Re: Question on replacementFunction
- To: mathgroup at smc.vnet.net
- Subject: [mg109233] Re: Question on replacementFunction
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sun, 18 Apr 2010 05:58:31 -0400 (EDT)
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, carlos 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.
>