Mathematics Mechanization And Applications - Dongming Wang

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Résumé :
Mathematics mechanization and applications provides surveys for major research for proving with diverse applications accomplished in Wu's extended Chinese group. The book addresses the frontiers of research, with new and original ideas and results, includes sophisticated and successful applications to scientific and engineering problems, covers polynomial system solving ; geometric reasoning ; computer algebra ; and mathematical software, is comprehensive, focused and easy to read with a uniform presentation, contains an extensive bibliography, of high value for reference, particularly for western readers. This book is of interest to researchers, software developers and graduate students in symbolic and algebraic computation, automated theorem proving, algorithmic mathematics, and computer-aided mathematical problem solving. It is relevant for researchers and university teachers in computer-aided instruction and education ; and for engineers and practitioners in mechanics, computer-aided geometric design, geometric modeling and robotics. People in many other related areas, from pure mathernatics to computer-aided design, particularly those who know of the Wu's method, but have little knowledge or understanding of it and the work that bas arisen around it, will also find the book good reading.

Biographie:
Dongming Wang bas been a senior researcher at CNRS since 1992. He is recognized for his work and expertise on automated geometric reasoning, elimination methods, and applications of symbolic computation to differential equations and neural networks. Xiao-Shan Gao has been a research professor at Academia Sinica since 1997. His major research interests include automated geometric reasoning, polynomial system and geometric constraint solving, intelligent computer-aided design and instruction.

Sommaire:
POLYNOMIAL SYSTEM SOLVING

• The characteristic set method and its applications
• Some algorithms for zero decomposition of polynomial systems
• The Eigenvalue approach to polynomial system solving
• Solving the Yang-Baxter Equation by Wu's method

• Wu's method for automated geometry theorem proving and discovering
• Mechanical theorem proving in differential geometry
• Points elimination methods for geometric problem solving
• Clifford algebra approaches to mechanical geometry theorem proving
• Proving by examples
• Search methods revisited
• First-order polynomial based theorem proving

• Greatest common right divisors, least common, left multiples, and subresultants of ore polynomials
• Algebraic factorization and GCD computation
• Conversion between implicit and parametric representations of algebraic varieties

• Centers foci, and limit cycles for polynomial differential systems
• Exact solitary wawe solutions of non-linear evolution equations
• Applications of mechanical methods to partial differential equations
• Equation solving in robotics and mechanisms
• Blending several implicit algebraic surfaces
• Geometric theorem provers and algebraic equation solvers