[Aldor-l] [wdjoyner at gmail.com: Re: FW: oscas axiom draft]

Fri Mar 23 00:50:12 EDT 2007

Stephen and Aldor folks,

The next issue of Communications in Computer Algebra will have
an OSCAS column devoted to Axiom and Aldor.  Is there any news
about Aldor going open source that could be mentioned before
this goes to press?  Right now there is just a somewhat vague
statement on the website that it is coming soon.

Thanks,

Emil Volcheck, Chair
ACM SIGSAM
http://www.sigsam.org/

----- Forwarded message from David Joyner <wdjoyner at gmail.com> -----

From: David Joyner <wdjoyner at gmail.com>
To: Bill Page <bill.page1 at synthesis.anikast.ca>
Subject: Re: FW: oscas axiom draft
Cc: daly at axiom-developer.org,
	Waldek Hebisch <Waldemar.Hebisch at math.uni.wroc.pl>,
	Gabriel Dos Reis <gdr at cs.tamu.edu>,
	Martin Rubey <martin.rubey at univie.ac.at>,
	Gregory Vanuxem <g.vanuxem at wanadoo.fr>,
	Emil Volcheck <volcheck at acm.org>
In-Reply-To: <00f501c76bcc$023f6d00$6900a8c0 at asus>

Here is the second draft, which I think addresses the comments
(thank you!) of Bill and Tim. I'm sending it out as a link
so it doesn't end up clogging up your mail box:
http://sage.scipy.org/tmp/oscas-cca2.pdf
Again, please be as critical as you want!

