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Re: [Axiom-developer] Lisp

From: Martin Rubey
Subject: Re: [Axiom-developer] Lisp
Date: 05 Mar 2008 10:49:56 +0100
User-agent: Gnus/5.09 (Gnus v5.9.0) Emacs/21.4

"Bill Page" <address@hidden> writes:

> Personally I really wish that that were true, but all of my experience with
> Axiom over the last few years demonstrates to me that using Axiom is still
> really rather difficult - too difficult for most people. 

I don't think that this is the reason. I believe rather the problem is that
axiom just can't do many things mathematicians want to do.  As a recent
example, the solver seems to be especially week.  How come that Mathematica
spits out the solutions to Rainer Gluege's problem without any tricks, while
axiom cannot do it at all?

> I think Axiom has some very good ideas, some of which have not yet really
> found their way into other more modern languages, but the gap has narrowed
> considerably in the last few years. And now there is a very active computer
> algebra project called Sage doing almost all of the things that would really
> be worth doing in Axiom, in Python instead.

Sage got - in my opinion - two things right: it started by packaging many other
excellent, specialised, programs with it, and it is lead by a charismatic,
skilled person.

Axiom, on the other hand, has the problem that it tried to do everything "in
axiom", which works only if you have some 20 mathematicians and another 20
programmers available.  In fact, it won't even work then.

As you know, I'm quite convinced that Axiom, especially with Aldor, got many
things right.  However, the way it currently is, it is mostly interesting for
people who want to implement well understood stuff.  (Axiom was never very good
for "experimental" programming, although it could be.  The recent bugs that
surfaced in the type inference machine indicate why.  My - currently stalled,
because of the laptop having the files on it - project to clean up Matrices and
Aggregates is done in the hope to make things a little easier)

The two biggest disappointments at the moment are the failure to make Aldor
free or, alternatively, integrate the more important Aldor's features in SPAD,
and, the difficulties encountered when actually trying to use the species
stuff.  Yes, the design (mostly by Ralf) is brilliant. But in axiom I have to

    lab: SetSpecies ACINT := set [i::ACINT for i in 1..n]
    all := [structures(lab)$Partition ACINT]$ACList Partition ACINT::List 
Partition ACINT::List SetSpecies SetSpecies ACINT::List ACList SetSpecies 
ACINT::List ACList ACList ACINT::List List ACList ACINT::List List List 
ACINT::List List List INT

to get all set partitions of [1..n] as a list of list of lists. Not that nice.
Note that this conversion is not "difficult", only tedious.  I might put an
effort into preparing a special "axiom" version of the species project, but
currently I'm trying hard to find a job in academia.


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