Next: 1 monomial operations Up: Monomial Representations for Gröbner Computations Previous: 1 Introduction

# 2 Basic monomial operations and representations

Given an integer n > 0 we define the set of exponent vectors Mn by . Notice that monomials usually denote terms of the form . However, in this paper we do only consider the exponent vector of a monomial and shall therefore use the words exponent vector and monomial interchangeably (i.e., we identify a monomial with its exponent vector).

We furthermore use Greek letters to denote monomials and the letter n to denote the a-priory given length of monomials (which is the number of variables in the corresponding polynomial ring).

Monomials play a central role in GB computations. In this section, we describe the basic monomial operations and discuss basic facts about monomial (resp. polynomial) representations for GB computations.

Next: 1 monomial operations Up: Monomial Representations for Gröbner Computations Previous: 1 Introduction
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