Re: Maple Vs Mathematica debugging

"Richard J. Fateman" <fateman@xxxxxxxxxxxxxxxxx> wrote in message
news:dn2e9b$16kg$1@xxxxxxxxxxxxxxxxxxxxx
>
> The reviewer in the cited article had a particular highly oscillatory
> integral that Mathematica could numerically integrate and Maple could
> do only very slowly. It seems to me that the method could be added
> to Maple without much difficulty, and also the method might be irrelevant
> to most people trying to decide between the two programs. Nevertheless,
> the reviewer seemed quite upfront about how he formed his opinion.

The reviewer was wrong in a few places writing about numerical integration
in Maple. In particular, specifying a method (including Monte Carlo for
multivariable integrals) is possible. The description of doing that can be
found in ?int,numerical . In cases like that, _Dexp often works quite well.
It is rather slow, because it is "Maple method", i.e. not compiled in a C
program. Besides, evaluating of BesselJ is also slow. In general, Maple uses
fast external NAG methods, such as _d01akc for numerical integration.
Unfortunately, current implementation of NAG methods doesn't work with
special functions - BesselJ in particular. That could be rather easily
corrected, I think, by including BesselJ in the list of functions available
to evalhf through the corresponding NAG procedure, but it is not done yet.

Alec


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