2015/08/27 by Katsusuke Nabeshima, Nabeshima, Katsusuke, Shinichi Tajima +1
Computer Science · Mathematics · #13D45 #13J05 #32A27 #32C37 #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Computer and information sciences #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #cs.SC #msc:13D45 #msc:13J05 #msc:32A27 #msc:32C37
paper · pdf · doi:10.48550/arxiv.1508.06724
31 pages
arxiv created 2015/08/27 · openalex publication_date 2015/08/27 · arxiv updated 2015/08/28 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, 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 several properties of input ideals and the output of our algorithm completely describes the multiplicity structure of input ideals. An efficient 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.