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Re: Re: Integrate 5.0

  • To: mathgroup at
  • Subject: [mg44310] Re: [mg44276] Re: Integrate 5.0
  • From: Andrzej Kozlowski <akoz at>
  • Date: Wed, 5 Nov 2003 10:00:33 -0500 (EST)
  • References: <bnnvfj$61s$> <>
  • Sender: owner-wri-mathgroup at

On 4 Nov 2003, at 17:23, Woz Grrl wrote:

> Selwyn Hollis  wrote:
>> I've come to the conclusion that Integrate has become nearly worthless
>> for computing definite integrals with symbolic limits ....
> I agree. Integrate under 5.0 has gone backwards. It is unreliable,
> gives wrong answers, and puts out shonky and usually irrelevant long
> error messages ... and it is slow slow slow. Yes -> very slow. This is
> not progress.
> Wozzie

Actually what is happening to Integrate is quite typical of the early 
stages of almost any major progress. Integrate in version 5 is 
attempting to do something much more ambitious than in the past 
versions. All past versions would sometimes give answers which were 
known to be wrong except in special cases (and sometimes in all cases) 
not because of bugs but because of the heuristic methods used to obtain 
these answers. This lead to endless complaints and disputes on this 
list as to whether this sort of answers should be considered bugs or 
whether they were inevitable in computer systems like Mathematica etc. 
Now Mathematica has moved to a vastly more ambitious paradigm, where 
every incorrect answer returned by Integrate can fairly be considered a 
bug. The very early stage of this process guarantees that there will be 
many such bugs, probably for a long time to come. Moreover, it was 
always known that the new approach would involve a substantial cost in 
performance, which is why it was not attempted until computers became 
fast enough. The question you have to ask yourself is whether you would 
rather have a program that always returns correct answers fast but only 
returns them in a few cases, a program that returns many answers fast 
but without making a serious attempt to guarantee their correctness, or 
a program that tries its best to return mathematically fully correct 
answers, at the expense of speed and with added complexity. There is no 
other choice at this stage.

Andrzej Kozlowski
Yokohama, Japan

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