decomposition of polynomials

From: Helmut Richter <a282244@xxxxxxxxxxxxxxxxxxxx>
Date: 15 Mar 2006 11:56:46 GMT

Let f be a polynomial over Z. It is a well-known task with smart known
solutions to find polynomials g and h over Z such that f(x)=g(x)h(x)
if such g and h exist. But I have never seen solutions to the problem
to find polynomials g and h over Z such that f(x)=g(h(x)) if such g
and h exist. Is it trivial? Has it never been attacked? I can hardly
imagine either.

Helmut Richter
.

Follow-Ups:
- Re: decomposition of polynomials
  - From: matthias
- Re: decomposition of polynomials
  - From: Dave Rusin
- Re: decomposition of polynomials
  - From: Halm
- Re: decomposition of polynomials
  - From: quasi

Prev by Date: Re: Angle Trisection
Next by Date: Re: sum of i.i.d. exponentially distributed random variables with geometrically distributed number of summands
Previous by thread: sum of i.i.d. exponentially distributed random variables with geometrically distributed number of summands
Next by thread: Re: decomposition of polynomials
Index(es):
- Date
- Thread

Relevant Pages

Re: Computer integer division
... > You do it by synthetic division of polynomials. ... Imagine you have a ...
(sci.math.num-analysis)
Re: decomposition of polynomials
... Helmut Richter wrote: ... solutions to find polynomials g and h over Z such that f=gh ... But I have never seen solutions to the problem ... a finite field into a composition of lower-degree polynomials. ...
(sci.math)
Re: Public Key, Symbolic Calculation
... I can't imagine this scheme [which you really ... With polynomials, you only perform simple multiplications and additions. ... Kiuhnm ...
(sci.crypt)
Re: decomposition of polynomials
... On 15 Mar 2006 11:56:46 GMT, Helmut Richter ... solutions to find polynomials g and h over Z such that f=gh ... A necessary condition is that h'must divide f', ... determines a finite set of possibilities for h, ...
(sci.math)
Re: decomposition of polynomials
... solutions to find polynomials g and h over Z such that f=gh ... But I have never seen solutions to the problem ... a finite field into a composition of lower-degree polynomials. ...
(sci.math)