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...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.展开更多
In this paper, we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure. We improve the classical result on Wronskian deter...In this paper, we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure. We improve the classical result on Wronskian determinant, which can be used to decide whether the elements in a partial differential field are linearly dependent over its constant field. Based on Wronskian determinant, we can describe the geometry statements in the surfaces by an algebraic language and then prove them by the characteristic set method.展开更多
文摘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.
基金the National Key Basic Research Project of China (Grant No.2004CB318000)
文摘In this paper, we generalize the method of mechanical theorem proving in curves to prove theorems about surfaces in differential geometry with a mechanical procedure. We improve the classical result on Wronskian determinant, which can be used to decide whether the elements in a partial differential field are linearly dependent over its constant field. Based on Wronskian determinant, we can describe the geometry statements in the surfaces by an algebraic language and then prove them by the characteristic set method.
