ON THE THEORY OF RESOLVENTS AND ITS APPLICATIONS
Xiao-Shan Gao · 1999
We extend the concept of the resolvent of a prime ideal to the concept of theresolvent of a general ideal with respect to a set of parameters and propose an algorithmto construct the generalized resolvents based on Wu-Rits's zero decomposition algorithm.Our generalized algorithm has the following applications. (1) For a reducible variety V,we can find a direction on which V is projected birationally to an irreducible hypersurface.(2) We give a new algorithm to find a primitive element for a finite algebraic extensionof a field of characteristic zero. (3) We present a complete method of finding parametricequations for algebraic curves. (4) We give a method of solving a system of polynomialequations to any given precision.