Irreducible polynomials / sum of products of linear factors
Subject: Irreducible polynomials / sum of products of linear factors
From: Richard Fateman
Date: Tue, 04 Aug 2009 17:20:24 -0700
andre maute wrote:
> On Sunday 19 July 2009, andre maute wrote:
> > Could Maxima do the following automatically?
....
no, not with a single command.
yes, you, or someone else, could write a program to exhaustively list
all possible rearrangements of terms of this nature.
Assume there are M terms in h, fully expanded. You supply k.
For each distinct partition P of the terms of h into k sets, factor the
members of P.
If they all factor into linear factors you are done.
> Two weeks and still no answer?
> Isn't this a topic in computer algebra,
> if one can't factor a given polynomial?
No, because what you are asking for is not to "factor" a given polynomial.
Factoring a polynomial P expresses P as a product of irreducible
polynomials.
Perhaps the reason you have not gotten an answer is that no one who has
looked at this has any suggestion as to how to do this other than the
obvious combinatorial search algorithm which is stated above.
RJF