Re: Replacing an expression by an expression

• To: mathgroup at smc.vnet.net
• Subject: [mg55647] Re: [mg55625] Replacing an expression by an expression
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Fri, 1 Apr 2005 05:36:19 -0500 (EST)
• References: <200503310624.BAA15217@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

> I have a 8 x 8 symbolic matrix B of complicated entries.
> Several partial expressions, however, can be simplified. Sample:
>
> rep= {(J12*x14-J11*y14)*(J12*(x32+x43)-J11*(y32+y43)) -> A0*(A1-A0)};
>
> The left expression appears verbatim in entry B[[1,1]], which is
>
> -(L21*(J12*x14-J11*y14)*(J12*(-x32-x43)+J11*(y32+y43)))/
> (16*A412*J*(J11^2+J12^2))
>
> But when I say B=B/.rep, nothing happens.  For a few entries I could do
> cut and paste by hand:
>
> -(L21*  A0*(A1-A0)    )/
> (16*A412*J*(J11^2+J12^2))
>
> But it get tedious and error prone for 64.  Any suggestions on how to
> get Mathematica to do the replacement?

Your notion of verbatim might need some tuning. Those expressions, while
mathematically equivalent, do not evaluate to the same thing (look at
placement of minus signs).

Algebraic replacement comes up from time to time, e.g. in

http://forums.wolfram.com/mathgroup/archive/2004/Feb/msg00205.html

Here is the tactic noted in that post.

replacementFunction[expr_,rep_,vars_] := If [
PolynomialQ[Numerator[expr],vars] &&
PolynomialQ[Denominator[expr],vars],
PolynomialReduce[expr, rep, vars][[2]], expr]

expr = -(L21*(J12*x14-J11*y14)*(J12*(-x32-x43)+J11*(y32+y43)))/
(16*A412*J*(J11^2+J12^2));

rep = (J12*x14-J11*y14)*(J12*(x32+x43)-J11*(y32+y43))-A0*(A1-A0);

InputForm[replacementFunction[expr, rep, Variables[expr]]]

Out[12]//InputForm=
(-((A0^2*L21)/(A412*J*(J11^2 + J12^2))) +
(A0*A1*L21)/(A412*J*(J11^2 + J12^2)))/16

Daniel Lichtblau
Wolfram Research

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