Re: Re: Integrate 5.0

*To*: mathgroup at smc.vnet.net*Subject*: [mg44310] Re: [mg44276] Re: Integrate 5.0*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Wed, 5 Nov 2003 10:00:33 -0500 (EST)*References*: <bnnvfj$61s$1@smc.vnet.net> <200311040823.DAA10476@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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 http://www.mimuw.edu.pl/~akoz/

**References**:**Re: Integrate 5.0***From:*wozzboy@yahoo.co.uk (Woz Grrl)