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Re: Inconsistent behaviour of Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112483] Re: Inconsistent behaviour of Integrate
  • From: Andreas Maier <asmaier78 at googlemail.com>
  • Date: Fri, 17 Sep 2010 06:40:22 -0400 (EDT)

Andrzej Kozlowski wrote:
> Well, on a fast computer Mathematica will consistently produce the better result, unless your CPU is busy with other things or you on purpose decide to reduce performance. On a slower computer you will get the better (more "reduced") result on a second attempt after cashing it. The alternative would be to let your computer run for much longer. That would make Integrate more consistent but would also probably make many users loose patience. 
> Having everyone get the "less good" result would not seem to me like "progress". 

The problem in my case is that the result produced on a slower computer is actually more useful
than the result produced on a faster computer. The solution

Out[1]= 1/6 (Sqrt[2] + ArcSinh[1])

is much more useful to me than

Out[2]= 1/24 (4 Sqrt[2] + Log[17 + 12 Sqrt[2]])

So not in every case more CPU-h means a better result. And the reason seems to be that
Mathematica can expand (1 + Sqrt[2])^4 to 17 + 12 Sqrt[2], but not factorize
17 + 12 Sqrt[2] to (1 + Sqrt[2])^4 again. So when running for a longer time Mathematica
seems to fall into a "trap" and is not being able to go back to the simpler result.
Another possibility is that Mathematicas algorithm somehow considers Out[2] as
simpler result than Out[1]. But this is odd, since Out[2] uses more operations
and bigger integer number than Out[1]. Here it would be nice if one could influence
the criteria Mathematica uses to consider one expression as simpler than another.

Andreas Maier


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