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### 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");

or

    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.

#### 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 The code is a little bit out of date now.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

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