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Re: Apply a rule to an expression only once
*To*: mathgroup at smc.vnet.net
*Subject*: [mg116366] Re: Apply a rule to an expression only once
*From*: Ray Koopman <koopman at sfu.ca>
*Date*: Sat, 12 Feb 2011 05:18:13 -0500 (EST)
*References*: <ij2v15$7vn$1@smc.vnet.net>
On Feb 11, 1:20 am, Guido Walter Pettinari <coccoinom... at gmail.com>
wrote:
> Dear Andrzej,
>
> thank you for your answer. Your example works indeed, but I would
> rather prefer not to modify my original rule, which is much more
> complex than the one I quoted in the example. I want the rule to
> stay the most general as possible, since it is used elsewhere in my
> package and a redefinition will break it.
>
> My package transforms mathematical equations from a real [x,y,z]
> space to a Fourier [kx,ky,kz] space. The main ingredient is a rule
> that applies the necessary derivative & coordinate transformations on
> single terms (e.g. Derivative[1,0,0][ f [x,y,z] ] -> I kx f [kx,ky,kx] ).
> This works perfectly fine on linear terms, but things get more
> involved when dealing with quadratic terms. In fact, the Fourier
> transform of a quadratic term, say f [x,y,z] g [x,y,z], is a
> convolution term of the form C [ f [k1,k2,k3] g[q1,q2,q3] ],
> where C[] denotes a convolution integral over k1,k2,k3 and q1,q2,q3.
>
> Aside from mathematical details, I would like to know a way to
> change the expression:
>
> expr = f [ x ] g [ x ] h [ x ] .....
>
> into
>
> f [ k1 ] g [ k2 ] h [ k3 ] ....
>
> by applying in a proper way the following rule:
>
> rule[k_] := f_@x :> f@k .
>
> No redefinitions of the rule are allowed :-)
>
> I thought that a solution could be an option for Replace (say,
> OnlyFirst) that applies the rule only to the first occurrence of
> the pattern:
>
> expr // Replace [ #, rule[k1], OnlyFirst->True ]& //
> Replace [ #, rule[k2], OnlyFirst->True ]& //
> Replace [ #, rule[k3], OnlyFirst->True ]& // ...
>
> but I do not know how to implement the "OnlyFirst" bit.
>
> Please note that (i) I do not care which function gets which
> dependence, e.g. f[k2]g[k3]h[k1] is equally good for me, and
> (ii) I do not know the names of the functions, I only recognize
> them by their coordinate dependence (usually x,y,z).
replaceFirst[expr_, rule_] := MapAt[ Replace[#, rule]&,
expr, Position[expr,rule[[1]]][[1]]]
expr = f[x] g[x] h[x];
rule[k_] = f_[Except[k1|k2|k3]] :> f[k];
Fold[replaceFirst, expr, rule/@{k1,k2,k3}]
f[k1] g[k2] h[k3]
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