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Re: Re: Re: Re: Integration
The former. This is what is meant by "in principle". There are lot's of
algorithms that work "in principle" but it is very easy to produce
fairly "simple looking" cases where no answer can be expected during
the life-time of the user (or sometimes even mankind).
The fact that Mathematica does not arrive at an answer before the
user's patience is exhausted or his computer runs out of memory does
not mean, of course, that Mathematica's implementation of an algorithm
is incomplete.
Andrzej Kozlowski
On 7 Nov 2003, at 19:16, Murray Eisenberg wrote:
> Is the difficulty here merely one of time and space, or an incomplete
> implementation in Mathematica? After all, Risch's by-now old algorithm
> determines whether a given elementary function has an elementary
> antiderivative and, if there is one, finds it in finitely many steps.
>
> Andrzej Kozlowski wrote:
>
>> On 4 Nov 2003, at 17:23, Alex wrote:
>>
>>
>>> Wolfram proudly declares that his Mathematika can handle any integral
>>> computable in terms of elementary functions. Well, here is one,
>>> which
>>> it can not handle, and I am pretty sure, this is not the only one.
>>>
>>> Alex
>>
>>
>> There is no computer program or a human being who can do that and no
>> sane person would make this sort of claim. Unless, that is,"can
>> handle"
>> means "can handle in principle" - in other words, there are no
>> specific
>> types of such integrals it "can't handle", in which case the claim is
>> valid.
>>
>>
>> Andrzej Kozlowski
>> Yokohama, Japan
>> http://www.mimuw.edu.pl/~akoz/
>>
>>
>
> --
> Murray Eisenberg murray at math.umass.edu
> 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
>
>
>
Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
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