Re: [Axiom-developer] A{ld,xi}o{r,m}-Combinat

[Ralf Hemmecke]

Hello,

On 04/29/2006 11:01 PM, Bill Page wrote:
> Martin,
>
> On April 29, 2006 3:39 PM you wrote:
> > attached you find a screenshot from some code and its output 
> > that has emerged from the Axiom Workshop 2006. I hope you like
> > it. Note that the two lines in the upper frame define TreeClass
> > completely as a domain, given the domain Atom and the functors
> > CrossClass and UnionClass...
>
> Cool. Of course I am very curious about the latter two functors. :)

You find the code below. But let me add a few words. The code is 
probably not identical to the one Martin actually used in his screen 
shot, but it is the first working version of that code.

I guess, most of you might now say: well, it looks completely trivial 
and natural. Yes, that is the point! Aldor allows this. The hard thing 
actually was, to understand the MuPAD-combinat design (in particular to 
understand what a "combinatorial class" is and then to translate it into 
an appropriate design for Aldor.

Actually, I must thank Nicolas quite a bit. He showed in his talks how 
useful recursion is. And how this is currently done in MuPAD. Basically, 
in MuPAD-combinat it is of importance that one should be able to define 
combinatorial classes via a grammer. MuPAD-combinat then computes a 
fixed point for this grammar in order to get the combinatorial classes. 
And as I understood Nicolas, that code is quite huge and complicated.

The amazing thing now is that the Aldor compiler computes the fixpoint. 
That makes the code below so short.

> I hope we somehow find it possible to arrange more (and more frequent)
> such "sprints" on all sorts of Axiom subjects.

I'm all for it. We had lot's of fun, too. ;-)

> Indeed. I was pleased to note today the Bob Sutor, one of the
> creators of Axiom, added his name and "good luck" wish to the
> FreeAldor page on Axiom Wiki. :)

I very much hope that the Aldor sources can be opened. But that is only 
the first step. There needs to be a lot of teaching, too, in order to 
show people the beauty of Aldor. It is not always easy to handle such a 
powerful language, since translating the design of a project written in 
some other language to Aldor is a nontrivial task.

> > The Axiom-Aldor Workshop 2007 is going to happen next year at 
> > the RISC in Hagenberg, near Linz, Austria. The topic will be
> > "Computer Algebra meets ???" where ??? might be one of Graph
> > Theory, Algebra or Analysis.

> Graph theory sounds nice but my "wish" is really that the topic
> could be "Computer Algebra meets category theory" ... in my
> opinion the potential for category theory in computer algebra
> has not even begun to be tapped and Axiom is in a particularly
> good position to take the lead.

Oh, though I have not worked much in category theory (I only know the 
basics), I would love that. Maybe until then we could even have some 
computations in category theory implemented in Axiom...
My fear is only that there are perhaps not so many people who would want 
to come. Other opinions?

> > I believe that we can say that in terms of produced code the 
> > workshop was a tremendous success.

I would say, it was of equal importance that we spread the idea...
Nicolas, am I wrong if I say that you and perhaps your "team" now more 
seriously consider Aldor/Axiom as an option? Of course, that all depends 
on the availablility of Aldor.

> Thanks for the quick report. I am glad to hear that it turned
> out so well. Perhaps we will hear also from some of the other
> participants? Any pictures?

Yes. But I need some rest. I had a light flu that started right before 
the workshop. Now I can hardly speak anymore. :-(

All the best and also a big thanks to Martin who first came up with the 
idea to have such a workshop at RISC and who worked quite a lot for it.

Ralf