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Re: Re: Looping

• To: mathgroup at smc.vnet.net
• Subject: [mg95929] Re: [mg95896] Re: Looping
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Fri, 30 Jan 2009 05:42:54 -0500 (EST)
• References: <glmt16$mqu$1@smc.vnet.net> <200901291056.FAA18117@smc.vnet.net> <96061AD3-433E-4217-AC48-C21E57BB602F@mimuw.edu.pl> <4981EC6A.6040809@wolfram.com>

On 29 Jan 2009, at 18:50, Adam Strzebonski wrote:

> Andrzej Kozlowski wrote:
>> On 29 Jan 2009, at 11:56, David Bailey wrote:
>>> Jeff Albert wrote:
>>>> I have a program written in Mathematica that has been running now  
>>>> for about three days.  How can I tell if it's in a loop?
>>>>
>>> The best approach is to start small, and work your way up to a big
>>> problem like that if necessary. Start by aborting the calculation  
>>> and
>>> then start testing much smaller examples.
>>>
>>> Some Mathematica functions - such as Simplify or FullSymplify -  
>>> seem to
>>> get stuck in this sort of way - if they do that, they will hang  
>>> for ever.
>>>
>>> David Bailey
>>> http://www.dbaileyconsultancy.co.uk
>>>
>> I doubt very much that they they ever get "stuck" in the way you  
>> describe. Both Simplify and FullSimplify make use of algebraic  
>> algorithms some of which have very high complexity (e.g.  
>> exponential or even double exponential in the number of variables).  
>> Even when it seems that the expression you are simplifying involves  
>> only a few variables, its algorithmic complexity may be high  
>> because transcendental parts of expressions are often treated as  
>> independent variables. Of course, the human time scale: minutes,  
>> hours, lifetimes, has not particular place in computer algebra so  
>> there is no reason at all why your program should not run for 10  
>> years and then suddenly come up with an answer.
>> In fact, I believe Simplify and FullSimplify have some built in  
>> protection against infinite loops so they are probably somewhat  
>> less likely to fall into them than some other functions. Also, note  
>> that both Simplify and FullSimplify have the option TimeConstraint,  
>> which can be sometimes useful in dealing with complex expressions.  
>> If you run FullSimplify on an expression with TimeConstraint set  
>> to, say, an hour, and if it returns to you the same expression that  
>> you originally gave to it as input, it won't necessarily mean that  
>> it had entered an infinite loop but more likely that it had  
>> attempted a transformation or a sequence of transformations which  
>> it could not complete before the time limit expired.
>> Andrzej Kozlowski
>
> Yes, Simplify and FullSimplify have built in protection against
> infinite loops, but no global time limit.
>
> The TimeConstraint option specifies a time limit allowed for a single
> transformation. If the time limit expires the current transformation
> is aborted, but then (Full)Simplify will attempt other transformations
> with a fresh time allowance for each new transformation. The default
> value of TimeConstraint is 5 minutes for Simplify and Infinity for
> FullSimplify.
>
> Best Regards,
>
> Adam Strzebonski
> Wolfram Research
>
>

Thanks a lot.  I have forgotten about his local limit/global limit  
matter. I now recall we have actually discussed it on this forum before.
I think both this time and last time I confused the option  
TimeContraint with the Mathematica function TimeConstrained. If I am  
not mistaken, that latter will provide  global time constraint on the  
entire computation but unfortunately, it will return $Aborted rather  
than the simplest form of the expression found so far when the time  
limit is exceeded. I think I know a rather clunky way to get this  
simplest form found by (Full)Simplify before the computation was  
aborted (roughly equivalent to doing a Trace) but is there a nice and  
efficient way of doing this? If not, would it not be possible and  
useful to add this ability to (Full)Simplify?

With best regards

Andrzej Kozlowski

• References:
  • Re: Looping
    • From: David Bailey <dave@removedbailey.co.uk>