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[Axiom-developer] Re: [Axiom-mail] Axiom v. Maxima

From: root
Subject: [Axiom-developer] Re: [Axiom-mail] Axiom v. Maxima
Date: Fri, 16 May 2008 00:05:29 -0400


Thanks for the feedback.

>I've been using Maxima a bit recently, and I've been thinking about Axiom in
>comparison.  I think Axiom's mathematical strengths are undeniable, but...

Maxima is an excellent program. I know several of the developers
and they do great work. I have used it most recently to check Axiom's
answers. I compared Axiom against Schaums and then did a doublecheck
using Maxima. Maxima has one really annoying feature in that it asks
me if -some-random-expression is positive.

>   1. The Axiom community seems to be worried about the wrong things.
>   Abstruse mathematical problems, matters relating to Aldor... and yet the
>   interface languishes.  In fact, for Windows users (who make up the bulk of
>   computer users) there is no decent interface.

I've been concentrating on making Axiom more useful in general. 
Some of the features are 

  * )show domain correctly identifies the source file

  * )d op foo shows an example of how to use that function
      Given that there are approximate 10k functions in Axiom it
      will take a while before all of them have examples but the
      machinery exists and some cases are covered. More will follow.

  * )help pages have been updated. 
      There are now about 100 help pages and more are in the pipeline.
      The help pages are flat text pages so you can write your own.
      If you put your text file in the proper directory it is automatically

  * There is a tutorial book available.
      The sources are distributed with the system (see
      src/doc/bookvol1.pamphlet, an ordinary latex file), the .dvi
      file is created automatically during build, a pdf copy is
      available for free from <>, and
      paper copies are available from or (search
      on amazon for "daly axiom")

  * The Jenks textbook is available
      The sources are distributed with the system (see
      src/doc/book.pamphlet, an ordinary latex file), the .dvi
      file is created automatically during build, a pdf copy is
      available for free from <>, and
      an html version is available at

  * Some domains are already literate. 
      Look at <> for the list, which
      contains only one at the moment but will be expanded at the 
      next release cycle point later this month.

  * Regression test files have more documentation
      The student can look at the latest input files for examples.
      In particular, there are 34 new src/input/schaumNN.input.pamphlet 
      files which show how to compute 619 indefinite integrals from a 
      standard reference work (Schaums Mathematical Handbook). They
      also illustrate methods of simplification. I've also collected
      all of the rule forms used and these will appear in a new help
      page and the next version of the tutorial.

  * System commands are beginning to know about pamphlet files
      Soon you'll be able to work directly in the literate format
      and the compiler and interpreter will "do the right thing".
      Pamphlet files are the native Axiom file format. Hopefully
      this will encourage more literate programming.

>   2. Help - Hyperdoc was all very well in its day, but now looks regressive
>   and old-fashioned.  Surely help based on HTML, or even a Windows Help
>   interface, should be provided?

I really liked wxMaxima and developed a wxAxiom version but decided
to trash it. Instead of creating more code to maintain I decided to
base the user interface on the Firefox browser. Hyperdoc and graphics
will go away in their present form and become standard web pages.

In the latest release of Axiom, the hyperdoc system is based on Firefox.
All you need to do is start Axiom and then type:
and visit the rootpage.xhtml file in your distribution.
If you don't have it available yet, you can see the static pages at:
These pages are live only if you use the )browse function locally.

Many hyperdoc pages have been translated but there are still more to
be done.  The richest subtree is under "Topics". The Axiom textbook is
available under the "Axiom Textbook" link. In addition, there is new
material in the Firefox version that does not exist in the hyperdoc
version. See
    Topics -> Cryptography
    Topics -> Mathematical Models (under construction)
    Topics -> CATS (under construction)

Note that this uses MathML so you may have to upgrade your browser fonts.
The fonts are available in the zips directory of the Axiom distribution.

This is standard html so you can write your own pages. See the book
src/hyper/bookvol11.pamphlet which describes the tools available if
you want to interact with Axiom on your own pages.

If you do develop coursework I'm willing to work with you to include
those pages into Axiom's Firefox browser. See

Future releases will have a primitive Firefox front end to Axiom,
similar in spirit (but not design) to the MMA, Maple, and Sage notebooks.
I'm working on various tools in javascript but they are not ready for
release yet. I'm also in design discussions with a graphics designer
to try to maximize the user viewpoint. This will take a few release
cycles to fully emerge.

>   3. Maxima seems streets ahead in its involvement with the mathematical
>   community.  Currently there are at least two major book writing projects
>   using Maxima: "Maxima by Example" on and
>   another on  There
>   are lots of other tutorials and documents (including one by me!) on the
>   Maxima page.  But where are the user-written Axiom books and introduction
>   documents?  The biggest one - in fact the only one available from the Axiom
>   page - seems to be Martin Dunstan's tutorial from 1996!

There are currently 12 volumes in development for Axiom, of which only
one has reached publication. Each release of Axiom contains updated
material in each volume. I'll post the current state of the volumes
on the website at the next release of the system. They already exist
and can be found by searching the source tree with
   find . -name "book*"

Writing readable source material takes an astonishing amount of time.

>   4. A new user, scouting around for a freeware CAS, would be led to the
>   undeniable conclusion that Axiom is simply a hobby for a few dedicated
>   users, whereas Maxima is being developed to be useful for everybody.

Sage is certainly taking the lead in the "freeware CAS" market and
I'm actively helping that to occur. I'm on their program committee
for the Sage Day and I build the MAC OSX 10.4 binary for them.

That said, I believe that Sage is badly designed (well, accretion is
more the philosophy) and is not the way to teach students to think
about computational mathematics. The litany of problems they have
left unsolved would have to be embedded in <rant> tags.

Axiom has the philosophy that it needs to be done as a literate
program so that future people can read, understand, maintain, and
modify the system. Axiom's approach to computational mathematics
strongly emphasizes the algebraic knowledge necessary to do correct
mathematics. The symbolic approach (everything is a token that can
be manipulated regardless of mathematical meaning) is sure to cause
grief to beginning students, if not professionals.

>   5. The various forks: Axiom, FriCAS, OpenAxiom, also must make it hard
>   for the new user - which one to choose, and why?  The many many
>   distributions of Linux make choosing one awfully hard for the beginner -
>   even I, who've been using Linux exclusively for over 15 years, get confused
>   on the rare occasions I have to install a new system.  Axiom has the same
>   problem.

Sigh. <joke> To misquote Neo and the Spoon Boy from the Matrix:
              SB:  "There is no fork"
              Neo: "There is no fork?"
              SB:  "It is not the code that forks, only yourself"

What you choose to teach is a strong influence on your system choice.

>Now don't get me wrong - I like Axiom very much indeed, and I will keep
>using it, and encouraging my students to do likewise.  But I think it needs
>to reach more users if it is to really succeed, and for this it needs more
>help and tutorials, and better interfaces.

I believe we are on the same page with this. Unfortunately, most of
the pages are blank. I'm writing as fast as I can. I'm hiring a
student out of my personal funds to do some Axiom work for me for the
summer. Making a fully documented, easy (well, easier) to use system
out of an undocumented research project of this size is a glacial


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