Question on replacementFunction

• To: mathgroup at smc.vnet.net
• Subject: [mg109214] Question on replacementFunction
• Date: Sat, 17 Apr 2010 06:04:46 -0400 (EDT)

```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],
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]],
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.

```

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