RE: [Axiom-math] Groebernbases

[Bill Page]

Bertfried,

On August 7, 2006 5:26 AM you wrote:
> 
> 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

> 
> 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.