几何定理机器证明

Clifford代数与几何定理机器证明

Clifford Algebra and Automated Geometric Theorem Proving

本文主要介绍Clifford代数在数学机械化的核心内容&几何定理机器证明中的应用。

In this paper we introduce some applications of Clifford algebra in automated geometric theorem proving the kernel of mathematics mechanization .

基于指标形式张量的微分几何定理机器证明

Mechanical theorem proving for tensor with indexes in differential geometry

吴文俊建立的数学机械化方法，极大的推动了几何定理机器证明领域的研究。

Wu-method greatly contributes to geometry theorem proving research in the field .

几何定理机器证明系统的开发与研究

Research and Development of Machine Proving System on Geometry Theorem

一种几何定理机器证明的零维化方法

A Zero - Dimensional Method for Mechanical Geomery Theorm Proving

几何定理机器证明的结式矩阵法

The sub - resultant method for automated theorem proving

近年来，随着计算机容量的扩大和计算速度的不断更新，计算机在数学领域的应用也不断深入，另一种几何定理机器证明方法&定理机器证明的数值方法，也得到了蓬勃发展。

Another method , namely numerical method for theorem prove was also been expanded vigorously .

几何定理机器证明的WE完全方法

We complete algorithm for automated theorem proving

一类初等微分几何定理机器证明的算法与实现

Algorithm and implementation of Mechanical Proving of a class of theorems in elementary differential geometry

基于多项式组主项解耦消元法的几何定理机器证明

Mechanical Geometry Theorem Proving Based on the Elimination Method with Decoupling of Leading Terms for Polynomial Set

然而，上述几何定理机器证明方法主要针对等式型定理的证明，不等式型定理的机器证明则一直是自动推理领域中的一个难题。

Nevertheless , all those methods were aimed at equality theorems and inequality theorem still was the difficult problem in automatic reasoning field .

在几何定理机器证明方法中，常用的有几何代数方法、演绎数据库方法和例证法等方法。

Methods , including geometric algebraic method , deductive database method and paradigmatic prove method have been widely applied in the geometric theorem prove field .

所提出的准线性变换消元法可应用于涉及非线性代数方程组求解的几何定理机器证明、计算机辅助设计、机器人等多个领域，具有十分重要的理论意义与实用价值。

The presented method provides a new way for solving the problem involving nonlinear algebraic equation in many fields such as geometric theorem machine proven , CAD , forward and inverse kinematics of robots .

中国传统数学的构造性和程序化思想启发和影响了吴文俊的几何定理机器证明和数学机械化工作，表明在现代数学发展中中国传统数学仍有巨大的潜力。

The mechanical thought of mathematics in ancient china made a deeply influence to Wu Wen-jun 's work about mathematics mechanization , it also exhibited the potential of mathematics in ancient china to modern mathematics .

构造型几何定理及其机器证明系统

A mechanical proving system for constructible theorems in elementary geometry

几何定理的机器证明&每个中国数学教师都应懂得的方法

Mechanical Theorem Proving in Geometry

几何定理的机器证明是自动推理和符号计算领域最为活跃的分支之一。

The automated prove of geometric theorem is one of the most active branch in automated reasoning and symbolic computation .

在该领域，先后出现了数值并行法、例证法、单例试验法等多种用数值方法对几何定理进行机器证明的方法，使得定理机器证明领域更得到了广阔的发展。

Many numerical methods such as numerical paradigmatic method , parallel numerical method were presented . All those brought out great progress in theorem automatic prove .

探讨了在初等平面几何范围内定理机器证明切实可行的2种方法：Grobner基方法与吴方法，介绍了它们相应的算法原理和实现方法，并进行了实践与比较。

Two feasible methods & Grobner basis-method and Wu method are probed in this paper for proving theorem with machine within the elementary plane geometry . Their relevant algorithm principle and realizing method are introduced , and a comparison is conducted in practice .

首先，本文的主体给出有关几何计算和推理方法的综述，简单介绍几何定理机器证明发展的情况和一些常用的方法及相关软件包。

It first gives a survey on geometric computation and reasoning , in particular the development of geometric theorem proving , and reviews some of the important methods and software packages .