RE: [Axiom-math] How to make symbolic computations?

[Bill Page]

On March 4, 2006 2:17 PM Fabio Stumbo wrote:

> ...
> Bill Page wrote:
> > I am interested in similar problems. There is are some domains
> > in Axiom for doing computations with non-commuting variables
> > developed by Michel Petitot. You can find some examples in the
> > Axiom book under the title XPolynomial but unfortunately the
> > explanations are a little terse.
> ...
> 
> Yes, I had a look (before asking for help... ;-) at the XPOLY 
> domain: I read its help on the axiom book and I also looked at
> anything else that looked related to it, but I didn't look at
> ofmonoid, even if I saw this domain was used in XPR, because
> it has no reference in the book...

There is so many interesting Axiom domains that are not mentioned
in the book! :( I hope that some day we can change this.

> Also looking for ofmonoid on the axiom site doesn't help: I 
> tried it now and the only response I get are the two messages
> you wrote after my mail. So, one question in this case arise:
> how can one get help in such a case, but asking on the mailing
> list?

Asking on the email list is the correct approach.

You can also search the Axiom algebra source code online at:

http://wiki.axiom-developer.org/axiom--test--1/src/algebra

Enter a search term in the box in the upper right corner and
press 'Enter'. For example you will see that 'OFMONOID' is only
used and defined in xpoly.spad. These files are supposed to be
"literate programs" but unfortunately we still have very little
useful documentation in these files. :( So the best you can do
is try to read and understand the intention of the program code.
After we understand it well, we hope to have time to write some
of the missing documentation ... but it seems life is too short.

> 
> In any case, after I had a look at xpoly I was thinking of 
> something like defining new rules to be applied to my
> polynomials, but I couldn't do it. Your solution is, in fact,
> much more correct from a mathematical point of view, as long
> as my rules are of the type I am using, ie substituting a 
> monomial with a smaller (in some sense) polynomial.
> 
> ...
> >
> > Look at the example at:
> >
> > http://wiki.axiom-developer.org/SandBoxNoncommutativePolynomials
> >
> 
> I see that you added a remark, and it is right: rules are to 
> be applied recursively as much as possible.
>
> ...
>
> > I hope this example helps.
> 
> It helps a lot!!!! Thank you very much. I will look at it carefully 
> in the next days, when I will have more free time.
> 
> Yet, I still have some question,  (not computational):
> 
> - I guess that your suggestion implied not to use the ofmonoid
> included in axiom, but the variant included in your example.

Yes. The version in Axiom has a bug: the function "div" is exported
but no implementation is given.

> I then created a file ofmonoid.spad and (by trials and errors)
> I got it compiled with )compile ofmonoid.

Great!

> Well, what should I do now to replace the old with the new? 
> Is it enough to replace the old
> /usr/local/axiom/mnt/linux/algebra/OFMONOID.o
> with the newly created
> /home/stumbo/OFMONOID.NRLIB/code.o
> ?

Maybe this will work (I did not try it yet), but I think it is
not the recommended way. In fact, I think it is not yet clearly
documented how to make such a local change to Axiom.

Eventually we will submit a patch to xpoly.spad.pamphlet
including this change to provide an implementation of "div" and
also (I hope) some documentation. This will become part of the
Axiom source distribution. At that time, a complete new version
of the Axiom library can be built from source.

But for your use now, after compiling the new 'ofmonoid.spad'
file, in later Axiom sessions you should include the following
command:

)lib OFMONOID

This will tell Axiom to load the new version of OFMONOID
directly from /home/stumbo/OFMONOID.NRLIB instead of the
old version of OFMONOID in /usr/local/axiom/mnt/linux/algebra/

> 
> - I see that in your reply in the Reply-To field your mail has
> your address 'address@hidden' and not the
> mailing list address, so I am writing directly to you. Is this 
> that you meant or should I have written to the ml, or added a 
> comment on the wiki?
> 

I am sorry that there is so much confusion about the email
list. There are some technical problems which I hope are soon
fixed.

My usual practice is too use the "Reply to all" option in my
email program. This will send a copy of your reply directly
to the author and also one to the email list.

Of course you can add a comment to the wiki and also (please!)
make changes to the page by clicking 'edit' if you want to
make improvements in the example or the explanation. Other
people will benefit from your corrections and improvements.

In the case of the web page

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

changes and comments made to this page will **not** be sent
to and email list because the name begins with "SandBox".
(SandBox means that this is only a kind of test and play.)
Changes to other pages that do not have the word SandBox
prefix will be sent as notices to the subscribers to
axiom-developer email list.

Usually I plan to make a page first with SandBox ... and then
later remove the prefix when it becomes stable and correct.
I think that right now there are many pages in the SandBox
that can be made permanent, but I have not had time yet to do
this - and no one else seems to have time or to be willing to
make these kind of changes to the wiki. :)

Regards,
Bill Page.