Optimal Algorithm for Algebraic Factoring

This paper presents an optimized method for factoring multivariate polynomials over algebraic extension fields defined by an irreducible ascending set.The basic idea is to convert multivariate polynomials to univariate polynomials and algebraic extension fields to algebraic number fields by suitable integer substitutions. Then factorize the univariate polynomials over the algebraic number fields. Finally, construct multivariate factors of the original polynomial by Hensel lemma and TRUEFACTOR test. Some examples with timing are included.