[Axiom-developer] Re: Aldor and Axiom

[Ralf Hemmecke]

Hi Cliff,

> Agreed.  Am I correct that the logical starting point is to identify
> where the compiler ends and the math begins (whether it is set/category
> theory or Axiom's domain and cagetory implementation or whatever) and
> get the core parts documented and working on top of Aldor?

Yes, I think that is a starting point, but it is not that simple.
The logical reason why there are two libraries in Aldor (libaldor and 
libalgebra) is that the first one just provides basic functionality. 
libaldor is a kind of low-level library.

Manuel Bronstein once explained to me that libaldor is just a 
non-mathematical library. Every mathematics comes in libalgebra.
In libaldor's design, speed was one issue. For example, Array indexing 
starts at zero and thus maps without overhead to C-arrays. That causes a 
little confusion at first, but if one works with Matrix from libalgebra, 
the minimal index is 1.

There is not need to use Array except to use it as a datastructure to 
store objects. If one needs a mathematical object than one should say 
so, for example choose Vector (which has minimal index 1).

I'd happy to translate libaldor into pamphlets. (Of course, help is 
appreciated.)

Ralf