Noether normalization guided by monomial cone decompositions

Authors:
Daniel Robertz
Affiliations:
Lehrstuhl B für Mathematik, RWTH Aachen University, Templergraben 64, D52062 Aachen, Germany
Venue:
Journal of Symbolic Computation
Year:
2009

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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.