Introduction to grobner (Maxima 5.44.0 Manual)

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### 63.1 Introduction to grobner

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

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.

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 The code is a little bit out of date now.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

Categories: Groebner bases Share packages Package grobner

#### 63.1.2 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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