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Re: Piecewise vs. /; ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104016] Re: Piecewise vs. /; ?
  • From: Dan Dubin <ddubin at ucsd.edu>
  • Date: Thu, 15 Oct 2009 07:19:33 -0400 (EDT)
  • References: <hashpc$qu8$1@smc.vnet.net> <hav19a$4gr$1@smc.vnet.net>

Folks --

I would respectfully disagree with the idea that /; is more general 
than Piecewise. The example given, a function that returns a 
different value in the morning than the evening, is simply a 
time-dependent function that could be constructed using Piecewise, as 
in

f[x_,h_] =  Piecewise[{{x, h < 12}, {-x, h >= 12}}];

and called via

f[x,DateList[[4]]]


  In fact, it seems to me that any difference in the way that 
Mathematica interprets Piecewise and conditionals should be removed 
from later editions of Mathematica, since as far as I can see the 
difference between them is merely a Mathematica-specific  matter of 
the mechanics of how the expressions are evaluated with little (or 
no?) utility, that causes considerable confusion among new users. I 
don't see any benefit in this distinction, but feel free to convince 
me otherwise!


>Szabolcs Horv=E1t wrote:
>>  In short, /; is a programming construct that affects evaluation.
>>  Piecewise[] is used to represent a mathematical concept: piecewise
>>  functions.
>>
>>  If you want to do mathematical operations like integration, then use
>>  Piecewise[].  Condition[] (/;) is a lot more general than Piecewise[],
>>  for example one could write a "function" that returns a different value
>>  in the evening than in the morning, which is obviously not a function in
>>  the mathematical sense, and thus can't be integrated.
>
>Got it!  Thanks to you and David for responding.
>
>--
>Erik Max Francis && max at alcyone.com && http://www.alcyone.com/max/
>   San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
>    God is love, but get it in writing.
>     -- Gypsy Rose Lee


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