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RE: [Axiom-developer] Sage on MathAction

From: Page, Bill
Subject: RE: [Axiom-developer] Sage on MathAction
Date: Wed, 16 Aug 2006 10:02:03 -0400


It's all yours - it's open source. :) I will update the MathAction
repositories later today after we get a little more testing done.
It should be easy for you to incorporate this into the Doyen CD

You might also be interested in the pamphlet support for Sage
which comes very naturally with the way pamphlets are implemented
on MathAction (MathAxiom? ;)

So now we can start to discuss literate programming with
the Sage developers.

You asked:

> Do people in Sage considering including Axiom???

Yes, this has been considered by some of the Sage developers.
They chose Maxima as the first system of this kind to integrate
with Sage apparently because it was easier. Axiom, however is
both more difficult and at the same time perhaps more interesting
than Maxima because of it's strong typing and underlying object-
orientation. Sage provides a strongly-typed object-oriented view
of mathematical objects not so different than SPAD and Aldor,
except that types are (mostly) static in Aldor but dynamic in
Sage. In principle it should be possible to develop an interface
between Axiom and Sage that preserves much more of the mathematical
structure than what is possible in other computer algebra systems.

The ability to transfer mathematical structures between very
different mathematical systems (only a little structure in some
cases, but it other cases a lot) is one of the most innovative
things about Sage. (This is in contrast to MathAction which only
provides a common user interface but does not transfer data
between systems.) So the way I see it, Sage provides the much
needed glue to take advantage of the huge prior investment in
mathematical software - of which Axiom is one very important
example. From the point of view of Axiom we can also view Sage
as a new user interface, not so different than what B# (Bnatural)
was intended to be.

I think the Sage developers were very bold - maybe even audacious -
to actually attempt this. And they are doing it in a largely
pragmatic way without attempting to incorporate the more formal
and theoretical ideas developed by the OpenMath community. One
might have been tempted to predict an early failure to this
effort but on the contrary Sage seems to be growing more rapidly
than any other computer algebra research and development effort.
I guess this just provides one more demonstration that software
development - particularly open source software development -
is not a linear process. :)

So I am very enthusiastic about the idea of developing a serious
Axiom interface for Sage and I hope we can find more resources
here in the Axiom developer group to work on this. I have read
most of the Sage Maxima interface code and I think it forms a
pretty good basis on which to start to build an Axiom interface.

Is anyone interested?

Bill Page.


        From: Alfredo Portes [mailto:address@hidden 
        Sent: Wednesday, August 16, 2006 8:35 AM
        To: address@hidden
        Subject: Re: [Axiom-developer] Sage on MathAction
        I want !!! I want !!! :-)
        Really nice work. MathAxiom just becomes better every week.
        Do people in Sage considering including Axiom???
        Whenever LatexWiki gets updated with these changes please 
        let me know or if you have plans of using the new version of 
        ZWiki available.
        Again, props on this incredible job,
        On 8/16/06, Bill Page wrote: 

                Axiom Developers and computer algebra enthusiasts!
                I have a very preliminary demonstration of the
                of Sage with the MathAction wiki here:
                I would like to encourage you to test this further. You
                find that Sage is quite different than any other
                algebra system with which you might be familiar - truly
                "new generation".
                This approach to interfacing with Sage is based directly
                the work of Gonzalo Tornaria and Joe Wetherell et al.
for use
                with LaTeX. The LatexWiki software on which MathAction
                based needed only minor modifications to make direct use
                of the 'examples/latex_embed' code in the Sage
                Long live open source... :-)
                Bill Page.

        Jose Alfredo Perez

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