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Re: More /.{I->-1} craziness

• To: mathgroup at smc.vnet.net
• Subject: [mg106555] Re: More /.{I->-1} craziness
• From: AES <siegman at stanford.edu>
• Date: Sat, 16 Jan 2010 06:11:27 -0500 (EST)
• Organization: Stanford University
• References: <200912300915.EAA17299@smc.vnet.net> <hhhmn8$o9t$1@smc.vnet.net> <hhpl28$9lf$1@smc.vnet.net> <hip8gf$t4d$1@smc.vnet.net>

> In article <hhpl28$9lf$1 at smc.vnet.net>,
>  Leonid Shifrin <lshifr at gmail.com> wrote:
> 
> > 
> > I stick to my view of replacement rules as being aimed primarily at advanced
> > users, or at least as a tool that should be used with much care.  


And one or two other responses in this thread have suggested that users 
should be given advanced training in the functioning and fine details of 
ReplaceAll before they even begin to use Mathematica.

This latter proposal strikes me as a really crazy proposition, and 
essentially impossible in the real world.  

Suppose an instructor of EE or physics undergraduates in an already 
crammed and time-limited introductory network analysis or mechanics 
course starts by going through some simple phasor analyses of linear 
electric circuits or coupled mechanical systems with one or two 
resonances "by hand". 

Then, as take-home exercises, the students are asked to analyze and plot 
some 3 or 4 or 5-resonance cases using Mathematica and Manipulate (which 
can be a very pleasant as well as educational experience) ­­ but to do 
this the students first have to have a training course on Mathematica at 
the level suggested above?  Not gonna happen.

Or, as a broader approach, suppose that training in Mathematica at this 
level is going to be expected or required (before or after admission) of 
all incoming college students who might go into any Mathematica-using 
field of study, before they can take meaningful courses in that field?   
Not gonna happen.

In any case, waking up this morning after reading 60 or 70 posts in this 
thread last night I realized that in 20+ years of using Mathematica I've 
always had a mental model of ReplaceAll as being essentially an 
**editing** tool, rather than a "mathematical" tool (whatever 
interpretation you might give to mathematical in that phrase).

When I typed in  f = expr /. rule, I expected that rule would be applied 
to expr as I originally typed it in -- or, better, to expr as 
Mathematica played it back to me in an Output cell when I typed it in 
earlier (very hard to argue with this latter interpretation, is it 
not?).  Only then would that edited version of expr be evaluated and 
assigned to f.  

Isn't this more or less how the Find and Replace All capabilities 
function in every other ordinary software program known to man?

(And isn't it how the construct /. almost always in fact functions, 
regardless of what internal shenanigans Mathematica goes through in 
processing it?)

And as a final query:  Is there a formal name in Mathematica for the 
string of characters that one types in and then sees in an Input cell 
before (and after) one hits the Enter key?  Referring both to this 
character string and to the internal representation of this input string 
inside Mathematica as an "expression" -- in fact, the same expression --  
is certainly a recipe for confusion, in debate and in understanding.