RE: [Axiom-developer] Openmath, Singular

[Bill Page]

On October 3, 2005 4:37 AM Michael Brickenstein wrote:
> 
> Actually I had a discussion in sci.math.symbolic and my
> conversation partner stated that he would like to see our
> functionality in your system.

I almost never hang out in the usenet news groups, but
I am glad that some people there are saying good things
about Axiom.

> Additionally I have heard in our team, that you have made
> some things about Openmath. So this was my entry point for 
> axiom. And  of course I have heard of your extremely
> mathematical type system.

Let me make clear here that when you say "you have made some
things" and you refer to Axiom as "your system", that does
not refer personally to me. I presume you mean it collectively
in the sense of all the people who have contributed to Axiom
over it's long history. If there is any single person right
now to whom this might apply personally, then it would have
to be Tim Daly. I just happen to be one of the most vocal and
verbose supporters of Axiom at this time.

I hope other Axiom developers will also comment about
OpenMath and Singular.

The closest thing that the Axiom project has to "leadership"
is referred to as the Axiom Foundation. See

http://wiki.axiom-developer.org/AxiomFoundation

This is a group of three people (called "members") who have
agreed to help steer the project by being responsible for at
least some of the critical decisions and controlling any
financial support. Although I helped to set this up, I am not
one of the three members. Neither is Tim Daly (by his choice).
Either fortunately or unfortunately, depending on one's point
of view, the Axiom Foundation so far has had very little to
do. The idea is that membership in the Axiom Foundation would
rotate through those individuals most motivated to support
Axiom, but always consist of at least three people.

> 
> Of course I am interested in MathAction, if we would be able
> to implement a Singular demonstration in the mid. future
> this would be extremely nice and a good demonstration for
> what I do.

Now, MathAction (as opposed to Axiom) is something for which
I am largely responsible. :) I would be start to look into
adding a web interface to Singular on MathAction.

> 
> So for further steps, I suggest
> 
> - for me to take a closer look at your openmath library

If you haven't already done this, I suggest you start by
reviewing references to openmath in the axiom-developer archives:

http://lists.nongnu.org/archive/cgi-bin/namazu.cgi?query=openmath&submit=Sea
rch%21&idxname=axiom-developer&max=10&result=normal&sort=date%3Aearly

For example:

http://lists.nongnu.org/archive/html/axiom-developer/2004-01/msg00035.html
http://lists.nongnu.org/archive/html/axiom-developer/2003-12/msg00030.html
http://lists.nongnu.org/archive/html/axiom-developer/2003-07/msg00000.html
http://lists.nongnu.org/archive/html/axiom-developer/2003-06/msg00078.html
http://lists.nongnu.org/archive/html/axiom-developer/2003-06/msg00069.html
http://lists.nongnu.org/archive/html/axiom-developer/2002-12/msg00003.html

and a few more ... :) Unfortunately as far as I know, none of this
discussion lead to any substantial work on resurrecting the OpenMath
work in the open source version of Axiom.

> - for you I suggest to
>      -check, if axiom is compatible with openmath 2
>      -have a look on the polyd CD which is not from the 
>       Singular team but especially suited for Gröbner bases
>       and everything which is based on it
> 
> At the moment, I use
> 
> "groebner"
> "DMP"
> "DMPL"
> "SDMP"
> "term"
> "graded_reverse_lexicographic"
> "lexicographic"
> "groebnerd"
> 
> from polyd.
> I also use the symbol "Q" from fieldname.
> In near future, there is a symbol FreeField or so which will be  
> supported.
>

Ok, I will look at this.
 
> 
> Further you are invited to make a wishlist, which functions from
> our System (http://www.singular.uni-kl.de) you like to see in a
> Openmath content dictionary.

Probably we need to start something similar for Axiom.

> 
> At the moment, the prototype is nothing as the pure mechanism
> with groebner basis as proof of concept (which is not the
> easiest possible  example).
>
> In the next weeks (I have a job as System Administrator and
> Software Developer for my institutes databases, so don't expect
> me to work full time on this), I will improve the basis for
> the implementation.

No problem.

> My Openmath implementation is based on Python which is embedded
> in Singular and plays together with the Singular interpreter 
> nicely (can dynamically call all (a the moment nearly all)
> interpreter and kernel functions). This is written by me and
> not yet released officially. Python is in fact a strongly typed
> language, which doesn't do implicit conversions (at default),
> I only mention this, as I know that axiom focuses very much on
> a type system. This basis will be improved (mainly bug fixing
> in the next weeks).

As I understand it Python is a dynamically typed language. To
use the word "strong" seems a little miss-leading.

MathAction is based on software (Zope) written in Python. So
your work with Python in Singular might be some advantage.
> 
> And then I will have time to spend more time the Openmath
> path.
> 
> I will send you some examples of polynomial system encodings
> using  polyd, you can of course check, if my understanding of
> the standard is  correct.

First I need to understand it. :)

> I also will send you an archive of the polyd CD , as http:// 
> www.openmath.org gives only internal errors at the moment
> (not so  unusual there).
> 

Thanks, I will look into this and probably ask you a lot
of questions later.

Regards,
Bill Page.