Re: [Axiom-mail] Help in axiom

[Martin Rubey]

"Alasdair McAndrew" <address@hidden> writes:

> And even in HyperDoc, there are very few examples.  For instance, I was
> trying to find the defining polynomial of a finite field.  I discovered that
> there is a command definingPolynomial, but I couldn't find any examples on
> its use, nor a comprehensive help page about it.  There are some simple
> examples in HyperDoc (calculus, graphics, linear algebra etc), which is
> incredibly helpful, but there doesn't seem to be this level of help available
> for ALL commands, as I believe there should be.

You are quite right.

Your best bet for examples is, I guess, to look into the Axiom Book by Jenks
and Sutor. It has many examples and comes with the distribution, or online:

http://wiki.axiom-developer.org/Mirrors?go=/public/book2.pdf&it=Axiom+Book

Waldek: I didn't find the book in wh-sandbox? How come?

I found "definingPolynomial" on page 359, Section 8.3 "Manipulating Symbolic
Roots of a Polynomial." using the search facility of my pdf viewer.

Since this is probably not the thing you had in mind, I looked for "finite
field", and found that section 8.11 is the right place. Thus,

F ==> FiniteField(2,12)
                                                                   Type: Void
(2) -> definingPolynomial()$F

         12    3
   (2)  ?   + ?  + 1
                                Type: SparseUnivariatePolynomial PrimeField 2
should be what you want.

I do agree however, that the examples of the book should be integrated into
HyperDoc. This should not be too difficult, only, it has not been done (yet).
There is a short tutorial within HyperDoc on how to write new pages: Reference
- HyperDoc. RECLOS has an example page, RECLOS.ht in hypertex/pages shows how
to do it.

If somebody has time, it would be great to make the various sections of the
book example pages in HyperDoc. I think that Waldek is the one who knows how to
do it properly.

Waldek: RECLOS.ht says at the beginning:

% Copyright The Numerical Algorithms Group Limited 1992-94. All rights reserved.
% !! DO NOT MODIFY THIS FILE BY HAND !! Created by ht.awk.

So, which one is the source file?

> From my limited understanding, it would seem that Axiom is superb for the
> development and implementation of mathematical algorthms (such as Martin
> Rubey's Guess package), but that it would go even further, and have greater
> reach in the mathematical community, with more comprehensive, and more easily
> accessible help.

I think you are quite right. For me, personally, the inversion of a matrix is
quite a neat example why axiom could succeed in teaching.


All the best, and PLEASE don't give up,

Martin