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Re: Show doesn't work inside Do loop ?

• To: mathgroup at smc.vnet.net
• Subject: [mg102013] Re: Show doesn't work inside Do loop ?
• From: AES <siegman at stanford.edu>
• Date: Sun, 26 Jul 2009 03:56:52 -0400 (EDT)
• Organization: Stanford University
• References: <32390795.1248259308283.JavaMail.root@n11> <h4951e$q2e$1@smc.vnet.net> <21621663.1248432817472.JavaMail.root@n11> <h4eeul$spv$1@smc.vnet.net>

In article <h4eeul$spv$1 at smc.vnet.net>,
 "David Park" <djmpark at comcast.net> wrote:  (emphasis added)

> 
> _On the other hand, Show does not generally generate a cell._ 
> 
> Of course, it is easier to just apply Print to the Show or Plot statements.
> So it is possible to make Show generate output cells, but it _normally_
> doesn't do so. It normally only generates expressions, which because of its
> special behavior a Do statement does not display.

1)  Re your statements above: executing a single Input cell containing 
just

   Show[ Graphics[ Circle[ {0, 0}, 1] ] ]

certainly generates an Output cell containing what looks like a 
"graphic" or "plot" to me.

Is executing a cell containing a simple expression somehow an "abnormal" 
process or action?

2)  On a more general note:  Suppose you have an expression which 
contains an explicit symbol x , such that if you execute three 
consecutive cells containing

   x=1; expr
   x=2; expr
   x=3; expr

or maybe

   expr/.x->1
   expr/.x->2
   expr/.x->3

you get three output cells containing three successive instances of expr 
(whatever that is) -- or appropriate error messages if executing expr 
one of those times has some side effect that messes up a subsequent 
execution.

Would it not be reasonable to expect a cell containing

   Do[ expr, {x,1,3} ]

to do _exactly_ the same thing?

In other words, would it not be reasonable -- consistent -- sensible -- 
helpful -- the most useful -- to expect Do[ ] to be simply a "wrapper" 
that functioned in exactly that manner?

I appreciate that Mathematica's Do[] apparently doesn't function that 
way -- or functions that way sometimes, based on mysterious criteria, 
but not other times; and suggest that this is not helpful or useful or 
consistent behavior for many users.  

Are there any fundamental reasons why a DoConsistently[ ] command could 
not be defined, such that DoConsistently[ expr, iterator ]  would 
repeatedly put expr into a cell with each iterator instance applied to 
it, and churn out the sequential outputs?  That, it seems to me, is what 
many users would want and expect.

• Follow-Ups:
  • Re: Re: Show doesn't work inside Do loop ?
    • From: Murray Eisenberg <murray@math.umass.edu>