Re: New to MuPad

Craig Ugoretz wanted to find some more pertinent information on
mathematical structures in MuPAD.

His second posting says:

> Although I said that I generally understand domains and
> categories, I become overwelmed when I look at the documentation of
> them. The issue is that although a high level overview of the
> functions they encompass is given, I would care to see examples like
> are given in the standard library documentation. Without examples, I
> feel lost.

I may be badly informed, but I have the impression that this question
in general deserves more study. There are newer (well, not SO new...)
systems, where some *mathematical* (as opposed to strictly *structural*)
hierarchization is exposed, MuPAD came after Axiom (and Magma?). And
they ARE considered not so easy to master, in their full sauce.
Actually, the learning problems may have contributed to the failure
of GAUSS (Monagan's Maple sub-package) popularity, although the idea
was nice and powerful!

We see, obviously, that a good deal of categorial thinking is injected
into, we see Rings, Fields, etc. And... although for more experienced
people those 'typing' issues facilitate the programming, the learning
curve becomes steep. I suggested to my students to look at the
documentation of various systems, in order to grasp the essential. To
read something about categories in general. To get acquainted with
Haskell and its 'classes of types' concept, in order to see that there
is a difference between context where an entity *belongs* to a given
category, with - what is suggested by MuPAD - it *possesses* a given
category, where an axiom in fact is a *constraint*, an attribute,
not an axiom from the fundamental point of view (I am NOT criticizing
the MuPAD terminology, it is as good as it could be, I like very much
the system), etc. Well, pedagogically it was an overkill...

Does anybody know of something in literature which would cover this
knowledge gap, something which would go far beyond in all senses, the
Klaus Drescher article about AxCaDo in MuPAD?

Where people not acquainted with the "general nonsense" math could
find something about mathematical subsumptions (such as the fact that
being an additive group implies being a Module over integers),
where the readers could find properly justified answers to questions
which recently polluted the lang.functional newsgroup about one
math domain (say, Integers) being a *subset* of another one (Rational),
and what is the relation between subsetting, subtyping, and
subclassing in mathematical setting?...

A theoretical mathematician won't rise his brow when extending, say,
Q on,to Q[x], or Q(x). But if somebody now poses the question: how
to *implement* such an extension, the answers become ambiguous,
especially for people conditioned by object-oriented approach to
programming constructs. *What* in reality is inherited, and is it
a "true" inheritance?... How far can we go with the static resolution
of domain/category of an expression, which would permit to compile
much more efficient code in CAS? (And which is one of foci of
attention of people interested in functional languages).

Co Craig Ugoretz is not the only one who is lost here. Plenty of
people are...


Jerzy Karczmarczuk






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