A new algorithm for computing logarithmic vector fields along an isolated singularity and Bruce-Roberts Milnor ideals

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.