Gro¨bner bases: a computational approach to commutative algebra
Gro¨bner bases: a computational approach to commutative algebra
Multigraded Hilbert functions and Buchberger algorithm
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Computation of Hilbert polynomials in two variables
Journal of Symbolic Computation - Special issue on differential algebra and differential equations
A theoretical basis for the reduction of polynomials to canonical forms
ACM SIGSAM Bulletin
Some properties of Gröbner-bases for polynomial ideals
ACM SIGSAM Bulletin
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Let R be a ring of polynomials in m+n variables over a field K and let I be an ideal in R. Furthermore, let (R"r"s)"r","s"@?"Z be the natural bifiltration of the ring R and let (M"r"s)"r","s"@?"Z be the corresponding natural bifiltration of the R-module M=R/I associated with the given set of generators introduced by Levin. The author shows an algorithm for constructing a characteristic set G={g"1,...,g"s} of I with respect to a special type of reduction introduced by Levin, that allows one to find the Hilbert polynomial in two variables of the bifiltered and bigraded R-module R/I. This algorithm can be easily extended to the case of bifiltered R-submodules of free R-modules of finite rankp over R.