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TitleIdeals, bifiltered modules and bivariate Hilbert polynomials
Author(s) Giuseppa Carrà Ferro
TypeArticle in Journal
AbstractLet 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_rs ) r , s ∈ Z be the natural bifiltration of the ring R and let ( M_rs ) 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 rank p over R .
KeywordsBidegree preserving term ordering, L-reduction, Characteristic set, Bivariate Hilbert polynomials
URL http://www.sciencedirect.com/science/article/pii/S0747717105001471
JournalJournal of Symbolic Computation
Pages112 - 121
Translation No
Refereed No