Algebraic local cohomology with parameters and parametric standard bases for zero-dimensional ideals. (September 2017)

• Record Type: Journal Article
• Authors: Nabeshima, Katsusuke; Tajima, Shinichi
• Is Part Of: Journal of symbolic computation. Volume 82(2017)
• Page Start: 91
• Page End: 122
• Publication Date: 2017-09
• Subjects: 13D45 -- 32C37 -- 13J05 -- 32A27; Standard bases -- Algebraic local cohomology -- Multiplicity structure -- Systems of parametric polynomials; 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.2017.01.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: A computation method of algebraic local cohomology classes, associated with zero-dimensional ideals with parameters, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the structure of algebraic local cohomology classes. This decomposition informs us on several properties of input ideals and the output of the proposed algorithm completely describes the multiplicity structure of input ideals. An algorithm for computing a parametric standard basis of a given zero-dimensional ideal, with respect to an arbitrary local term order, is also described as an application of the computation method. The algorithm can always output "reduced" standard basis of a given zero-dimensional ideal, even if the zero-dimensional ideal has parameters.