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Re: Re: Re: Integration

• To: mathgroup at smc.vnet.net
• Subject: [mg44371] Re: [mg44308] Re: [mg44277] Re: Integration
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Fri, 7 Nov 2003 05:16:14 -0500 (EST)
• Organization: Mathematics & Statistics, Univ. of Mass./Amherst
• References: <bmg0li$e9k$1@smc.vnet.net> <bmj2os$prs$1@smc.vnet.net> <200311040823.DAA10480@smc.vnet.net> <200311051500.KAA26314@smc.vnet.net>
• Reply-to: murray at math.umass.edu
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: Re: Re: Re: Integration
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>

• References:
  • Re: Integration
    • From: akhmel@hotmail.com (Alex)
  • Re: Re: Integration
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>