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Re: Re: Integration

On 8 Nov 2003, at 18:51, Alex wrote:

>>   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.
> 1) I expected from you more than just play on words, but rather an
> advice on how to make Mathematica compute an elementary integral.
> 2) I did compute this particular integral and I challenge you and
> anybody else to give me an integral, which is computable as indefinite
> in terms of elementary functions, so that I couldn't handle it by
> myself.
> Alex

Here is an extract form MathWorld:

The Risch algorithm is a decision procedure for indefinite integration 
that determines whether a given integral is elementary, and if so, 
returns a closed-form result for the integral. It builds a tower of 
logarithmic, exponential, and algebraic extensions. The case of 
algebraic extensions is quite complicated and is therefore not 
completely implemented in any computer algebra system. Liouville's 
principle, which dates back to the 19th century, is an important part 
of the Risch algorithm. There are extensions to the Risch algorithm, 
notably by Cherry, to be able to handle some special functions.

I really do not intend to waste my time on trying to construct an 
"example" for you to "handle." In my fairly long career as professor of 
mathematics I have come across people who claimed that had proved 
Fermat's Theorem (none of their names was Wiles), disproved The Theory 
of Relativity and constructed the "Perpetuum Mobile". As a rule I 
politely agree and change the subject. Unless you are a re-incarnation 
of Evarist Galois your claim as dubious as theirs.

Andrzej Kozlowski
Yokohama, Japan

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