Solving Systems of Algebraic Equations by a General Elimination Method

A method of factorisation of a U-resultant into linear factors is given. Using this method we can obtain solutions and their multiplicities of a system of algebraic equations, provided the system of algebraic equations has finitely many solutions. We directly calculate a matrix A which gives all solutions of the system by using a Grobner basis of the ideal generated by the polynomials of the system of algebraic equations.