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Limits & predicates with options.

• To: mathgroup at smc.vnet.net
• Subject: [mg6999] Limits & predicates with options.
• From: Jack Goldberg <jackgold at math.lsa.umich.edu>
• Date: Thu, 1 May 1997 14:48:45 -0400 (EDT)
• Organization: Mathematics Department, University of Michigan
• Sender: owner-wri-mathgroup at wolfram.com

Hi folks:

I need some guidance in handling this call:

	Limit[f[x,a],x->0]

because the function  f[x,a]  is constructed deep inside other code.
I want to take different actions depending on whether this limit exists. 
However, I don't know how to distinguish these alternatives without
staring at the result.  The problem seems to be that Limit can return a
far larger set of outputs than I initially (and somewhat naively)
thought.  Besides the obvious, Limit can return this 

	a*Inteval[-1,1]

whose Head is Times.  So "head" testing doesn't seem like a good idea. I
am stuck here. 

What I would like ideally is a Predicate, say,  LimitQ[...] which
returns True if the limit exists and False otherwise.  Of course, at
this level of generality, one might have to wait forever for an answer!
Which leads me to a second question.

Can Predicates have options?  In this case and obvious option would be a
time constraint:  The output is False, if CPU time exceeds a preset 
upper bound. 

Thanks all

Jack Goldberg
Mathematics
University of Michigan