Automated Reasoning in Geometry and Mechanics

几何和力学中的自动推理

• 批准号: 9002362
• 负责人: Robert Boyer
• 金额: $ 6.45万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-09-01 至 1991-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002362&HistoricalAwards=false
• 关键词: Automated; Reasoning; Geometry; Mechanics

The goal of this project is to study automated reasoning in elementary geometry, differential geometry, and mechanics as an extension of our previous and current work. It covers not only theorem proving, but also formula derivation. In each of these three areas, the following research will be conducted: (1) to improve existing proving techniques; (2) To further study mechanical formula derivation; (3) to collect a significant number of worked examples; (4) to improve Ritt- Wu's decomposition algorithm and other key algorithms; (5) to combine Ritt-Wu's method with Collins' method in elementary geometry; (6) to release an automated reasoning system; (7) to study practical applications of our techniques to areas such as kinematic synthesis of linkages and mechanisms, CAD/CAM, etc; (8) to study theoretical issues related to our techniques.

这个项目的目标是研究自动推理在小学 几何，微分几何和力学作为我们的扩展 过去和现在的工作。 它不仅包括定理证明， 还有公式推导。 在这三个领域中， 研究将进行：（1）改善现有的证明 （2）进一步研究力学公式推导;（3） 收集大量的工作实例;（4）改善Ritt- 吴的分解算法等关键算法;（5）将联合收割机 Ritt-Wu方法与柯林斯方法在初等几何中的应用;（6） 发布一个自动推理系统;（7）学习实用 应用我们的技术领域，如运动合成的 连杆机构、CAD/CAM等;（8）研究理论问题 与我们的技术有关。