- David

+++++++++++++++++++++++++++++++++++++++++++++

On 3/21/07, Bill Page <bill.page1 at synthesis.anikast.ca> wrote:
>Tim, Gaby, Waldek, Martin and Greg,
>
>Perhaps you might wish to read and comment on the attached
>article about Axiom by David Joyner. His article will be
>published in the OSCAS (Open Source Computer Algebra Systems)
>SIGSAM newsletter. For comparison see his recent article on
>Maxima:
>
>http://www.sigsam.org/bulletin/articles/157/oscas-maxima-DavidJoyner.pdf
>
>My initial reply to David is included below.
>
>Regards,
>Bill Page.
>
>-----Original Message-----
>From: David Joyner [mailto:wdjoyner at gmail.com]
>Sent: March 20, 2007 10:05 PM
>To: Bill Page
>Cc: David Joyner; Page, Bill
>Subject: oscas axiom draft
>
>
>Hi Bill:
>
>Do you have any comments on this? Please be as
>critical as you want! I think it needs more history
>and maybe some nicer examples. What do you think?
>
>The axiom4sage package works fine but clicking on
>some of the examples caused the HyperDoc to
>crash, so I had trouble finding examples that way.
>
>- David
>
>
>
>-----Original Message-----
>From: David Joyner [mailto:wdjoyner at gmail.com]
>Sent: March 21, 2007 7:14 AM
>To: Bill Page
>Subject: Re: oscas axiom draft
>
>
>On 3/21/07, Bill Page <bill.page1 at synthesis.anikast.ca> wrote:
>> David,
>>
>> On March 20, 2007 10:05 PM you wrote:
>> >
>> > Do you have any comments on this? Please be as
>> > critical as you want! I think it needs more history
>> > and maybe some nicer examples. What do you think?
>> >
>>
>> My reaction after a first reading of your draft article is
>> that it is a brief and somewhat "journalistic" account of the
>> current status of Axiom. By "journalistic" I guess I mean
>> something like "lacking in depth but otherwise accurately
>> reported". :-) Probably both perceptions (that is brief and
>> lacking in depth) is mostly a result of me being very close
>> to the subject myself.
>>
>> I think the history content of your draft is fine unless your
>> intention was specifically to address the historical context
>> of the ScratchPad project at IBM, in which case that probably
>> desires a paper all of it's own.
>>
>> The examples are also quite good. But in order to judge that
>> better, I guess I would have to understand the point you
>> would like to emphasise. Right now it seems to suggest that
>> Axiom can do what most other large scale computer algebra
>> systems can do and that is certainly correct as it stands.
>>
>> But I think that perhaps your article misses one key point
>> that sets Axiom apart from Maxima, Reduce, Mathematica and
>> Maple - the design of the Axiom mathematical library. The
>> SPAD language (and Aldor) was designed specifically to make
>> it possible to write mathematical algorithms in a flexible
>> but type-correct manner which today might be referred to as
>> a polymorphic object-oriented paradigm such as you might
>> find in Haskell and to a lesser extent in Python and similar
>> languages.
>>
>> I specifically left Mupad out of the above list because it
>> is a somewhat different story, having explicitly borrowed a
>> large part of the Axiom concepts of Domain and Category in
>> the design of it's mathematical library.
>>
>> The Axiom library implements a rich hierarchy of abstract
>> data structure types, from simple Aggregates to Keyed
>> Dictionaries and Lazy Streams, which collectively make SPAD
>> a very high level programming language. This is important
>> for the representation of mathematical objects and the Axiom
>> library uses these to provide an even richer hierarchy of
>> algebraic categories, from Sets to FiniteFields and Partial
>> Differential Rings, etc. Together there are over 1,300
>> mathematical concepts defined in the library.
>>
>> One of the purposes of the HyperDoc component of Axiom was
>> to make it possible to search and navigate this large and
>> tightly inter-related library.
>>
>> If one is interested in history, it is hard not to notice
>> that both of these developments - the SPAD language and the
>> HyperDoc browser - predated contemporary interest in these
>> subjects by almost two decades.
>>
>> Actually it is this aspect which strongly attracted me to
>> Sage since to some extent Sage seems to be re-inventing (or
>> at least re-implementing) a lot of the same library structure
>> in Pythonic form. I really hope that by providing Axiom as
>> an external package for Sage, some of this early experience
>> will eventually influence the evolution of Sage.
>>
>> > The axiom4sage package works fine but clicking on some
>> > of the examples caused the HyperDoc to crash, so I had
>> > trouble finding examples that way.
>> >
>>
>> The axiom4sage-0.1 package is based on an early version of
>> the new 'build-improvements' branch of Axiom development.
>> I chose this branch because one of it's main goals was to
>> enable building of Axiom on a much wider range of systems
>> and that seemed most compatible with the goals of Sage.
>> But there is a new sub-branch development called wh-sandbox
>> which corrects many problems such as the HyperDoc crashes
>> that you experienced. It is my intention to release real-
>> soon-now a new axiom4sage-0.2 package which is based on
>> wh-sandbox. Eventually all of this will become mainstream
>> Axiom development at which point I would hope to provide
>> an official "axiom4sage-1.0" package for Sage.
>>
>> I am a little concerned that your impressions of Axiom are
>> filtered by accessing Axiom through the Sage interface.
>
>These are great comments!
>
>I am running the axiom in
>.../sage-x.y/local/axiom/target/x86_64-suse-linux/bin/axiom
>from the command line - no SAGE interpreter (AFAIK).
>
>> axiom4sage is a full version of Axiom but the current Sage
>> interface only exposes the Axiom interpreter in a manner
>> that makes it appear superficially similar to Maxima.
>> I am hoping that I somehow find the time to improve the
>> Axiom interface in Sage to better exploit the underlying
>> similarity between many Sage classes and Axiom domains;
>> and going even further, to expose the Axiom compiler and
>> the SPAD language to Sage programmers.
>>
>> Anyway, you were probably more interested in my direct
>> criticism of your article than an oratory on my plans and
>> hopes for the relationship between Axiom and Sage. :-)
>> To that end I would recommend that you include in your
>> article at least one example of SPAD coding and a few
>> comments on the Axiom mathematical library.
>
>Will do.
>
>>
>> Let me now give your article a second more careful reading
>> and I will try to get back to you in the next few days
>> with some more specific suggestions.
>>
>> BTW, would you have any objection if I were to forward a
>> copy of your article and my comments to some of the other
>> Axiom developers, specifically Tim, Gaby and Waldek? I
>
>
>Please do!
>
>
>> suspect that Tim Daly especially might have a somewhat
>> different orientation and therefore a different reaction
>> to your article than I do.
>>
>> Regards,
>> Bill Page.
>
>

----- End forwarded message -----

-- 
Emil Volcheck
volcheck at acm.org
http://acm.org/~volcheck