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Re: Removing constant multiples from polynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg73417] Re: [mg73383] Removing constant multiples from polynomials
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 16 Feb 2007 00:53:49 -0500 (EST)
• References: <200702150955.EAA04553@smc.vnet.net>

On 15 Feb 2007, at 10:55, Azumanga wrote:

> I am working on an algorithm which manipulates sets of polynomials.
> Often it produces (after an application of FullSimplify) polynomials
> like:
>
> 1276(x-1)(y-2)/397
>
> I'm only interested in the solutions to the polynomial, so to me this
> is "equivalent" to:
>
> (x-1)(y-2)
>
> As a short-term solution I call "GroebnerBasis" on the single
> polynomial, which seems to perform this simplification. However is
> there a simpler method?
>
> Thank you,
>
> Chris
>
>

GroebnerBasis does it because it outputs a reduced Groebner basis of  
the polynomial ideal containing your polynomial(s). I can't imagine  
what you can possibly mean by a "simpler method" in this case? Both  
in terms of the length of the code you need to write and of the  
actual algorithm that is used I don't think there is any genuinely  
"simpler way". Of course there is a practically countless number of  
programs you could write that yourself that will do it; for example:

Times @@ (Power @@@ DeleteCases[
       FactorList[1276(x - 1)(y - 2)/3], _?(FreeQ[#, x | y] &)])

but you can hardly call this "simpler".

Andrzej Kozlowski

• Follow-Ups:
  • Re: Re: Removing constant multiples from polynomials
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>

• References:
  • Removing constant multiples from polynomials
    • From: "Azumanga" <4zumanga@gmail.com>