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吴文俊全集:数学机械化卷Ⅴ
  • 书号:9787508855547
    作者:
  • 外文书名:
  • 丛书名:
  • 装帧:圆脊精装
    开本:B5
  • 页数:683
    字数:880000
    语种:zh-Hans
  • 出版社:科学出版社
    出版时间:2019-05-01
  • 所属分类:
  • 定价: ¥298.00元
    售价: ¥238.40元
  • 图书介质:
    纸质书

  • 购买数量: 件  可供
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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。
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目录

  • 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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