Irreducible polynomials / sum of products of linear factors
Subject: Irreducible polynomials / sum of products of linear factors
From: andre maute
Date: Wed, 5 Aug 2009 00:39:24 +0200
On Sunday 19 July 2009, andre maute wrote:
> Could Maxima do the following automatically?
>
> Suppose one has
>
> h1 : (n+r+1)*a*d + (n+r+1)^2*d - n*b*c
> + (r+1)*a*c - (n^2-(r+1)^2)*c - n^2*b
> + n*(n+2*r+2)*a + (2*r+2)*n*(n+r+1);
>
> h2 : (a+n+r+1)*(n+r+1)*(c+d+2*n) - (c+n)*n*(a+b+2*n+2*r+2);
>
> These two polynomials are equal!
>
> Is there an algorithm to find one (all) possibility(ies),
> rewriting a given polynomial as sum of k products of linear factors?
> With k a fixed positive integer. For the example k=2 was used.
>
> Andre
>
> P.S. h doesn't factor
typo: read h1 instead of h
Two weeks and still no answer?
Isn't this a topic in computer algebra,
if one can't factor a given polynomial?
Andre