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Re: Re: Re: Re: Integration

No, not concrete grounds. However, I think any complex algorithm that 
has never been fully implemented is subject to doubt. The doubt need 
not concern just its mathematical correctness as is the case with 
proofs, but also practicability. If an algorithm  is felt to be too 
complex to implement fully it seems likely that a "full implementation" 
will not perform reasonably in practice. In such cases the only value 
of a "full implementation" is the ability to claim that you have one.

Actually, the situation with proofs is not so different. I know of more 
than one proof that has been published in a top class journal but when 
you privately asks experts in the field about it they turn out to be 
unsure of its correctness. These are extremely complex proofs that were 
accepted essentially because the referee could not find anything wrong 
with them and which very few people if anyone can inspect in every 
detail. In the case of algorithms implementation provides a more 
reliable test. Without one I think the algorithm has to be considered 
as doubtful.

Andrzej Kozlowski
Yokohama, Japan

On 11 Nov 2003, at 09:55, Murray Eisenberg wrote:

> Do you have some basis for doubting the correctness of the Risch
> algorithm?
> (Risch's work is described in a long paper in Transactions of Amer.
> Math. Soc. and a shorter one in Bull. Amer. Math. Soc., both around
> 1969-70.  It's been a while since I've looked at those; I did not check
> all the proofs myself.)
> Andrzej Kozlowski wrote:
>> Personally I am not even convinced that Risz's the algorithm correct.
>> You obviously seem to know a better one so you would do everyone a
>> favor if you implemented it for us, ort at least described it as a
>> sequence of implementable steps. Now that's a challenge worth taking
>> up.
> -- 
> Murray Eisenberg                     murray at
> Mathematics & Statistics Dept.
> Lederle Graduate Research Tower      phone 413 549-1020 (H)
> University of Massachusetts                413 545-2859 (W)
> 710 North Pleasant Street            fax   413 545-1801
> Amherst, MA 01003-9305

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