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Re: [Axiom-developer] Learning Axiom (Literate programming, LaTeX etc)

From: Bill Page
Subject: Re: [Axiom-developer] Learning Axiom (Literate programming, LaTeX etc)
Date: Wed, 16 May 2007 21:06:48 -0400
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Quoting Alasdair McAndrew <address@hidden>:

... One of the problems in learning Axiom is that it seems more
"difficult" than other CAS's, and there's no elementary beginners
guide.  There are the books, yes, and wonderful they are, but
nobody seems to have produced a smaller "getting started"
document, such as exists for every other CAS.

I presume that you have visited:

Have you read the introduction to Axiom by Martin N. Dunstan at:

I believe that it starts at a fairly basic level.
I have programmed in Maple, Mathematica, MuPAD, Maxima, as
well as with Matlab and Scilab, and to a certain degree they are
all very similar.   So it's just a matter of minor syntactical differences
moving from one to the other.

Well, Axiom *is* different. It is certainly not "just a matter of minor
syntactical differences". In some respects Axiom is most like MuPad
(depending on how you use MuPad). Some of the internal design of
MuPad was influenced directly by Axiom, specifically it's concept of
domains (types) and categories.
Axiom gives the impression of being the domain of the few,
rather than a workhorse for the many.

At this point in time I believe that that is a fairly accurate impression. :-( But there once was a time ... back in the early days at IBM and
largely before Maple, Mathematica and MuPad, when Axiom was
definitely in a lead position. I believe that the reasons things are
different now has more to do with how personalities, politics and
business decisions affect scientific research than any inherent
deficiency in Axiom's design.
This impression is not lessened by reading that Axiom aims to be
the "best" CAS in terms of its algorithms and implementation.  This
seems to imply that plonkers like me, who are happy if a program
just works, should keep away from trying to write code in Axiom.

Don't worry, that is just a "motherhood" statement of goals. :-) The truth
is rather different. Certainly Axiom does aim to provide the foundation
on which to build a truly comprehensive mathematical library based on
rigorous and often abstract mathematical concepts. The extent to which
it does this might still be considered very close to the "state of the art"
in spite of it's age. I think this says more about the difficulty of obtaining
this goal than it does about Axiom.
There also doesn't seem to be a repository of programs developed
by other users, a "share" directory, if you like, both for seeing
examples of Axiom programs, and also to see what's also been

There are some listed at:

but it is not complete nor is it necessarily representative of the way most
people use Axiom.
We are looking for people like you with experience in other CAS who are
willing to explore Axiom and compare and contrast it to other systems. Your input is important to the process of creating the documentation for
Axiom that you feel is currently missing as well as identifying things that
are unclear or incompletely described. I hope it will be possible for you
to contribute to this effort while you learn Axiom.
If you have questions about Axiom, there a many people on this list
who are willing to help.
Bill Page.

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