel]

Post by Peter Pan

Post by Jon
The attempt is made to find the roots to polynomials.
Jon Giffen

Mr. Jon Giffen
Dear Jon,
I am normally a very friendly and patient person, and I haven't flamed
anybody since I got my first computer some 30 years ago.
But enough is enough ...
Since about 4 weeks I am reading your attempts to make yourself a name
as a super-mathematician claiming to have solved what is not solvable
in principle, and trying to tyrannize this newsgroup with your
numerous nonsense posts and useless links to your website.
You have been asked to put your money where your mouth is and to prove
to us what you are claiming - you haven't. You haven't even made the
slightest attempt.
It appears that the only 'creative' idea in your approach is to write
a polynomial as p = N*T+a_0. There's NOTHING else what's new in your
approach. So I believe that you are just one of those nerds who claim
to have doubled the cube or found the recipe to turn iron into gold.
Jon, I'm afraid I have to say that very frankly: IT'S JUST PLAIN
BULLSHIT, SO LEAVE US ALONE.
Sorry for having used strong language, but you don't seem to
understand other statements.

idiot. you just wasted your "first flame" on a usenet crackpot. and
for your info, writing a polynomial as the product of some column
vectors is far from new. in fact it's very very old.