The goal of this research is to continue investigation of automated reasoning in elementary geometry, differential geometry, and mechanics. 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 study practical application of resulting techniques to areas such as kinematic synthesis of linkages and mechanisms, CAD/CAM, etc.
