[Axiom-developer] StepThrough

[C Y]

--- Martin Rubey <address@hidden> wrote:

> C Y <address@hidden> writes:
> 
> > I'd be curious - how many of these bugs are due to mathematical
> > errors (e.g. algorithms that are incorrect) vs. "programmer level"
> > bugs (e.g. "whoops, semicolon there")?  (Not rhetorical - I really
> > am interested.
> 
> Well, most bugs (or, maybe: surprising results) I encountered so far
> are really design problems. For example: that %pi < %e is really a
> design problem of the EXPR domain...

Hmm.

> Although I think that there are cures, they involve a lot of work.
> Currently I have little time for Axiom, so I try to fix small things.

That's open source - do what can be done with available resources.
Unless some generous soul with mucho dinero wants to give us all day
jobs doing this :-).

> > Well, once I get the units package figured out (if I ever do...
> > grumble...) 
> 
> you reallly should.

I intend to.  I'm still reading papers and looking over other systems
out there - I'm going to try my best to do this right.  Hopefully in
another week or so I'll have something I can send Dr. Sit without
feeling like I'd be wasting his time.

> > I'd be glad to start trying to document the foundational design
> > principles of set theory used in the Axiom libraries. (I guess 
> > that would be the core of the SPAD/Aldor language design as well?) 
> 
> I'm not quite sure what you mean.

Well, I might be saying it wrong.  My understanding was that Axiom's
design tries to represent the basic theories and axioms of mathematics
and build subsequent mathematics off of them.  I know this is imperfect
- there are circularities in the design which cause significant
problems for the bootstrap build process - but this part of Axiom has
always appealed to me.  I wanted to relate the most basic concepts in
Axiom to their mathematical roots - Axiom, unlike any other system
except maybe MuPAD, is said to be well founded in modern mathematical
theory.  I would like to document what we are considering the
foundations of modern mathematical theory and how our design reflects
them, and tie that documentation to the code that actually does the
job.  Surely this will have to be done eventually if we are to hold up
the design of Axiom to review and criticism successfully.

> But I'd advise you anyhow to take up a small project (especially if
> you find units too big for the moment) and implement this first.

Not a bad idea.  (In fact, that was my original idea with units ;-)

> In fact, here is something for you:
> 
> Currently, there is a category StepThrough defined in catdef.spad. It
> is used only in very few places, and as I noted in 
> 
> http://wiki.axiom-developer.org/220StepThroughIsBraindead
> 
> it is braindead.

I fear I am too, as I am not quite following what you want this
function to do.  You say it provides the following:

"a function init() which yields an initial element of the domain and a
function nextItem(n) which produces the element after n"

How does one define what the "initial element" is in any particular
domain?  How do you define what element comes "after" another element? 
I suppose Postive Real Integers would be obvious - init()->0, after
that comes 1, etc., but you suggest "Float" should have StepThrough
implemented? I have absolutely no idea what "next" means in this
instance.  I suppose initial element would be 0.0 - is the element
"after" this element 0.1?  0.0001?  Clearly I'm missing something
fundamental but I'm not sure what.

> What it really should do is to implement the notion of a countable
> set. I was surprised at first, but this can be effectively 
> implemented.

I'll have to read up on the idea of a countable set.
 
> So, maybe you would like to do this. You will probably learn a *lot*
> about axiom rather quickly, since you will have to implement 
> nextItem and prevItem for many domains, and you will have to 
> document what it is used for in those few where it is already used, 
> i.e., GENPGCD and in PFBRU.

Sounds interesting, but I'd have to be comfortable first with what
StepThrough is supposed to achieve, and I'm obviously missing some
critical pieces.
 
> I have already working code for fraction.spad, so if you are
> interested, I'll send you the details.

I'd be interested certainly, but I need some background first.  (BTY,
this is why I said earlier I was unlikely to make any spectacular
mathematical contributions. ;-)  Undoubtedly this should be obvious to
me.)

Cheers,
CY


        
                
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