The Mathematica Journal
Volume 9, Issue 3


In This Issue
Tricks of the Trade
In and Out
Trott's Corner
New Products
New Publications
News Bulletins
New Resources

Download This Issue 

About the Journal
Editorial Policy
Staff and Contributors
Back Issues
Contact Information

In and Out
Edited by Paul Abbott


Q: An option for specifying the MonomialOrder in GroebnerBasis is to provide an explicit weight matrix. But I do not understand the syntax for doing this. Are there examples of this available? In addition, I would like to see a weight matrix for some of the standard monomial orderings.

A: Daniel Lichtblau ( answers: What is required for variables is an rational (or integer) matrix of full rank that comprises a well-founded term ordering. This in turn is fulfilled iff the first nonzero entry in each column is positive. Here is an example from a set of problems posed as a challenge for the ISSAC 1997 conference.

For lexicographic ordering, you can use, for example, an identity matrix.

For degree reverse lexicographic ordering, you can use a matrix with first row set to all ones, next row all zeros except last entry negative one, then move the negative one step to the left in successive rows.

About Mathematica | Download Mathematica Player
© Wolfram Media, Inc. All rights reserved.