Computer algebra and Bruce-Roberts Milnor number (Developments in Computer Algebra : Recent Research and Re-Formation of Basic Theory)

Abstract

Bruce-Roberts Milnor number is a generarization of the Milnor number, a multiplicity of an isolated critical point of a holomorphic function germ. This number is defined for a critical point of a holomorphic function on a singular variety. In the hypersurface isolated singularity case, Bruce-Roberts Milnor numbers can be considerd in the context of symbolic computation, or computer algebra. In this note we report on some computational experiments for Bruce-Roberts Milnor numbers of polynomial functions on semi-quasi homogenous singularities.