       Re: Better use of PolynomialReduce?

• To: mathgroup at smc.vnet.net
• Subject: [mg121062] Re: Better use of PolynomialReduce?
• From: Peter Pein <petsie at dordos.net>
• Date: Fri, 26 Aug 2011 05:21:44 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j35al3\$og1\$1@smc.vnet.net>

```Am 25.08.2011 13:11, schrieb Irretrev Unable:
> I've been using
>
>
> scPhiDecomp[expr_]:= PolynomialReduce[expr, {x^2-y^2,2 x y}, {x,y}]
>
> which works great on
>
> scPhiDecomp[a x^2 + 2c x y -a y^2]
>>> {{a,c},0}
>
> but doesn't do what I want on
>
> scPhiDecomp[y (a x^2 + 2c x y -a y^2)]
>>> {{0,(a x)/2+c y},-a y^3}
>
> How do I make scPhiDecomp produce
> {{a y, c y}, 0}
> on the second expression?
>
> Thanks,
> Keith
>

Hi Keith,

the results of PolynomialReduce often depend on the order of the
variables ( {x, y} vs. {y,x} ).

Try both and select the less complex one.

In:= newscPhiDecomp[expr_] :=
SortBy[
PolynomialReduce[expr, {x^2 - y^2, 2*x*y}, #1] &
/@ {{x, y}, {y, x}},
LeafCount][]

In:= newscPhiDecomp[a*x^2 + 2*c*x*y - a*y^2]
Out= {{a, c}, 0}

In:= newscPhiDecomp[y*(a*x^2 + 2*c*x*y - a*y^2)]
Out= {{a*y, c*y}, 0}

hth,

Peter

```

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