RE: [Axiom-developer] groebner?

[Bill Page]

Ray,

On February 16, 2006 7:41 AM

> 
> Could someone tell me if this is wrong; or if it's right why?
> 
> -------------------------
> list:=[p,Vr,Vt,e]
> eq1H:=((-Vr^3+Vr^2)*Vt+Vr^3-Vr^2)*p :: HDMP(list,POLY INT)
> 
> Excerpt from an axiom session:
> 
> (24) -> eq1H
>                3     2        3     2
>    (24)  ((- Vr  + Vr )Vt + Vr  - Vr )p
> Type:
> HomogeneousDistributedMultivariatePolynomial([p,Vr,Vt,e],Polyn
> omial Integer)
> (25) -> groebner [eq1H]
> (25) ->
>    (25)  [p]
> Type: List
> HomogeneousDistributedMultivariatePolynomial([p,Vr,Vt,e],Polyn
> omial Integer)

It might help if you explained what you thought was wrong ... :)
But perhaps this result is what you have in mind?

(5) -> groebnerFactorize [eq1H]

   (5)  [[p],[Vr - 1],[Vr],[Vt - 1]]

Type: List List HomogeneousDistributedMultivariatePolynomial([p,Vr,Vt,e],
Integer)

-----------

Have you read section 9.31 GroebnerFactorizationPackage, page 569,
of the Axiom book? Axiom has several different Groebner packages
optimized for different purposes - all, unfortunately, rather
poorly documented. Some times you can find some useful clues and
comments in the source code:

http://wiki.axiom-developer.org/axiom--test--1/src/algebra/GbSpad
http://wiki.axiom-developer.org/axiom--test--1/src/algebra/GroebfSpad
http://wiki.axiom-developer.org/axiom--test--1/src/algebra/GroebsolSpad
http://wiki.axiom-developer.org/axiom--test--1/src/algebra/LingrobSpad
http://wiki.axiom-developer.org/axiom--test--1/src/algebra/PgrobnerSpad

Regards,
Bill Page.

Regards,
Bill Page.