内容简介: 本卷收录了吴文俊在数学机械化领域发表的46篇论文,内容包括:几何定理机器证明的吴方法、多项式系统符号求解的Ritt-吴特征列方法、构造性微分代数几何理论、不等式机器证明与优化问题的有限核定理等数学机械化领域的奠基性成果,还包括数学机械化方法在数学定理的自动发现、天体中心构型问题求解、平面机构定理的机器证明、机器人的运动学问题的自动求解、几何设计中的曲面拼接等问题中的应用。 目录: 1.On the Decision Problem and the Mechanization of Theorem-Proving in Elementary Geometry 1 2.初等微分几何的机械化证明 17 3.初等微分几何的机械化证明 19 4.Toward Mechanization of Geometry||Some Comments on Hilbert's “Grundlagen der Geometrie” 30 5.Some Remarks on Mechanical Theorem-Proving in Elementary Geometry 46 6.Some Recent Advances in Mechanical Theorem-Proving of Geometries 51 7.Basic Principles of Mechanical Theorem Proving in Elementary Geometries 58 8.A Constructive Theory of Differential Algebraic Geometry Based on Works of J.F.Ritt with Particular Applications to Mechanical Theorem-Proving of Differential Geometries 96 9.On Zeros of Algebraic Equations||An Application of Ritt Principle 110 10.A Mechanization Method of Geometry IElementary Geometry 1 ...
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