On Factorizing the Symbolic U-resultant — Application of the ddet operator —

This paper presents a new, practical, efficient algorithm for factorizing the U-resultant of a system of algebraic equations with finitely many solutions. Given a matrix whose determinant is the U-resultant, our algorithm obtains the true linear factors with exact multiplicities, directly from the matrix without expanding the multivariate determinant. The main focuses are laid upon the use of a new operator, which enables us to treat only matrices of univariate polynomial elements, and also upon the exact treatment of multiplicities, which is made possible by the symbolic representation of solutions in simple algebraic extensions of Q. The algorithm is probabilistic in the sense that there exists no deterministic method to give an appropriate parameterization. The efficiency of our algorithm will be demonstrated with some empirical problems