本卷收錄了吳文俊在數(shù)學機械化領域發(fā)表的56論文篇。內(nèi)容包括：幾何定理機器證明的吳方法，多項式系統(tǒng)符號求解的Ritt-吳特征列方法，構造性微分代數(shù)幾何理論，不等式機器證明與優(yōu)化問題的有限核定理等數(shù)學機械化領域的奠基性成果。還包括數(shù)學機械化方法在數(shù)學定理的自動發(fā)現(xiàn)、天體中心構型問題求解、平面機構定理的機器證明、機器人的運動學問題的自動求解、幾何設計中的曲面拼接等問題中的應用。
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目錄
1. On the Decision Problem and the Mechanization of Theorem-Proving in Elementary Geometry 1
2. 初等微分幾何的機械化證明 17
3. 初等微分幾何的機械化證明 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》軟件系統(tǒng)概述 149
13.《解方程器》或《SOLVER》軟件系統(tǒng)應用舉例 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. 幾何學機械化方法及其應用 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中代數(shù)曲面擬合問題 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. 分角線相等的三角形——初等幾何機器證明問題 651
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