Re: [Axiom-developer] SAGE, Axiom, and usage

[Gabriel Dos Reis]

"Bill Page" <address@hidden> writes:

| On August 23, 2006 2:21 PM Gaby wrote:
| > | > 
| > | > Yes, and as a matter of fact, I'm deeply sceptical of your
| > | > previous assertion.
| > | 
| > | Which assertion?
| > 
| >   #  Gaby would like to introduce his students to "symbolic
| >   #  computation", *but really Axiom (and Aldor) are not very
| >   #  good at this -- by design.*
| > 
| > (emphasis is mine).
| >
| 
| Sorry. I did not mean to imply that Axiom and Aldor are not good
| "by design". Certainly a lot of effort went into making Axiom
| with Aldor the best possible tool for doing general mathematics by
| computer. The point I was trying to make was that the basic design
| of Axiom was such as to emphasise mathematical *structure* over
| linguistically oriented formal symbolic computation.

and my point is that that distinction is largely an academic exercise
in ways we approach the subject matter, and NOT a really deep one (though
it may be given substance).  And the level of a graduate course where I
would like to attract students and get them excited about the 
subject, and potential contributors, that is largely a pointless and
confusing exercise.   As a matter of fact, *there are structures* in
formal symbolic computation -- rewriting rules are seldom used bindly
without structures, nor assumptions.  It is a matter of how and when
those structures are expressed and taken advantages of.

| It is clear
| from the early literature on Axiom that this was a deliberate design
| choice. Other early systems being developed at the same time, such
| as Reduce, took the opposite view.

Clearly, Axiom emphasis structures -- that is one of the aspects I
refer to when I say "principled CAS".  However, my thesis is that it
is -paradigmic- aspect of the subject matter, not a "semantically"
different field.

| > | On the contrary, I do not think I am "painting it into a corner".
| > 
| > what you said only reinforces the perception I have had since
| > some time now, from discussions on this list.
| >
| 
| Could you explain what you mean "the perception you have had"?
| Do you mean that idea that I am (we are?) are "painting Axiom
| into a corner" by emphasising how it differs from some other
| systems? I don't understand why you would think that.

As I said, it is a perception I have had for some time, it is not a
perception given by the single message you just sent.

it is NOT a general matter of showing how different Axiom is; but it
is the matter of saying we are targetting a narrow field, with
unfocused means.

| >...
| > between 1995 (when I first heard of it, and later got presentation
| > by Stephen about A# at FRISCO workshops, and repeated "conversion
| > attempts" from colleagues -- mostly French you suspect) and 2002,
| > nearly nothing widely appreciated happened to Axiom -- contrast
| > that to other CAS on the market.
| 
| On the contrary this was the period of time when NAG was investing
| a lot of time and money into developing Axiom as a commercial
| product. An entirely new and I think potentially quite revolutionary
| user interface was developed. Axiom was ported to a new lisp environment
| that permitted Axiom to be delivered on Windows. And the numerical
| abilities of Axiom were greatly extended.

yes, but how widely was it noticed and appreciated?

| Perhaps it is true that this
| is not now "widely appreciated" but I think that is only because it
| turned out that NAG decided to abandon it's attempt to market this
| new version of Axiom. :(

we can hardly accuse NAG to stop losing money :-/

OK, I appreciate other CAS company have been more effective at
marketing that acheiving technical advances.


[...]

| > | Could you explain what you mean by "retroactively used to redesign
| > | its past foundation"?
| > 
| > My understanding of your comments is that "people tried to show Axiom
| > as competing symbolic computation systems, it fails.  Let's try to
| > present it as not having anything to do with that, by design."
| 
| I think that is an unfair assessment of my statements.
| 
| > I don't believe Axiom's foundational and design principles can be
| > meaningfully understood that way.  I don't believe earlier failure
| > had to do with the fact that Axiom was presented a symbolic
| > computation system.
| 
| I did not say that. The reasons for Axiom's failure as a commercial
| product were no doubt very different and largely non-technical.
| 
| > But I suspect all have our own religions and beliefs :-)
| 
| Yes I suppose, but what does that have to do with Axiom?

our respective beliefs of why Axiom failed.

-- Gaby