Irreducibility algorithm for the Weierstrass polynomials of two complex variables and the Puiseux expansions: Part[A], Part[B], Part[C]

Abstract

It is very fundamental to study irreducible plane curve singularities in algebraic geometry. The contents of the paper consist of three parts, called Part[A], Part[B] and Part[C] with Good Appendix. Our aim is to prove by Part[B] and Part[C] that a complete irreducibility algorithm for the Weierstrass polynomial of two complex variables and the Puiseux expansions in Part[A] can be explicitly and rigorously computable in an elementary way, as follows. For brevity, Weierstrass polynomials may be written by W-polys throughout this paper.