Elimination Method and Its Applications

Author: Wang Dongming
Publisher:
Publish Date: 2002-02-01
Features: This book can be used as a reference for scientific research and engineering technicians, and also as a teaching reference for senior undergraduate and graduate students in mathematics and computer science departments of higher education institutions. The book systematically introduces elimination algorithms for the decomposition of zero sets of polynomial systems. These algorithms can decompose any multivariate polynomial system into triangular systems, regular systems, simple systems, triangular systems with projection properties, and irreducible triangular systems. Theoretically, various triangular systems have distinct properties, are computationally of varying difficulty, and have different strengths in applications. The book also briefly describes elimination algorithms based on resultants and Gr?bner bases, discusses the equidimensional and irreducible decomposition of algebraic varieties, and the quasi-prime decomposition of polynomial ideals. It introduces several applications of symbolic elimination methods, including algebraic equation solving, geometric theorem proving, polynomial factorization, and qualitative analysis of differential systems.