Re: [Axiom-mail] The capabilities of Axiom

[root]

No, it wasn't a mareting ploy. Barry Trager's thesis
contains a "decision procedure" for these integrals.
It either returns an answer or the original integral
there is no integral. Failure to return an answer
implies that the integral does not exist. This code
is implemented. (Barry Marshall Trager, 
Integration of Algebraic Functions, Ph.D Thesis 1984
MIT EECS dept.)

Manuel Bronstein did the same for elementary functions 
(Manuel Bronstein "Integration of Elementary Functions"
Ph.D. thesis 1987 UC Berkeley ).

All cases of the Risch algorithm are not coded however.
Manual has worked on several cases, I believe the
transcendental cases, from time to time.

The source code is available as part of the open source
version of Axiom. The thesis work will be integrated as
part of the documentation of these domains when time
permits.


>    I seem to recall having read that the commercial
>version of Axiom contained a complete implementation
>of Risch's algorithm for computing integrals in terms
>of elementary functions. 
>
>    The marketing blurb would then boast that if Axiom
>is not able to return an integral in closed form in
>terms of such functions then it has effectively proved
>that such an integral does not exist.
>
>    This raises two questions:
>
>    1) Was that assertion a truthful one, or just a
>marketing ploy?
>
>    2) If it was true, is such code available in the
>open source version?

Tim Daly
address@hidden
address@hidden