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Re: Replace not spotting a replacement

• To: mathgroup at smc.vnet.net
• Subject: [mg103584] Re: [mg103399] Replace not spotting a replacement
• From: "David Carter-Hitchin" <david at carter-hitchin.clara.co.uk>
• Date: Tue, 29 Sep 2009 07:38:05 -0400 (EDT)
• References: <200909201021.GAA24204@smc.vnet.net> <52579.98.212.148.221.1253480392.squirrel@webmail.wolfram.com>

Hi Daniel,

Awesome - that's a start - thank you.  Actually it doesn't spit out the
simplest variant (i.e. "mu tau") but it's a step in the right direction.  MM
internally must be doing this kind of stuff to carry out functions like
FullSimplify.

Regards,
David.

> -----Original Message-----
> From: danl at wolfram.com [mailto:danl at wolfram.com]
> Sent: 20 September 2009 22:00
> To: claranet news
> Cc: mathgroup at smc.vnet.net
> Subject: Re: [mg103399] Replace not spotting a replacement
> 
> > Hi Folks,
> >
> > Seems the replace function is being a bit dim here.  This fails:
> >
> > Sqrt[2 \[Pi]] \[Tau]^(3/2) /. Sqrt[ 2 \[Pi] \[Tau]] -> \[Mu]
> >
> > Apologies if this is an FAQ - I couldn't see anything about it.  What
> do I
> > need to do here to coerce Mathematica into making this replacement? I
> > tried using the
> > Collect function on tau first, but that didn't seem to work.  I also
> tried
> > re-writing the replacement rule as
> >
> > Sqrt[2 \[Pi]] \[Tau]^(3/2) /. Sqrt[ 2 \[Pi] ] t^(1/2) -> \[Mu]
> >
> > But still no joy.
> >
> > Anyone know?
> >
> > Many thanks,
> > David.
> 
> It's more of an Occasionally Asked Question. Replacement is working
> fine;
> the fact is, your expression does not contain \[Tau]^(1/2). Syntactic
> replacement cares about niceties of that sort.
> 
> What you want can usually be attained by algebraic replacement. I say
> "usually" because it can be a bit tricky to get the right algebraic
> relation recognized where it is needed. Here is a slight alteration of
> some code from a few years back, that works on your example.
> 
> 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[hed] === Symbol &&
>       MemberQ[Attributes[hed], NumericFunction],
>      Map[replacementFunction[#, rep, vars] &, expr],
>      PolynomialReduce[expr, rep, vars][[2]]]]]]
> 
> In[10]:= replacementFunction[Sqrt[2 \[Pi]] \[Tau]^(3/2),
>  Sqrt[2 \[Pi] \[Tau]] - \[Mu], \[Tau]]
> 
> Out[10]= \[Mu]^3/(2 \[Pi])
> 
> Some day I'll have an epiphany, or at least a minor vision, and see a
> way
> to code this so that it always just "does the right thing", whatever
> that
> might be.
> 
> Daniel Lichtblau
> Wolfram Research
> 
> 
> 
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  • Replace not spotting a replacement
    • From: "claranet news" <david@carter-hitchin.clara.co.uk>