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Re: Re: Replace and ReplaceAll -- simple application

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106083] Re: [mg106038] Re: Replace and ReplaceAll -- simple application
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Fri, 1 Jan 2010 05:33:31 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <200912270006.TAA12080@smc.vnet.net> <hh72dp$kud$1@smc.vnet.net> <hh9vfo$1rk$1@smc.vnet.net> <200912290618.BAA02632@smc.vnet.net> <hhf5kg$go6$1@smc.vnet.net> <200912310814.DAA24681@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

That's an instructive example on the point being discussed. As you note,

   R  + I w L /. I -> -I

works "as expected".  But so does:

   I /. I -> -I

What does NOT work is either of:

   R - I w L /. I -> -I
   -I /. I -> -I

Each pair of results is consistent within itself, whereas the second 
pair seems on first exposure to be inconsistent with the first pair.

Evidently a case of unwarranted generalization by the "naive" user, 
worthy of further digging: how does ReplaceAll really work?  (I say 
"naive" here without intending any negative connotation!)

In my experience, eventually the same sort of dissonance will arise with 
any system where one is using only heuristics to accomplish tasks rather 
than the actual parsing/evaluation rules of the language.  Not a moment 
for grief or cause for complaint about inconsistencies, but rather an 
opportunity for learning more.

Language designers might claim, "Well, that's just the way it is."  But 
that's really an inadequate response.  Yes, one does eventually just 
have to learn and accept the underlying principles and rules.  Still, 
there are interesting cognitive and pedagogical issues here (but NOT 
issues of flawed language design).

But enough of "an I for an I" for today: time to celebrate the approach 
of New Year!

P.S. I'm not sure what MathWorld is supposed to do with this: MathWorld 
is about mathematics, not Mathematica; it just happens to have some 
Mathematica code available. I would not at all expect MathWorld to 
instruct me on using Mathematica.


AES wrote:
> In article <hhf5kg$go6$1 at smc.vnet.net>,
>  Murray Eisenberg <murray at math.umass.edu> wrote:
> 
> [Re the  I -> -I  problem in particular:]
>  
> ... it's very tempting to note that these 
> tFunc's contain nothing but purely real circuit elements (R's. L's and 
> C's, or masses and spring constants, or whatever), and I.  
> 
> And a quick test confirms that the rule {a->-a} does what it's supposed 
> to (whether or not a has a minus sign in front of it).  Or, a quick test 
> confirms that I->-I properly converts R  + I w L  into R - I w L.  Why 
> shouldn't it???  It just does what you'd expect a global find and 
> replace to do, or what you'd do "by hand" -- right?
> 
> Take a look at the Mathworld entries for "phasor" and "transfer 
> function" and see how far down you'd have to dig to get an explicit 
> warning that the previous paragraph is misleading.  (And note that the 
> entry for "Phasor" does not contain a "SEE ALSO:" for the term "Complex 
> Conjugation", and the link to that term within the text does not -- so 
> far as I can see -- give any hint the the rule I->-I will fail for an 
> expression containing -I.)

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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