Ideals, bifiltered modules and bivariate Hilbert polynomials

• Autores: Giuseppa Carrá Ferro
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 1, 2006, págs. 112-121
• Idioma: inglés
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• Resumen

  • 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 be the natural bifiltration of the ring R and let 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={g1,¿,gs} 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 over R.