A new algorithm for computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor ideals. (November 2021)

• Record Type: Journal Article
• Authors: Nabeshima, Katsusuke; Tajima, Shinichi
• Is Part Of: Journal of symbolic computation. Volume 107(2021)
• Page Start: 190
• Page End: 208
• Publication Date: 2021-11
• Subjects: 68W30 -- 14Q10 -- 32S05 -- 32S65; Logarithmic vector fields -- Local cohomology -- Isolated singularities -- Gröbner bases; 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.2021.03.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: A new algorithm is introduced for computing logarithmic vector fields along a hypersurface with an isolated singularity. The key ideas of the algorithm are computing an ideal quotient in a polynomial ring and the use of algebraic local cohomology. The use of these ideas allows us to compute a module, over a local ring, of germs logarithmic vector fields. The resulting algorithms are much faster than our previous algorithms in computation speed. As the applications, an effective method of computing Bruce-Roberts Milnor and Tjurina ideals (or numbers) is also introduced.