Equation Solving and Machine Proof - Problem Solving Based on MMP

Author: Gao Xiaoshan
Publisher:
Publish Date: 2006-09-01
Features: This book first introduces the basic functions and usage methods of the mathematical mechanization software platform MMP in the first three chapters. Subsequently, it presents the fundamental theories and recent developments of mathematical mechanization, particularly in equation solving and machine proving, through running examples of MMP in the following chapters. Chapter 4 introduces Wu's characteristic column method and the projection theorem for polynomial equation systems, ordinary differential equation systems, and partial differential equation systems. Chapter 5 covers Wu's method and several recent advancements in automatic theorem proving and discovery in elementary and differential geometry. Chapter 6 discusses Wu's characteristic column method for algebraic equation solving, parameterized equation solving, resolvent theory, and their applications in robotics, surface patching, and the implicitization of algebraic varieties. Chapter 7 introduces Wu's characteristic column method for differential equation solving, as well as methods for finding elementary function solutions, traveling wave solutions, and power series solutions of differential equations. Chapter 8 presents Wu's finite kernel theorem for global optimization of algebraic systems, as well as the automatic proving and discovery of inequalities. At the end of each chapter, an introduction to the literature related to the content of the chapter and the implementation methods of MMP is provided. This book can serve as both a user manual for MMP and a reference for researchers, teachers, and graduate students to understand the fundamental methods and recent achievements of mathematical mechanization.