Resultant And Construction Methods

As we know,resultant is one of the classical elimination theories.Resultant matrices are important tools for constructing resultant in elimination theory.In this paper,we introduce several construction methods of resultants,such as Sylvester resultant,Dixon resultant and mixed Cayley-Sylvester resultant.In this paper,we mainly extend the entry formula for mixed Cayley-Sylvester resultant matrix from bivariate polynomial system to any-variable polynomial system by using the properties of the determinant and the exact division by truncated formal power series.We also give the concept of brackets and give the entry formula of?₃for the three-variable mixed Cayley-Sylvester resultant matrix.