[Axiom-developer] Of pamphlets, volumes, and algebra

[C Y]

Back in November, Tim gave the following as an overall "structure"
within which we will be working to define, describe, and document the
Axiom system.

vol 1:  tutorial
vol 2:  programming
vol 3:  reference
vol 4:  developers guide
vol 5:  interpreter
vol 6:  compiler
vol 7:  browser
vol 8:  hyperdoc
vol 9:  algebra
vol 10: numerics

1-4 are not literate documents in the sense of being both documentation
and source code, so they pose no serious complications and can be
handled without difficulty as normal latex documents.

5+ are more complex, because they involve literate programming in its
true sense.  Fortunately, the interperter and compiler are both well
defined conceptually, and we have sufficient tools and mechanisms in
place to make this workable.  I'm thinking vol 6 will be postponed
until Aldor becomes Free (if it does) but Tim has already started on
vol. 5.

7 and 8 I am slightly less clear on - is hyperdoc the current graphical
environment for interacting with Axiom?  Is the browser a pamphlet
browser, or the wiki environment?  will the hyperdoc volume become the
UI volume if a new "standard" graphical interface/environment is
created?  Would graphing techniques be part of one of these volumes? 
That's far enough in the future that these questions are premature -
just curious.

Volumes 9 and 10 are my real concern.  I agree algebra and numerical
categories are a logical breakdown from a user standpoint, but they are
both so incredibly huge as categories that each one might in itself
consititute several large volumes.

Is the plan to simply not publish these volumes as printed works?  I
suppose that might be logical but it would be a shame - if the Axiom
project realizes its full ambition and reaches a "stable" configuration
I would rate it as a must for any serious university library.  It is
true that it changes frequently but the same might be said of the
Oxford Unabridged dictionary (assuming it is kept current with the
living language) and that is a staple of most large libraries.

Also, most algebra work exists as discrete pamphlets which concentrate
on a single subject - these will need to be integrated into volumes and
as of now our automatic mechanisms cannot achieve this.  And if people
write papers as pamphlets and publish them, those too will need to be
incorporated while remaining available as individual entities.

Wouldn't it make sense to organize the algebraic and numerical volumes
of Axiom according to accepted mathematical cagetories, insofar as this
can be done?  I have no idea how many that would prove to be or what
the form of it would take, beyond the vague notion of building logicly
from a foundation to "high level" math, but it seems to me that we
might want to organize along some such lines.  We have discussed in the
past the need for some kind of organized mapping of mathematical fields
and how they inter-relate - as we develop this map, couldn't we use it
to break down "algebra" into more useful chuncks?  Maybe (just as an
example, I'm sure this is wrong:)

Volume 9.1  Category Theory
Volume 9.2  Numbers - Integers, Floats, Reals, Complex, etc.
Volume 9.3  Polynomial Equations
Volume 9.4  Matricies, Arrays, Vectors and Operations on Them
Volume 9.5  Series, Limits, etc.
Volume 9.6  Special Functions
Volume 9.7  Calculus - Differentiation and Integration
Volume 9.8  Differential Equations
etc. etc. etc.


Volume 10.1 Fundamental Numerical Methods
Volume 10.2 <insert logical topics here>

Volume 11.1 Fundamentals of Descriptive Systems - Physical, Economic,
etc.
Volume 11.2 Physics
Volume 11.3 Chemistry
Volume 11.4 Economics

etc. etc. etc.

Then we can assign each pamphlet a "category" from the list of volumes,
and (maybe) establish coding standards such that each pamphlet written
on a particular subject is ready to be plugged into the file defining
the volume in question.  I don't have a clear idea how to do that yet
(or rather a clear idea that would be accepted, since the most obvious
way involves a separation of content from preambles.)

One advantage of this would be that it would make it relatively simple
for a specialist to judge Axiom's abilities within a particular field,
and what is needed.  Also, the bibliography included with each volume
of this nature would be far more useful as an overview of the field,
because it would be separate from the huge core bibliography.  Indeed,
my favorite idea is a per-chapter (or per-pamphlet) bibliography style,
with a per-volume bibliography at the end if comprehensiveness is need
or required.  We might want a "last edited" date in each pamphlet as
well, so we know how current the work on a particular subject is and
where to start looking for research not yet considered.

Sorry if I'm not terribly focused, but I started considering the
bibliography problem again today and it brought a lot of issues to
mind.  Clearly we will need to standardize reference names and
accomidate DOI, arXiv, and other citation styles whenever possible, but
that's just a beginning.  The potential scope of Axiom suggests it must
organize virtually all mathematics into a coherent structure which is
understandable and extendable.  So I guess my real question is - inside
Vol 9, how are we planning to organize?

Cheers,
Cliff

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