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 116 11. A Mechanization Method of Geometry and its Applications I. Distances, Areas and Volumes 132 12.《解方程器》或《SOLVER》软件系统概述 149 13.《解方程器》或《SOLVER》软件系统应用举例 159 14. A Mechanization Method of Geometry and its Applications II. Curve Pairs of Bertrand Type 173 15. On Reducibility Problem in Mechanical Theorem Proving of Elementary Geometies 178 16. Mechanical Derivation of Newton's Gravitational Laws from Kepler's Laws 202 17. A Mechanization Method of Geometry and its Applications III. Mechanical Proving of Polynomial Inequalities and Equations-Solving 211 18. 几何学机械化方法及其应用 234 19. A Mechanization Method of Geometry and its Applications IV. Some Theorems in Planar Kinematics 240 20. On the Foundation of Algebraic Differential Geometry 256 21. On the Generic Zero and Chow Basis of an Irreducible Ascending Set 290 22. A Mechanization Method of Geometry and its Applications V. Solving Transcendental Equations by Algebraic Methods 312 23. A Mechanization Method of Geometry and its Applications VI. Solving Inverse Kinematic Equations of PUMA-Type Robots (A Sketch) 315 24. On a Projection Theorem of Quasivarieties in Elimination Theory 321 25. On the Chemical Equilibrium Problem and Equations-Solving 330 26. Decomposition Theorems for the Zero-set of an Ordinary or Differential Polynomial Set and Their Applications 349 27. On the Construction of Groebner Basis of a Polynomial Ideal Based on Riquier-Janet Theory 357 28. Mechanical Theorem Proving of Differential Geometries and Some of its Applications in Mechanics 378 29. On a Finiteness Theorem about Optimization Problems 403 30. A Report on Mechanical Geometry Theorem Proving 420 31. On the Char-Set Method and the Linear Equations Method of Nonlinear Polynomial Equations-Solving 442 32. A Mechanization Method of Equations-Solving and Theorem-Proving 452 33. On Problems Involving Inequalities 492 34. On a Linear Equations Method of Nonlinear Polynomial Equations-Solving 503 35. On a Hybrid Method of Polynomial Equations Solving 520 36. On Surface-Fitting Problem in CAGD 530 37. On a Finiteness Theorem about Problems Involving Inequalities 541 38. CAGD中代数曲面拟合问题 553 39. Some Remarks on Factorization and GCD of Multivariate Polynomials 561 40. Central Con-gurations in Planet Motions and Vortex Motions 576 41. On Algebrico-Differential Equations-Solving 590 42. On “Good" Bases of Algebraico-Differential Ideals 606 43. On Wintner's Conjecture about Central Con-gurations 616 44. Polynomial Equations-Solving and its Applications 620 45. Mathematics Mechanization and Applications after Thirty Years 633 46. 分角线相等的三角形——初等几何机器证明问题 651
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