2006/06/06 by M. V. Kondratieva, Marina Kondratieva, Kondratieva, Marina +2
Computer Science · Engineering · Mathematics · #12H05 #13N10 #13P10 #Advanced Numerical Analysis Techniques #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AC #msc:12H05 #msc:13N10 #msc:13P10
paper · pdf · doi:10.48550/arxiv.math/0606124
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openalex publication_date 2006/06/06 · arxiv created 2006/06/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the problem of computing a Kolchin characteristic set of a radical differential ideal. The central part of the article is the presentation of algorithms solving this problem in two principal cases: for ordinary differential polynomials and in the partial differential case. Our computations are mainly performed with respect to orderly rankings. We also discuss the usefulness of regular and characteristic decompositions of radical differential ideals. In the partial differential case we give an algorithm for computing characteristic sets in the special case of radical differential ideals satisfying the property of consistency. For this class of ideals we show how to deal with arbitrary differential rankings.