Re: [Axiom-developer] ADVI browser

[Bertfried Fauser]

Hi,

I have not yet seen the ADVI browser / viewer, but reading the 7 views, I
would kindly like to add a few more meta remarks.

Regarding my current view on mathematics, ist far from beeing a static
sort of things. Many people do belife that methamatics is given as-is and
has only to be 'described' or 'explained'. However, I personally expect a
great reworking of many areas of mathematics in a more 'categorial' way.
Any documentation of a project like AXIOM should be capabal of such
reorganization, and you do indeed think about this.

QUESTION: How can descriptions be separated into an algorithmic part which
most likely does not change (unless the code is replaced) and the more
meta-mathematical aspects, like the decision what is 'basic' math and what
is derived.

Might there be a couple of mandatory tags for any AXIOM (algebra).spad
file which sepatates such information, perhaps by a new 'protocoll' like
<<synopsis:///...file1>>
<<algorithm:///...file2>>
However one would need such a thing as a math level, which may be
numbered, say "meta-mathNN", where NN is a number and 00--99 indicates the
increasing intricacy of the involved math. Such a 'rating' has to be
discussed, but would allow to extract a description of the AXIOM
capabilities on the user level. E.g. Maple has in undergraduate teaching
the problem that students don't know enough mathematics to appreciate that
Maple does not symilify an expression (say typically x^2=2) for such a
reason (e.g. x may be rational). Indeed one could even think about a
'named' or 'prohfiled' such numbering, specifying the needs of say
linear algebra, group theory, category theory, set theory to provide
specific views on the involved math.

Regarding the HTML protocoll, one does use currently sxearch engines like
google (ht-dig, for local purpose) It would be possibleto index all of
AXIOMS pamthlet files and even .spad files etc. However, it is quite
difficult to reate such hits and if you ask for ay quite common term you
will have too much hits to be able to retrieve the desired information.
Therefore the HTML protocoll shall be enlaged in future by the W3C to have
meta tags which describe the content. Such a thing woudl be very helpful
in reworking the wast amount of documentation needed for AXIOM. Such meta
tags might describe things like
definition, theorem, algorithm, but also a sophistication level, say once
more from 00--99

My own experience shows, that documentation of code takes away 2/3 of the
total amount of work needed and only 1/3 goes into codeing and testing.
Waht is clear to oneself has to be described very precicely in a
documentation and there has to be a mechanism guaranteeing that code and
documentation are recent and mutually related. Perhaps this is already
guaranteed by using literate programming. However, there is a notorious
tendency to make small hacks and 'forget' about documenting them, since
one thinks about doing this in the next major realeas.... which never
happens.

If someone of you invests work on extending / customizing ADVI such things
may be worth to be considered first.

cheers
BF.



% |   | PD Dr Bertfried Fauser    Fachbereich Physik    Fach M 678  |
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