       Re: Simplifying Ploynomials

• To: mathgroup at smc.vnet.net
• Subject: [mg5678] Re: Simplifying Ploynomials
• From: Daniel Lichtblau <danl>
• Date: Tue, 7 Jan 1997 11:22:53 -0500
• Organization: wolfram.com
• Sender: owner-wri-mathgroup at wolfram.com

```Ersek_Ted%PAX1A at mr.nawcad.navy.mil wrote:
>
> Dear Math Group,
>
> The two polynomials "messy" and "clean" below are equivalentl.
>
> messy = c0 + a*c1 - b*c1 + a^2*c2 - 2*a*b*c2 + b^2*c2
>
> clean = c0 + c1(a-b) + c2(a-b)^2
>
> If I get a polynomial like the messy one, how can I get Mma
> to convert is to the clean polynimial.
>
> I don't yet have Version 3..0.
> Using Collect and Factor in version 2.2 does no good.
> Maybe FullSimplify in version 3.0 will work.
>
> Still I would like to do this without using FullSimplify,
> because it can take a very long time.
>
>              T.E.

Simplify and FullSimplify both give

In:= Simplify[messy]
Out= c0 + (a - b) (c1 + (a - b) c2)

To get the factorized coefficients in version 3.0, you can use either
the three-argument form of Collect, or else the grossly-underdocumented
MonomialList followed by Factor.

In:= MonomialList[messy, {c0,c1,c2},
CoefficientDomain->RationalFunctions]
2            2
Out= {c0, (a - b) c1, (a  - 2 a b + b ) c2}

In:= Apply[Plus, Map[Factor, %]]
2
Out= c0 + (a - b) c1 + (a - b)  c2

In:= Collect[messy, {c0,c1,c2}, Factor]
2
Out= c0 + (a - b) c1 + (a - b)  c2

Daniel Lichtblau
Wolfram Research
danl at wolfram.com

```

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