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More puzzles on Check[ ], Off[ ] , Indeterminate , Overflow[ ] , etc.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg67245] More puzzles on Check[ ], Off[ ] , Indeterminate , Overflow[ ] , etc.
  • From: AES <siegman at stanford.edu>
  • Date: Wed, 14 Jun 2006 06:29:03 -0400 (EDT)
  • Organization: Stanford University
  • References: <e6ge2h$nhn$1@smc.vnet.net> <e6lhn1$nf3$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Here are some puzzles, or confused queries, about definitions and 
behavior of Indeterminate, Overflow, Underflow, Off, Check, NumericQ, 
and related symbols and operations:

(Note sure why I get caught up in these arcane situations, but I do.)

The original problem (for me) was how to make an Indeterminate numerical 
result for a symbol (call it myResult) print as just a "*" rather than 
as the word "Indeterminate" in the output from a Table definition.  The 
reason for worrying about this was order to keep the column width as 
narrow as possible, since all the successful results in my particular 
case were just single-digit integers.  I had partial success in 
accomplishing this with

   myResult = Check[myExpression, "*"]

This stopped working, however, when I Off[ ]'ed  all error messages, 
which I wanted to do just to keep the rest of the notebook printout 
neat, since all the other error messages coincided with the final 
Indeterminate result anyway.  

A reply from dh <dh at metrohm.ch> suggested switching off *all* messages 
by clearing the value of $Messages and later restoring it with

   oldmsg = $Messages; $Messages = {} and later $Messages= oldmsg
 
I didn't try this, but assume it will work.  It involves steps external 
to the actual problem calculations, however, which is an added 
complexity.  Another message, whose author I've lost, suggested just 
using

   myResult /. {Indeterminate->"*"}

in the Table specification, and that worked fine.  Another solution that 
I came up with was to write

   If [NumericQ[myResult] , myResult , "*"]

in the Table definition.  This works even *inside* a ToString[] 
operation in fact.  

But then, as I ran more cases, my expression started turning out 
Overflows and Underflows as well as Indeterminates; and I discovered 
that NumericQ didn't seem to catch Overflows and Underflows (???), and 
Off[ ] (with no argument) didn't seem to suppress the related msgs.  So, 
I'm presently using in my Table definition

    myResult /. {Indeterminate->"*", Overflow[]->"+", Underflow[]->"-"}

which seems to work, and gives me additional information in a terse 
form.  But even after some digging into the Help messages, I remain 
confused about several points:

1)  Just which messages are Off'ed by Off[ ]  (with no argument), and 
which aren't?  (and why?)

2)  Indeterminate is apparently non-Numeric, but Over/Underflow 
apparently are still Numeric?

3)  Suppose that executing myResult = myExpression leads to an 
Underflow.  Does executing  myResult = myExpression//Chop also lead to 
an Underflow?  How about a subsequent use of just myResult//Chop?

4)  Do Over- and Underflow have different behavior with respect to 
Off[ ] (or other tests or operations)?  (There were times I'd swear they 
did.)

5)  If I execute a notebook that contains Off[ ]  in the initial cell 
several times, then change Off[ ] to On[ ] and execute the complete 
notebook again, does this cancel Off[ ]?  (Again, I'd swear there were 
times that the Off[]'ed messages were not restored until I Quit 
Mathematica and re-Opened it.)


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