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Re: A Problem with Simplify

  • To: mathgroup at smc.vnet.net
  • Subject: [mg87908] Re: A Problem with Simplify
  • From: Alexey Popkov <popkov at gmail.com>
  • Date: Sat, 19 Apr 2008 23:51:03 -0400 (EDT)

> Indeed. However, there would be two problems. First,
> someone would  
> have to devise suitable algorithms and implement
> them. This may not be  
> totally impossible, but it would certainly take a lot
> of effort.  But  
> then, we would see the second problem. This "ideal
> integrate "would  
> run for ever on almost any non-trivial problem. You
> would get nice  
> "mathematical" answers to trivial ones, which would
> make you feel  
> good, and no answers to non-trivial ones, which would
> probably make  
> you a annoyed enough to complain (to the MathGroup?).
> Would that be a good way to use the time and effort
> of programmers and  
> your own money?
> 
> As for Reduce -  you should try it a little more on
> harder problems  
> than the one you have just presented. It uses some
> very beautiful and  
> powerful algorithms like Cylindrical Algebraic
> Decomposition  but they  
> have exponential or in this case "double exponential"
> complexity (in  
> the number of variables) so if you it try on
> something with more than  
> 3 variables involved you will see what I mean. Given
> the choice  
> between a program that does everything in the spirit
> of "true  
> mathematics" but can only sole trivial problems that
> can be done by  
> hand and one that gives only "generic" solutions but
> can deal with  
> cases that would take you a hundred years to do by
> hand, which one  
> would you choose?
> 
> Andrzej Kozlowski 
>

I do not see the reason why in the case of Integrate keeping track for the conditions will take more time than in the case of Reduce. As I understand it is just the same or something like.


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