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>