Advertisement

Monomial Orderings and SAGBI Bases

  • H. E. A. Eddy CampbellEmail author
  • David L. Wehlau
Chapter
  • 1.2k Downloads
Part of the Encyclopaedia of Mathematical Sciences book series (EMS, volume 139)

Abstract

Let S denote the polynomial ring \(\mathbb{K}[x_{1},\ldots,x_{n}]\). The set of monomials in S is \(\mathcal{M} :=\{x_{1}^{a_{1}}x_{2}^{a_{2}}\cdot\ldots\cdot x_{n}^{a_{n}} \mid a_{1},a_{2},\ldots,a_{n} \in \mathbb{N}\}\). A term in S is an element of the form cm where \(c \in \mathbb{K}\) and \(m \in \mathcal{M}\).

Keywords

Polynomial Ring Lexicographic Order Dual Basis Permutation Representation Lead Term 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Sir Howard Douglas Hall, Dept. MathematicsUniversity of New BrunswickFrederictonCanada
  2. 2.Dept. Mathematics & Computer ScienceRoyal Military College of CanadaKingstonCanada

Personalised recommendations