RE: [Axiom-developer] about Expression Integer (with Quizzes)

[Bill Page]

On February 27, 2006 4:25 AM Gaby wrote:
> 
> Bill Page writes:
> 
> [...]
> 
> | > )set mess bot off
> | > (6) y:DMP([y], INT);
> | >     variables (2*y+1/y)
> | >
> | 
> | I wrote: "Error same as in (2)". So I have to admit I got this
> | one wrong but I should not have. The explanation is simple. This
> | is not a package call as it was in (2), so the interpreter is
> | free to apply the usual coercion to 'FRAC DMP([y], INT)' in order
> | to obtain a selection for '/'.
> 
> When it takes so many Axiom experts to get those things wrong --
> no matter how obvious they might seem with hindsight -- I believe
> the "free hands" given to the interpreter may be questioned :-)

Although I am not sure that number of available "Axiom experts"
should be interpreted as any sort of "guarantee" of convergence
;) I think your conclusion is right. I think the Axiom interpreter
currently does several things (some of which have already been
documented as Issues) that even experienced users might find
surprising - even though they might be able to offer a more or
less clear explanation of the behaviour. Thus Axiom clearly
violates the "principle of least surprise" that has been advocated
as one of the more important principles in user interface design.
But user interface design, being in large part more of an "art"
than a science, does not provide many well-understood solutions
to this problem.

I think some of what we have been discussing are not interpreter
issues as such, but rather what the best "categorical" representation
of certain mathematical objects such as polynomials, might be. This
is more a matter of how to match an object-oriented design to the
mathematics when that part of mathematics often does not naturally
inherit such a tradition.

> 
> What I retain from this fascinating thread is that the
> implemented underlying mechanism for interpreting polynomials
> is, hmmm, far from "obvious" and "intuitive".

I think one of the reasons that Axiom fails to be obvious here
is that it attempts to be both powerful and intuitive at the same
time. These are often conflicting goals and as a result Axiom
sometimes seems to fail at both (though I think more often it is
powerful but not so intuitive). However intuition is often a poor
guide when it comes to mathematics, so we should expect that we
need to sharpen our intuitions by reading the documentation.
Unfortunately a lot of this documentation still needs to be
written. :(

Regards,
Bill Page.