An algorithm for computing the Hilbert–Samuel multiplicities and reductions of zero-dimensional ideals of Cohen–Macaulay local rings. (January 2020)

• Record Type: Journal Article
• Authors: Shibuta, Takafumi; Tajima, Shinichi
• Is Part Of: Journal of symbolic computation. Volume 96(2020)
• Page Start: 108
• Page End: 121
• Publication Date: 2020-01
• Subjects: Hilbert–Samuel multiplicity -- Integral closure -- Formal power series ring; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2019.02.014
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: In this paper, we present an algorithm for computing the minimal reductions of m -primary ideals of Cohen–Macaulay local rings. Using this algorithm, we are able to compute the Hilbert–Samuel multiplicities and solve the membership problem for the integral closure of m -primary ideals.