Title  Basic Tools for Computing in Multigraded Rings 
Author(s)  Martin Kreuzer, Lorenzo Robbiano 
Type  Article in Conference Proceedings 
Abstract  In 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. 
Keywords  multigraded ring, homogenization, Macaulay basis, Gröbner basis 
Length  20 
File 

Language  English 
Series  NATO Science Series II 
Pages  197216 
Publisher  Kluwer Academic Publishers 
Address  Dordrecht 
Year  2003 
Editor  J. Herzog and V. Vulutescu 
Edition  0 
Translation 
No 
Refereed 
Yes 
Book  Commutative Algebra, Singularities and Computer Algebra 
Conferencename  NATO Workshop 2002 (Sinaia/Romania) 