[Axiom-developer] Re: A bit of statistics trivia for Maple and Mathematica

[TimDaly]

On Nov 19, 1:55 pm, Roman Pearce <address@hidden> wrote:
> On Nov 19, 5:55 am, "Nasser M. Abbasi" <address@hidden> wrote:
>
> > I did a count of the number of functions in Mathematica 7 the other day, and
> > I figured I should do one like this for Maple as well.
> ...
> > Yes, I know, counting number of functions can be misleading as an indication
> > of the functionality provided by the system. As one function can be
> > implemented to have many different options which ends up doing the work of
> > 50 other smaller functions...but still, useful to get an idea about this.
>
> My knowledge of both is limited, but Mathematica does seem to put a
> lot of its core functionality into options.  For example, the Groebner
> Walk algorithm is an option to the GroebnerBasis command (not sure
> about FGLM).  Maple has this as well, but there are also separate
> commands to run the FGLM or Groebner walk algorithms, assuming the
> input is a Groebner basis.  I prefer this approach, but the option
> routine is not bad either because people complain all the time that
> Maple has too many commands :)
>
> What I would love to see is a side-by-side comparison of algorithms,
> organized into different domains, with some kind of subjective
> rankings for generality and speed.  Call it "the world's longest
> flamewar" :)  It would be useful and interesting though.

A side-by-side comparison of algorithms would be excellent.
Even a function-to-function rosetta-stone translation is great.
There are lots of fascinating things to be found.

I have compared the answers to integration for Axiom, Maple,
MMA, and Maxima on the issue of branch cuts. Curiously it
seems that Axiom and Maple make the same choice and
MMA and Maxima make the same choice, different from the
Axiom/Maple choice. Since the choice is somewhat arbitrary
it would be nice to have some flame in this area. In fact,
there seems to be no reason why this can't be a dynamic
choice.

Sage is claiming an effort to reimplement some of the
integration algorithms. I do not know in which camp they
will end up but hopefully it won't be a third camp.

How would such an effort be organized?

Tim