I would guess that most (maybe 85%) of indefinite integration
problems posed to macsyma are done by trivial heuristics and the
"derivative divides" method. Another 10%
by second-stage transformations in Moses' SIN program.
Maybe 3% need the Risch algorithm.
And 2% can't be done.
That is not to say the Risch algorithm is not interesting.
Just not as important as you might think, in practice.
It does not deal with functions integrable in terms of
special functions, for example.
Much info on this is described in a paper in Comm. ACM by Joel Moses.
(August, 1971).
I personally like the approach of the Mathematica reference
book, but I understand that many people find it difficult
to use.
For many commands there is a difficult line to draw between
describing too much and too little. Some kind of layered
approach "for more details, click here..." might help.
RJF
synthespian wrote:
> On 18 Apr 2002 09:31:33 -0500
> James Amundson <amundson@fnal.gov> wrote:
>
>
>>On Sat, 2002-04-13 at 13:53, synthespian wrote:
>>
>>>Hi-
>>>
>>> This is a very good question. In the documentation, it said
>>>the risch fucntion would automatically be called in the case of nested
>>>exponentials and algorithms, which obviously didn't happen.
>>>
>>It's just a bug. It is/will be fixed.
>>
>>
>>> Also, I feel the documentation is not clear regarding
>>>integration.
>>>
>>Exactly what did you find unclear in the documentation?
>>
>>--Jim
>>
>>
>
> Hi Jim-
>
> Well, I felt the use of the risch function, being such a common and often-executed task, seems kind of "lost" in the text.
> More emphasis should have been given to it in the help file, IMHO.
>
> Regs
> Henry
> synthespian@uol.com.br
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