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TitleBasic Tools for Computing in Multigraded Rings
Author(s) Martin Kreuzer, Lorenzo Robbiano
TypeArticle in Conference Proceedings
AbstractIn this paper we study $\mathbb{Z}^m$-gradings on the polynomial
ring $P=K[x_1,\dots,x_n]$ over a field $K$ which are suitable for
developing algorithms which take advantage of the full amount of
homogeneity contained in a given problem. After introducting and
characterizing weakly positive and positive gradings we provide the
basic properties of Macaulay bases and multihomogenization with
respect to such gradings as well as the connection between these notions.
Finally, we formulate the multihomogeneous version of the Buchberger
algorithm for computing homogeneous Gröbner bases and minimal
homogeneous systems of generators.
Keywordsmultigraded ring, homogenization, Macaulay basis, Gröbner basis
Length20
File
LanguageEnglish
SeriesNATO Science Series II
Pages197-216
PublisherKluwer Academic Publishers
AddressDordrecht
Year2003
EditorJ. Herzog and V. Vulutescu
Edition0
Translation No
Refereed Yes
BookCommutative Algebra, Singularities and Computer Algebra
ConferencenameNATO Workshop 2002 (Sinaia/Romania)
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