Introduction to grobner (Maxima Manual)

51.1 Introduction to grobner

grobner is a package for working with Groebner bases in Maxima.

A tutorial on Groebner Bases can be found at
http://www.geocities.com/CapeCanaveral/Hall/3131/

To use the following functions you must load the grobner.lisp package.

load("grobner");

A demo can be started by

demo("grobner.demo");

batch("grobner.demo")

Some of the calculation in the demo will take a lot of time therefore the output grobner-demo.output of the demo can be found in the same directory as the demo file.

Notes on the grobner package
Implementations of admissible monomial orders in grobner

51.1.1 Notes on the grobner package

The package was written by Marek Rychlik http://alamos.math.arizona.edu and is released 2002-05-24 under the terms of the General Public License(GPL) (see file grobner.lisp. This documentation was extracted from the files

README, grobner.lisp, grobner.demo, grobner-demo.output

by Günter Nowak. Suggestions for improvement of the documentation can be discussed at the maxima-mailing-list maxima@math.utexas.edu. The code is a little bit out of date now. Modern implementation use the fast F4 algorithm described in "A new efficient algorithm for computing Gröbner bases (F4)", Jean-Charles Faugère, LIP6/CNRS Université Paris VI, January 20, 1999.

51.1.2 Implementations of admissible monomial orders in grobner

lex pure lexicographic, default order for monomial comparisons
grlex total degree order, ties broken by lexicographic
grevlex total degree, ties broken by reverse lexicographic
invlex inverse lexicographic order