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From: "John D'Errico" <woodchips@rochester.rr.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: polynomial factorization
Date: Fri, 22 Feb 2008 23:26:03 +0000 (UTC)
Organization: John D'Errico (1-3LEW5R)
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"Dejun Wang" <dejunwang@yahoo.com> wrote in message 
<fpnkeu$h3g$1@fred.mathworks.com>...
> Hi, I have a polynomial in the following form:
> H(z)=[z^4+a3*z^3+a2*z^2+a1*z+a0]/
> [z^5+b4*z^4+b3*z^3+b2*z^2+b1*z+b0], where a3-a0,b4-b0 are 
> known.
> I want to obtain a factorized polynomial in the form of 
> H(z)=A/(z-p0)+B/(z-p1)+C/(z-p2)+D/(z-p3)+E/(z-p4), I know 
> I can use roots to get p0-p5, but is there a function that 
> I can use to get the value of A,B,C,D,E? Or do I need to 
> create my own symbolic equations to solve this?

It is impossible in general to factorize a
symbolic polynomial of degree 5 or higher.

http://en.wikipedia.org/wiki/Abel-Ruffini_theorem

John