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RE: [Axiom-developer] Knuth's literate style

From: C Y
Subject: RE: [Axiom-developer] Knuth's literate style
Date: Mon, 14 May 2007 15:35:43 -0700 (PDT)

--- Bill Page <address@hidden> wrote:

> There seems to be a strong desire - at least on
> their part - to replace the current "hacks" that allow one to
> produce mathematical documents and computer algebra system
> output for the web from LaTeX as a source or as an intermediate
> language, which is what we do right now on the Axiom wiki.

I share that desire, and if the STIX fonts ever see the light of day
there may be real progress in that direction.  However, I would regard
MathML and OpenMath as computer-computer and program-program
interaction methods, not human-computer (except as rendered output, of

> What I was thinking was that in spite of Knuth's extensive and
> detailed literate documentation of TeX and even it's fairly wide
> spread use, Tex was not the mark-up language used in the prototype
> implementation of the WWW, so it is not (normally) the language
> we use today to write documents for the web. So just documenting
> Axiom may not be such a big factor in it's longevity. There are a
> lot of other factors, including some over which we have no control,
> that may determine whether Axiom lives another 30 years or whether
> future computer algebra developers will be writing in Python.

I rather doubt there will be agreement on the best language to write
CASs in, ever.  My hope is that at some point most writing for computer
algebra systems will take place in languages designed to be close to
the mathematics (SPAD/Aldor) and have a solid framework which only
needs a little tweaking now and then.

> > For example, the arXiv accepts other formats then TeX only 
> > very reluctantly. All the large (math-) publishers use TeX
> > for typesetting.  I have not yet been to any conference which
> > would accept something other than LaTeX source.
> You might be surprised how many people I work with who want so
> badly to write their scientific and technical documents in
> Microsoft WORD. I would say that the number of authors who are
> LaTeX users in our environment is currently less than 50% and
> it is falling. :-(

Gah.  Why is that, do you think?  My experiences with Word have seldom
been positive.  Sheer mass action and familiarity?

> > Finally, I'd like to state that more important than talking 
> > about literate programming is providing documentation, or,
> > if you like, literate programming. I think it's quite sad
> > that so little documentation has been provided to the
> > algebra sources yet.
> Yes I agree. We should discuss why this is the case.

I see two immediate reasons.  One is the difficulty of understanding
the code.  The second is the inherent difficulty of the subjects

There are other more "fuzzy" possibilities, such as people waiting to
see if Axiom will emerge as a major player again in the CAS world.  It
cannot be denied that Mathematica has very flashy graphics, marketing
and polish - it's only human nature to be impressed by these things.  
> Surely one reason is that analyzing an existing program is still
> much more difficult than writing a new program. Witness for
> example how happily SymPy and Sage developers are to re-write
> existing code in their own favourite language.

That will remain true until the benefits gained by understanding the
environment in which the original code was written outweigh porting the
ideas into your own.  This is HARD.  I believe Axiom can achieve a
sufficiently strong environment that NOT learning it is a bigger
inconvenience than learning it, but the benefits provided must be
major.  We aren't close yet.

> Another is the issue of "ownership". People are often very
> reluctant to change something someone else has written - even
> when invited explicitly to do so.

I can only speak for myself, but I think this is much less of a problem
for me than simply getting up to speed enough to feel I can do
something worthwhile.  Axiom is a large territory to learn.

Also, Tim's warnings of very subtle breakages and complex code in Axiom
are somewhat intimidating.  As the territory gets mapped I think this
problem will ease somewhat. (An undocumented codebase in that state is
broken by definition, in my book - the only thing to do is get busy
breaking stuff until everything that can be broken is broken and fixed
to be more robust ;-)

> How can we make doing this attractive to other people? (This
> is especially biting since neither you nor I have done much
> in this area - although your guess package for Axiom does
> provide a good example for newly written code.)

I really think a framework within which to work would help this
problem.  I have seen references to something called Mathematical
Knowledge Management which may be a good place to look for ideas.  As I
look over the 2001 MKM proceedings
I am seeing names I recognize ;-).  Pity the rest are not available
online, oh well...
> How will they obtain appropriate "credit" and peer recognition
> for this work? What other motivation can we offer them?

That's a point, actually - has anyone published any papers recently
showcasing work done in/for Axiom?  That seems like the most logical
pathway to me, although it would mean writing at least two papers - one
for the Axiom codebase and one for publishing, since those journals
generally take copyright...


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