Noether normalization guided by monomial cone decompositions

Abstract

This paper explains the relevance of partitioning the set of standard monomials into cones for constructing a Noether normalization for an ideal in a polynomial ring. Such a decomposition of the complement of the corresponding initial ideal in the set of all monomials–also known as a Stanley decomposition–is constructed in the context of Janet bases, in order to come up with sparse coordinate changes which achieve Noether normal position for the given ideal.