Re: Factor x^12+15/11*exp(1/3*x^3) as a product of 6 reals.

On Jan 28, 12:03 am, Gerry Myerson <ge...@xxxxxxxxxxxxxxxxxxxxxxxxx>
wrote:
In article
<68121acd-00a8-48de-8c0f-1fe30fb14...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,





 Gerry <Gerry...@xxxxxxxxx> wrote:
On Jan 27, 10:10 pm, Robert Israel
<isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
Gerry <Gerry...@xxxxxxxxx> writes:
Hi all,

how easy or difficult is this REAL factoring challenge?
I could be totally wrong but it doesn't look easy to me at all.

After tinkering a bit with this i came to the conclusion that

x^12+15/11*exp(1/3*x^3)

can be written as a product of maximum 6 reals.

For example for x=2 we get:

2^12+15/11*exp(1/3*2^3)=4115.6253401297498556...

which can be written as a product of R1*R2*R3*R4*R5*R6 reals.

What in the world are you talking about?  Any real number can be
written as the product of as many reals as you want.

The smallest factor being R1=0.69084445965123865356...

And R1 is t * (R1/t) for any nonzero real t.  So what?

And i am sure that someone can show me
how easy it is to determine the other factors.

Only if you tell us what you're really trying to do.
--
Robert Israel              isr...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics        http://www.math.ubc.ca/~israel
University of British Columbia            Vancouver, BC, Canada- Hide
quoted text -

- Show quoted text -

Hi Robert,

you are probably right however consider that we have a degree 12
polynomial

No, we don't - x^12+15/11*exp(1/3*x^3) is not a polynomial
of degree 12 or of any other degree.

which can be written as a product of prod(i=1,12,x-g(a*exp(b*x)))

Can it? What are g, a, b? Maybe you should give us a simpler example.
Can you show us how to write x^2 - e^x as a product of two things
of the form x - g( a exp( b x))? If you can do that, maybe we'll get
a clue as to what you are on about.

--
Gerry Myerson (ge...@xxxxxxxxxxxxxxx) (i -> u for email)- Hide quoted text -

- Show quoted text -

Hi Gerry,

nice to here from you !

For you i have the following example :

-x^2-exp(x)

which can be written as a product of maximum 2 factors in this case.

Factor1=(x-F1)=-I + (-1 - 1/2*I)*x - 1/8*I*x^2 - 1/48*I*x^3 -
1/384*I*x^4 - 1/3840*I*x^5 - 1/46080*I*x^6 - 1/645120*I*x^7 -
1/10321920*I*x^8 - 1/185794560*I*x^9 + O(x^10)

Factor2=(x-F2)=I + (-1 + 1/2*I)*x + 1/8*I*x^2 + 1/48*I*x^3 +
1/384*I*x^4 + 1/3840*I*x^5 + 1/46080*I*x^6 + 1/645120*I*x^7 +
1/10321920*I*x^8 + 1/185794560*I*x^9 + O(x^10)

(x-F1)*(x-F2)=1 + x + 3/2*x^2 + 1/6*x^3 + 1/24*x^4 + 1/120*x^5 +
1/720*x^6 + 1/5040*x^7 + 1/40320*x^8 + 1/362880*x^9 + O(x^10)

Which is the series expansion (first 10 terms) of -x^2-exp(x)

So tell me why can i not see this as a second degree polynomial?


Regards

Gerry
.

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