[Axiom-math] Groebernbases

[Bertfried Fauser]

Dear All,

I have experimented with the AXIOM Groebner bases package and was somehoe
wondering how to define an ordering and how to define elimination orders.
In the code I couldn't find any hint how to impose these conditions and
groebner() takes as input only a list of polynomials, not an order
function and not a list of to be kept or elimated variables?

Any hint welcome....

There is a tremendouly fast package for computing Groebner bases,
http://www-calfor.lip6.fr/~jcf/ it is written in C and I wonder if AXIOM
could use it via a sort of interface. Where to look how to write such an
interface.

ciao
BF.

% PD Dr Bertfried Fauser
% Institution: Max Planck Institute for Math, Leipzig <http://www.mis.mpg.de>
% Privat Docent: University of Konstanz, Phys Dept <http://www.uni-konstanz.de>
% contact|->URL : http://clifford.physik.uni-konstanz.de/~fauser/
% Phone : Leipzig [phone] Konstanz [phone]

[Bill Page]

Bertfried,

Post by Bertfried Fauser
I have experimented with the AXIOM Groebner bases package and
was somehow wondering how to define an ordering and how to
define elimination orders. In the code I couldn't find any
hint how to impose these conditions and groebner() takes as
input only a list of polynomials, not an order function and
not a list of to be kept or elimated variables?
Any hint welcome....

Concerning defining orders, this might help

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

There are several different packages for Groebner basis in Axiom.
You can try browsing:

http://wiki.axiom-developer.org/axiom--test--1/src/algebra/FrontPage/searchw
iki?expr=Groebner

Post by Bertfried Fauser
There is a tremendouly fast package for computing Groebner bases,
http://www-calfor.lip6.fr/~jcf/ it is written in C and I wonder
if AXIOM could use it via a sort of interface. Where to look how
to write such an interface.

I looked at the above link but all I could find were the binary
libraries with the Maple interface for both linux and windows -
no source code. Without the source code it would be hard to
integrate this with Axiom - maybe not impossible - but one would
have to try to emulate Maple's external library interface.

We have has some initial discussions about how to call external
routines from Axiom via an Aldor wrapper. See:

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

and also Gernot Hueber's recent posts to axiom-developer list

http://lists.gnu.org/archive/html/axiom-developer/2006-08/msg00108.html
http://lists.gnu.org/archive/html/axiom-developer/2006-08/msg00102.html

Regards,
Bill Page.

[William Sit]

On Mon, 7 Aug 2006 11:26:01 +0200 (CEST)

Post by Bertfried Fauser
Dear All,
I have experimented with the AXIOM Groebner bases package
and was somehoe
wondering how to define an ordering and how to define
elimination orders.
In the code I couldn't find any hint how to impose these
conditions and
groebner() takes as input only a list of polynomials, not
an order
function and not a list of to be kept or elimated
variables?
Any hint welcome....

There is a domain constructor GDMP (Generalized
Distributed Multivariate Polynomials) which has a
parameter which is any term-ordering you like. The
Groebner basis package then takes any polynomial ring
domain as parameter.

Gianni's code Bill Page referenced earlier are good
examples of how to set things up. Special cases are DMP,
HDMP polynomial domains.

In Aldor you can call external functions written in C, but
I have not tried it myself.

William

William Sit,
City College of New York
Office: R6/202C Tel: [phone], Fax: [phone]
Home Page: http://scisun.sci.ccny.cuny.edu/~wyscc/

[David Joyner]

Hello,

SAGE is a software system with a planned interface with Axiom.
SAGE Days 2 will take place October 6-10, 2006.

Come and work very hard to build, using the best open source tools
available, what I hope will soon be the finest general purpose
mathematics software available:

http://modular.math.washington.edu/sage/days2/

- William Stein, David Joyner (organizers)