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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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