2009/07/28 by Daniel de Andrés, Viktor Levandovskyy, Jorge Martín Morales · 13 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Affine transformation #Algebra over a field #Algorithm #Bernstein polynomial #Commutative Algebra and Its Applications #Computation #Computer science #Gröbner basis #Ideal (ethics) #Intersection (aeronautics) #Mathematics #Polynomial #Polynomial and algebraic computation #Pure mathematics #Subalgebra
paper · doi:10.1145/1576702.1576735
openalex publication_date 2009/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We present a general algorithm for computing an intersection of a left ideal of an associative algebra over a field with a subalgebra, generated by a single element. We show applications of this algorithm in different algebraic situations and describe our implementation in Singular. Among other, we use this algorithm in computational D-module theory for computing e.g. the Bernstein-Sato polynomial of a single polynomial with several approaches. We also present a new method, having no analogues yet, for the computation of the Bernstein-Sato polynomial of an affine variety. Also, we provide a new proof of the algorithm by Briançon-Maisonobe for the computation of the s-parametric annihilator of a polynomial.