Re: Question on replacementFunction
- To: mathgroup at smc.vnet.net
- Subject: [mg109282] Re: Question on replacementFunction
- From: carlos at colorado.edu
- Date: Tue, 20 Apr 2010 05:51:49 -0400 (EDT)
- References: <hqel40$m31$1@smc.vnet.net>
On Apr 18, 3:58 am, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote:
> I can see a bug in replacementFunction. The following code fixes it:
>
> replacementFunction[expr_, rep_, vars_] :=
> Module[{num = Numerator[expr], den = Denominator[expr],
> hed = Head[expr], base, expon},
> If[PolynomialQ[num, vars] &&
> PolynomialQ[den, vars] && ! NumberQ[den],
> replacementFunction[num, rep, vars]/
> replacementFunction[den, rep, vars],
> If[hed === Power && Length[expr] == 2,
> base = replacementFunction[expr[[1]], rep, vars];
> expon = replacementFunction[expr[[2]], rep, vars];
> PolynomialReduce[base^expon, rep, vars][[2]],
> If[PolynomialQ[expr, vars],
> PolynomialReduce[expr, rep, vars][[2]],
> If[Head[Evaluate[hed]] === Symbol &&
> MemberQ[Attributes[Evaluate[hed]], NumericFunction],
> Map[replacementFunction[#, rep, vars] &, expr],
> PolynomialReduce[expr, rep, vars][[2]]]]]]]
>
> replacementFunction[x*y - w*z, x*y - w*z - 2*A, {x, y, z, w}]
>
> 2 A
>
> Andrzej Kozlowski
>
> On 17 Apr 2010, at 19:04, car... at colorado.edu wrote:
>
>
>
> > Could somebody explain why replacementFunction fails for
> > the simpler x*y-w*z but works for (x*y-w*z)^2? Of course the
> > erratic behavior of ReplaceAll is well known. Here are the tests
> > (I took replacementFunction from an earlier thread):
>
> > replacementFunction[expr_, rep_, vars_] :=
> > Module[{num = Numerator[expr], den = Denominator[expr],
> > hed = Head[expr], base, expon},
> > If[PolynomialQ[num, vars] &&
> > PolynomialQ[den, vars] && ! NumberQ[den],
> > replacementFunction[num, rep, vars]/
> > replacementFunction[den, rep, vars],
> > If[hed === Power && Length[expr] == 2,
> > base = replacementFunction[expr[[1]], rep, vars];
> > expon = replacementFunction[expr[[2]], rep, vars];
> > PolynomialReduce[base^expon, rep, vars][[2]],
> > If[Head[Evaluate[hed]] === Symbol &&
> > MemberQ[Attributes[Evaluate[hed]], NumericFunction],
> > Map[replacementFunction[#, rep, vars] &, expr],
> > PolynomialReduce[expr, rep, vars][[2]]]]]] ;
>
> > expr1 = x*y-w*z; res=x*y-w*z-2*A;
> > Print[replacementFunction[expr1,res,{x,y,w,z}]//Simplify]; (* fails *)
> > Print[ReplaceAll[expr1,x*y-w*z->(2*A)]]; (* OK *)
> > Print[ReplaceAll[expr1,-x*y+w*z->-(2*A)]]; (* fails *)
> > expr2 =(x*y-w*z)^2;
> > Print[replacementFunction[expr2,res,{x,y,w,z}]//Simplify]; (* OK *)
> > Print[ReplaceAll[expr2,x*y-w*z->(2*A)]]; (* OK *)
> > Print[ReplaceAll[expr2,-x*y+w*z->-(2*A)]]; (* fails *)
>
> > Summary: it works for expr =(x*y-w*z)^n if n=2,3,4...
> > also n=-2,-3,... but fails for n=1 or n=-1. Any fix? Thanks=